claims depot shelf
Quantum Gravity
Formal claims (Lean)
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In the pure O(N)^3 tensor field theory with imaginary tetrahedral coupling, the quartic couplings are asymptotically free at large N because the matter self-interactions are antiscreening. The paper adds a gravitational contribution $-f_\lambda \lambda_i$ to each quartic $\beta$ function, with $f_\lambda<0$ for screening gravity, computed at one loop from the functional renormalization group. The
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The authors claim that the state sum amplitude $A_\Gamma$ of Eq. (5.1.1), defined as an integral over edge-vector configurations with 4-simplex amplitudes built from non-commutative delta functions imposing triangle closures and edge identifications, is a valid quantum gravity amplitude. Using the expansor-based link between translation-group representations and the balanced (simple) representatio
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On the paper's own terms, the central result is a closed-form evaluation of the quantum relative entropy S for the Schwarzschild metric. Using the vacuum ansatz G̃ = g − βG R̃ for the metric induced by geometry, the Lagrangian reduces to L = −Tr ln(G̃$g^{{-1}}$) = −ln[(1−2βG R_s/$r^{3}$)^2(1+βG R_s/$r^{3}$)^4], defined only for r > r_0 = (2βG R_s)^{1/3}. The entropy is then the integral of this La
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The central claim is that the AOS loop-quantized Schwarzschild black hole is not rigid: when subjected to a static external scalar, vector, or axial gravitational tidal field, it develops a nonzero induced multipole response. The static tidal Love numbers are all negative and nonvanishing for every multipole $\ell\ge s$ except the scalar monopole, and at leading order in the quantum parameter they
Stated claims
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The central assertion is Eq. (91) for pure conformal quantum gravity and Eq. (100) for gravity coupled to conformal matter: C4 \bar\Gamma_div^(1) = 0. In words, the one-loop divergent part of the effective action is annihilated by the conformal generator in four dimensions, so the divergences are conformally invariant and no non-conformal counterterm such as R^2 is generated.
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The paper's central claim, stated on its own terms, is that after the Born-Markov and secular approximations and an explicit counterterm renormalization of the ultraviolet-divergent Lamb shift, the oscillator's reduced dynamics is exactly Lindblad for each bath state, with jump operators quadratic in the phonon operators. The universal tidal interaction $H_I = -\frac{m}{4}\ddot{h}_{xx}(t,0)x^2$ is quadratic in the displacement $x$, so one graviton exchanges with two mechanical phonons. In vacuum $L_V=b^2$, making $|0\rangle$ and $|1\rangle$ dark and preserving the coherence of the qubit they span; a coherent bath has the same dissipator plus a coherent-shift Hamiltonian that reproduces the classical geodesic-deviation equation; number and thermal baths add the excitation jump $b^{\dagger 2}$, coupling $\rho_{01}$ to an infinite ladder of coherences; and a squeezed bath yields the single jump operator $L_S=\cosh r(2\omega_m)b^2 - e^{i\phi(2\omega_m)}\sinh r(2\omega_m)b^{\dagger 2}$, whose kernel contains one dressed dark state in each parity sector, so the mutual coherence of $|D_+\rangle$ and $|D_-\rangle$ is exactly preserved by the dissipator. Quantitatively, all rates are multiples of the small vacuum rate $\gamma_V = \frac{32}{15}t_P^2\omega_m^3$.
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The paper's central claim is that the complete three-loop five-point $\mathcal{N}=4$ SYM amplitude admits a manifestly CK-dual integrand: 42 trivalent graph topologies, with numerators generated from two master topologies by dual Jacobi relations, at most quadratic in loop momenta, and fixed uniquely up to generalized-gauge freedom. Double copy of these numerators yields the $\mathcal{N}=8$ supergravity integrand. At $D_c=6$, the SYM ultraviolet pole contains no double-trace term, has color dependence $N_c^3+36\zeta_3 N_c$, and matches the two-loop five-point single-trace structure, while the SUGRA pole is the expression in Eq. (8), agreeing with the closed-string-inspired prediction for four-dimensional external states. Replacing the four-dimensional prefactors $\gamma_{ij}$ by $D$-dimensional tree-level expressions $\gamma^D_{ij}$ reproduces the open-string prediction for the SYM pole at generic kinematics, but for gravity the same replacement differs from the string-inspired result by the evanescent combination $E$ that vanishes in four dimensions. The paper therefore concludes that the four-dimensional representation, although complete as a four-dimensional amplitude, does not by itself determine the full integrand of the higher-dimensional theory.
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The central discovery claimed is that the areal-radius form of the effective polymer metric yields a two-parameter stellar structure system that reduces to the standard TOV equations when $A_\lambda \to 0$, and that increasing $A_\lambda$ produces a controlled upward shift of the equilibrium sequence. For the Chandrasekhar equation of state the undeformed maximum is $1.4166\,M_\odot$ at radius $1010.7$ km; with the Coulomb lattice correction it is $1.3850\,M_\odot$ at $980.5$ km. At $A_\lambda = 100$ these maxima rise to $1.7125\,M_\odot$ and $1.6907\,M_\odot$, with the configurations remaining inside the inverse $\beta$ decay domain. Varying $\eta = 0.5$ or $2$ changes $M_\mathrm{max}$ by less than $0.1\%$ and the radius at maximum mass by less than $0.33\%$, so the paper identifies $A_\lambda$, not $\eta$, as the parameter that controls the super-Chandrasekhar displacement.
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On the paper's own terms, the central discovery is that the charged loop-quantum-gravity black hole is not spectrally identical to Reissner-Nordström even though it shares the same horizons and shadow radius. For massless scalar waves, the quantum parameter $b_0 > 1$ lowers the effective potential barrier, so more of the incident wave tunnels into the black hole; consequently the total absorption cross section grows with $b_0$ from the low-frequency regime up to moderate frequencies, while remaining pinned to the same black-hole area at low frequency and the same geometric capture cross section at high frequency. The numerical spectra also show an anti-correlation between peaks and troughs as $b_0$ varies: the configuration with the largest peaks has the deepest troughs. Increasing $Q/M$, by contrast, raises the barrier and suppresses absorption at all frequencies. The greybody-factor calculation shows the same two trends, with the $l \geq 1$ partial waves reversing the $b_0$ effect in some frequency windows.
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The paper argues that, for torus universes in AdS$_3$, the $T\bar{T}$-deformed partition function is obtained from the Wheeler–DeWitt wavefunction $\Psi(T,m_a)$ by the kernel transform $Z_{T\bar T}(\lambda,m_a)=\int_0^\infty dT\, K(\lambda,T)\Psi(T,m_a)$ with $K(\lambda,T)=2\sqrt{\pi}\,\lambda^{1/2}e^{2\lambda(1-\cosh T)}$. The derivation matches the flow equation for the deformed partition function to the WdW equation in WdW time $T$, using the same shifted Maass Laplacian as the spatial operator; the physical solution is the modified Bessel function $K_{ir}(2\lambda)$ with the $\cos(rT)$ mode, normalized so the $\lambda\to\infty$ limit gives the undeformed CFT partition function. In that limit the kernel tends to a delta function and the partition function reduces to the boundary value of the wavefunction. For finite $\lambda$ the kernel has finite width and its center, in proper radial coordinate, sits at $\rho_*=\frac14\sinh^{-1}(4\lambda)$, so a fixed-coupling partition function is a finite-width bulk wavepacket. The inverse transform (4.3) reconstructs the exact wavefunction from the family of deformed partition functions, and the same transform, with different geometric identifications of $T=0$, applies to closed AdS$_3$ torus universes and to dS$_3$ torus universes.
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On the paper's own terms, the central claim is that the Gregory–Laflamme instability is a UV/IR bridge: when a black string thins to a horizon radius of order the inverse species scale, Λ_s^{-1}, gravitational effective field theory breaks down and the system must be described as a bound state of Λ_s-energy quanta. This replacement of the string scale by the species scale is asserted for general theories of quantum gravity, and it yields the prediction that a fraction of order ΔE ∼ M_pl^{d−2}/Λ_s^{d−3} of the initial black-hole mass is converted into particles of energy Λ_s, with no dependence on the number of internal dimensions. For charged black holes, the paper derives two thresholds: Q_
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The central claim is that the vacuum energy density between two parallel plates in rainbow spacetime is the standard Minkowski Casimir energy times an overall factor that depends on the choice of rainbow functions. Concretely, after solving the deformed scalar field equation and relating the vacuum expectation value of the deformed energy-momentum tensor to the Green's function, the paper finds that the reduced Green's function acquires a multiplicative factor (1 + (alpha + k) E_o) relative to the Minkowski result, and that this translates into Casimir energy and force rescaled by (1 - 2 k E_o). For the first rainbow function f(E)=g(E)=1/(1 - lambda E_o/E_P), k = lambda/E_P, so the magnitude
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On the paper's own terms, the discovery is that the vacuum-subtracted von Neumann entropy of the dual CFT state in the dressed Type-II algebra is, at leading order O(λ²), exactly one quarter of the vacuum-subtracted area of the HRT surface: ΔS(ω_h,A) = S(ρ_{\tilde ω_h}) = (1/4)(Ar[Γ_λ,g(λ)] − Ar[Γ_0,g(0)]). This is equation (6.16). Distinctly, the proof also derives the JLMS equality — relative entropy of any bulk state with respect to the vacuum equals relative entropy of the dual CFT state — as a direct consequence of the holographic map's isometric and reconstruction properties, before any crossed-product construction is invoked.
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In the paper's own formulation, the generalized Bergshoeff-de Roo identification equates the auxiliary gauge-group degrees of freedom with the composite Lorentz degrees of freedom, F_{aBC} = −g E_μ^a (t_μ)_BC = E_{aBC}. Using a coset parametrization of the O(D,D+k) generalized vielbein and gauge fixings that break the extended Lorentz group to the standard one from the outset, the identified flux becomes a generalized Riemann tensor and the action takes the manifestly Lorentz-covariant form (8). Its derivative expansion up to O(α′²) is summarized by Eq. (112), which contains only three independent couplings built from the torsionful curvature R^{(+)}: R^{(+)}², (D^{(+)}R^{(+)})², and R^{(+)}
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The paper's core claim is that the previously uncontrolled tensor intersections in 6d N=(1,0) supergravity are universally finite, and the bounds follow from two low-energy inputs: the gravitational anomaly vector b0 lies in the cone generated by primitive BPS strings, and distinct primitive BPS strings have non-negative mutual intersections. From these inputs the authors construct a unique lattice Zariski decomposition b0 = P + N, where N is supported on a negative-definite tensionless sector; the unit pairing b0·e = 1 then forces the coefficient of any generator in N to give Ci·e ≤ 1/αi. This yields C_-3·e ≤ 3 and C_-2·e ≤ 7 for (-2)-charges in non-Higgsable clusters, while the maximal emb
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The central claim is that quantum mechanics and gravity both emerge from a single fractal-entanglement substrate: the paper states 'the Schrödinger equation is not postulated but derived as the geodesic equation of a particle moving in a fractal spacetime' and 'Gravity arises from the time dependence of the entanglement-induced metric, yielding Einstein gravity in the macroscopic limit.' If true, both quantum theory and general relativity would be emergent consequences of the information-theoretic geometry of an entanglement network.
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The paper's central claim is that the 'absolute consistency criterion' (ACC)—Δs_bh > 0, the requirement that the net change in the correction to the Bekenstein-Hawking area formula be positive—is the right way to marry the gravitational-wave-validated area theorem with the generalized second law. Under this criterion, the additive expansion of the correction s_bh = s0 log S_BH + s1/S_BH + ... is constrained in its sign. For F(R) gravity, the Wald entropy formula S_bh = F'_R(R_S) A_S, together with the inverse-area expansion and the identification R_S = a/A_S, leads to the parameter inequalities F'_R(A_S^{-1}) < F'_R(0) and F''_R(0) < 0, and to further inequalities if higher-order terms are k
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The central claim is a rate formula: a coherent graviton wave packet containing N gravitons, with central frequency ω_s and bandwidth σ_ω, decays in vacuum into photon pairs at dP/dt = 3 G^2 N^2 ω_s^3 σ_ω^2/(25π), so the photon count grows as N_γ(t) ≈ G^2 N_0^2 6ω_s^3 σ_ω^2 t/(25π). Two features matter here: a single plane-wave graviton field produces no photons at leading order, and the quadratic photon-gravity coupling vanishes classically in vacuum. The process appears because the coherent state is a many-graviton superposition and because the calculation is carried to second order in the metric; the paper shows the quantum result matches a semiclassical treatment whose photon source is t
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The central claim is that the spinfoam construction yields a genuine quantum-gravity path integral. In three dimensions this is established: the Ponzano-Regge state sum is invariant under Pachner moves via the Biedenharn-Elliott identity, projects onto flat connections, and its 6j-symbols satisfy recursion relations that become the Wheeler-DeWitt equation in the semiclassical limit. In four dimensions, the paper argues that the EPRL vertex amplitude, built from the weak imposition of linear simplicity constraints, is the correct discrete path integral for Lorentzian quantum gravity. The construction embeds each SU(2) spin j into the SL(2,C) representation (p, k) = (γ(j+1), j), giving the Y_γ
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The central claim is that LQC inverse-volume corrections, evaluated at second order in the slow-roll expansion, induce a prominent negative shift in n_s while leaving r almost unchanged, thereby translating the theoretical predictions of fractional power-law potentials horizontally leftward in the r–n_s plane. For the allowed ranges of the LQC parameters σ (the scale-factor exponent of the correction) and δ (its amplitude at the CMB pivot scale) listed in Tables I and II, the classically excluded potentials n = 1/3, 2/5 and 2/3 fall within the 68% and 95% confidence regions of the P-ACT-LB-BK18 dataset. The paper thus claims that strictly perturbative quantum-gravity corrections can restore
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For a disk with an S^1 boundary of proper length ℓ in two-dimensional Λ>0 pure gravity, the genus-h contribution to the gravitational path integral takes the form W^(h)(ℓ) = κ^(2h−1) e^(−ℓ/2) Σ_{n=0}^{3h−2} ζ_n ℓ^(n+1/2), with rational coefficients ζ_n for h≥1. The paper derives genus-one and genus-two by semiclassical path integration, and genus-three through genus-six by a heat-kernel recursion; the genus-four, genus-five, and genus-six formulas are new. In the large-ℓ limit, the ratio of successive genus contributions scales as κ²ℓ³ and approaches α_h = 1/(384(1+h)), matching the behavior of two-dimensional topological gravity and its intersection numbers. The paper also argues that these
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The central claim is that diagonal R-symmetry gauging—gauge group U(1)_R+ whose generator is the sum of the usual U(1)_R and a U(1) inside the quaternionic-isometry group Sp(n_H) acting on hypermultiplets—passes all local and global anomaly tests in a much larger class of 6D (1,0) models than ordinary U(1)_R gauging, and yields supersymmetric Minkowski vacua. Concretely, the paper exhibits 706 G_1×U(1)_R+ and 1,559 G_1×G_2×U(1)_R+ anomaly-free spectra under its stated rank and charge bounds, and shows by explicit coset parametrization (rank-one ansatz on SU(n_H,2)/(U(n_H)×SU(2)_R)) that vanishing of all moment maps is achievable exactly when the gauging is diagonal, leading to C_+ = C_z' = 0
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The central claim: for any initial graviton state, the reduced coherence factor is D = e^{iΔΦ} Tr[ρ_g D[Δα]], where Δα is the difference of the coherent displacements induced by the two branches. In the vacuum, Γ = -ln|D| = ½N_Δ, half the mean number of gravitons the difference source would radiate. In the nonrelativistic quadrupole limit with a Gaussian closed trajectory, Γ_vac = (8/15) G m² d⁴/(ℏ c⁵ τ⁴) = (8/15)(m/m_P)^2(u/c)^4. For a general two-mode squeezed vacuum, the response is reweighted by factors between e^{-2r} and e^{2r}; for the inflationary squeezed background, the rapidly oscillating squeezing phase averages out, leaving Γ_inf = (π/20) Ω_inf (m d² H_0/ℏ)², which with Ω_inf =
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The central claim is Theorem 3.16: over a super-torsion-free (1,10|32) super-spacetime with C-field super-flux of the form (133), the lS^4-Bianchi identities dG4 = 0 and dG7 = 1/2 G4∧G4 hold if and only if the Einstein, Rarita-Schwinger, Maxwell-Chern-Simons, and duality equations of 11D supergravity hold rheonomically on superspace. Here lS^4 is the characteristic L∞-algebra with generators v3 and v6 and the single non-trivial bracket [v3,v3] = v6; it is the rational Whitehead algebra of the 4-sphere. Because these duality-symmetric Bianchi identities are equivalently closure conditions for L∞-valued differential forms, the paper turns them into global field data: a choice of classifying sp
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The Wheeler-DeWitt equation is presented not as a law of nature but as an artifact of applying constrained Hamiltonian quantization to gravity while discarding gauge degrees of freedom and assuming asymptotic boundary conditions in the path integral. Refusing those assumptions, the paper derives a mathematical Schrödinger equation for the extended phase-space wave function, then, using the gauge condition as a quantum constraint, a physical Schrödinger equation whose Hamiltonian depends explicitly on the chosen gauge condition. The wave function gives the probability amplitude for the geometry of the Universe as it appears to an observer in the reference frame fixed by that gauge condition.
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The central claim is that a first-quantised wavefunction on a 2^L-point lattice carries a built-in generalised uncertainty principle. The low-energy version reduces to the Heisenberg principle as ΔL/ℏ→0, but for finite ΔL yields three momentum-dependent regions; a wavepacket can reach zero position uncertainty at a finite momentum spread. The high-energy version begins from p^H_x = Σ κ_{n-1} p_x^n. Setting the κ to the special-relativistic series p/√(1−p²/m²c²) and assuming point-momentum behaviour (δp^(n)_x = 0) gives δx δp^H ≥ (ℏ/2)[1 + τ_2 (δp^H)² + ...], with τ_2 = 3/(2m²c²) − (ΔL)²/(2ℏ²). In the continuous limit ΔL→0 this is a quadratic GUP with β_m = 3ℏc/(2Gm²), so (δx)_min = (√3/√2)ℏ/
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The paper's load-bearing claim is that the GKNS quadrangular ensemble forms a universality class absent from dynamical triangulations: its percolation critical exponents are ν=1.588(17), γ=2.83(2) at p0=0.4851(13), deviating from ordinary percolation (ν=4/3, γ=43/18), and its asymptotic Hausdorff dimension is ΔH≈2, while DQ and GQ have ΔH≈4. The abstract concludes: 'GKNS and GQ define distinct classes of random geometry, implying a different underlying measure in the space of random surfaces and a possible geometric framework for a new class of noncritical string theories.' If correct, these ensembles genuinely extend the taxonomy of two-dimensional random geometry.
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The paper establishes a direct link between gravity-induced entanglement (GIE) of two quantum clocks and the quantum formulation of local position invariance. For two identical clocks trapped at a fixed separation, the effective Hamiltonian places the rest Hamiltonian and the gravitational Hamiltonian as operator-valued masses. The central theorem states: entanglement is generated from an eigenstate of the rest Hamiltonian if and only if the rest and gravitational Hamiltonians do not commute—i.e., if and only if there is a genuinely quantum violation of LPI. In the complementary scheme with an equal superposition initial state, the entanglement oscillates at a frequency ω̃e = G ΔẼ²/(2ℏc⁴ℓ₀)
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The paper's central claim is that the pattern of SMEFT coefficients at an asymptotically safe gravity-matter fixed point is dictated by the maximal global symmetry of the free kinetic terms. For the fermion sector, that is a U(N_W) symmetry rotating all Weyl fermions into each other. The single four-fermion interaction compatible with this symmetry - the axial current interaction - has a nonzero, irrelevant fixed point (the shifted Gaussian fixed point), and six of the seven studied couplings inherit nonzero values through this symmetry. The mixed-chirality coupling c+_quqd, which is incompatible with U(N_W), vanishes at the fixed point. The paper shows that this coupling can be promoted to
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For the time-radial covariant quantum black hole metric, the Hawking temperature remains exactly T = 1/(8πM), identical to Schwarzschild. The quantum corrections act only on the effective potential barrier that emitted particles must cross. In the low-mass regime, the greybody factors for scalar, spin-half neutrino, and graviton modes deviate from their Schwarzschild counterparts, while photon greybody factors remain essentially unchanged. Consequently the mass-loss rate is suppressed for scalar and graviton emission, enhanced for neutrino emission, and nearly equal to Schwarzschild for photons. For larger black hole masses, the quantum corrections become negligible and all results converge
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The paper's central claim is that the decay of quantum coherence of an inertial two-level detector coupled to a Lorentz-violating vacuum is controlled by the detector's rapidity β. For a Lorentz-invariant field the transition rates are β-independent, giving coherence C = |sinθ| e^{−γ0τ/2}. With a modified dispersion ω_|k| = |k| f(|k|/M*), the rates γ± acquire a step-function threshold that depends on β, and coherence becomes C = |sinθ| e^{−(c+ + c−) γ0 τ/2}, with c± functions of β. For a polymer-quantized scalar field, f(g) dips below unity and the excitation channel switches on abruptly when the resonance condition on β is met, producing a pronounced drop in coherence at βc ≈ 1.3675. This t
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Central claim: the homology of a simplicial complex built from an observer's local measurements reproduces the topology of the accessible spacetime region even when quantum fluctuations make geometric regions ill-defined. Vertices are time intervals during which some detector is active; a k-simplex is a set of k+1 measurement events that share a common active detector and span a time window no larger than Λ. Shared detector activity stands in for overlapping open sets, so the complex plays the role of a nerve construction. The paper checks the construction on a 2+1 spacetime with and without a hole, getting the expected Betti numbers, and uses persistent homology over the threshold θ and the
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On the paper's own terms, the central discovery is that the quasinormal spectrum of the rotating LQG black hole separates into opposite trends: quantum deformation (P and, weakly, a0) lowers the real part of the frequency and broadens the effective potential barrier, whereas rotation a raises the frequency and at high spin reverses the spin-dependence of the damping rate. This is obtained by reducing the scalar Klein–Gordon equation, under the slow-rotation approximation, to a Schrödinger-like radial equation with effective potential Vℓ(r) = Δ(r)/(r²+a²)² [ℓ(ℓ+1) + 2M(r)r/(r²+a²)], where Δ(r) = r²F_LQG(r;P)+a² encodes the quantum-deformed radial sector. The authors compute complex frequencie
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The paper's central claim is that the strong-field imprints of self-dual loop quantum gravity do not stay hidden in the near-horizon region: they feed into the orbital phase and therefore into the gravitational-wave signal over the long EMRI inspiral. Using geodesic evolution and leading-order quadrupole radiation reaction, the authors generate waveforms for both the static and the rotating LQG-corrected geometry and find phase deviations that grow with time. Quantitatively, their Fisher matrix analysis on a geometrically defined observable vector yields fiducial constraints a = 0.902^(+0.0042)_(-0.0041), P = 0.030 ± 0.00015, and a0 = 21.4^(+23)_(-15), leading them to conclude that EMRI obse
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The central discovery is the exact formula (3.12): U_QG = ∫ dβ_obs μ(β_obs,u1,m) e^{-β_obs H}, where the measure μ is obtained by integrating out the fluctuating JT boundary, the massive worldline, and the einbein modulus. The measure is assembled from the AdS heat kernel for the worldline and from Wheeler-de Witt wavefunctions of JT gravity in the chordal-distance basis, and is therefore an ordinary one-dimensional integral. At large mass or small β the integral is dominated by a saddle point at which β_obs equals the geodesic distance between the anchor points; the variance around this saddle separates into a Brownian term ~ β*/m and a quantum-gravity term that scales as β/φ_r (weak backre
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The central claim is that in a canonically quantized flat FLRW universe with dust as internal time, the back-reaction of each electromagnetic mode on the quantum geometry produces a mode-dependent dispersion relation whose photon group velocity is always less than one. Concretely, the modified dispersion is determined by a factor F(k,T) = [⟨V^{-1}⟩_k ⟨V^{1/3}⟩_k / (⟨V^{-1}⟩_o ⟨V^{1/3}⟩_o)]^{1/2} multiplying the standard frequency, and the measured 3-velocity is V = F (1 - E d/dE log F). The authors show analytically and numerically that for LQC, F < 1 and V < 1 for all accessible times and momenta, with V → 1 - 2ε as k → 0 (ε ∝ ℏ k / p_T), and ∂V/∂k < 0, meaning bluer modes travel slower. In
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Strong-to-weak spontaneous symmetry breaking occurs for the BTZ black hole and is dual to wormhole geometries that join the two thermofield-double copies; equivalently, SWSSB is the emergence of global symmetries under ensemble averaging, which in turn suggests a new swampland conjecture for ensemble-averaged quantum gravity.
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Among seven explicitly defined deformations of a four-qubit product-EPR holographic code, only the matter-controlled bond-moving generator produces a leading quadratic logical-state dependence of the boundary entropy. After a state-independent physical recovery is fixed by coherent-information optimization, a nonzero variational proto-area survives, and a certified quadratic boundary witness—obtained by projecting the stabilizer-Rényi form away from all pairwise Pauli tangents—is strictly positive solely for that generator and zero for the six comparisons.
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Functional renormalization-group constructions of gravity and loop quantum gravity can remain distinct quantum theories, the former best suited to scale-dependent continuum phenomenology and the latter to ultraviolet completion of classically singular regimes; matching Bekenstein–Hawking entropy and the continuum limit then identifies the undetermined LQG parameters as G_LQG = g_* G and γ = γ_0 / g_*.
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Once redundant off-shell contributions are absorbed by field redefinitions in an essential scheme, the proper-time beta function for Newton's constant becomes independent of both gauge parameters of the general linear gauge (to third order in the coupling in the four-derivative truncation, and to all orders in the coupling and the Ricci scalar on a sphere), and the resulting essential flow still exhibits a gauge-independent non-Gaussian fixed point.
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The critical anomalous dimension γ_c, fixed by requiring that the holographically shifted bulk mass sit exactly at the Breitenlohner-Freedman bound, is the threshold that forces dual scaling dimensions into the complex principal series Δ_dS = d/2 ± iμ after Wick rotation to de Sitter space; the resulting log-periodic spacing Δ ln f = 2π/μ in the stochastic gravitational-wave background is therefore a direct imprint of OPE associativity.
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In unimodular cosmology, energy exchange between a scalar field and a bath of harmonic oscillators (quantum-gravity defects) produces an Ohmic diffusion equation that drives an initially vanishing cosmological constant to a positive asymptotic value Λ∞ = (γ mp Hd)/2, thereby generating the observed dark energy from primordial dissipation alone.
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CRT is not a gauge symmetry of quantum gravity in general. It is an asymptotic gauge symmetry in asymptotically flat and AdS space, acting on the boundary Hilbert space exactly as continuous isometries and scalar charges do. In eternal de Sitter it can be viewed as spontaneously broken only if an Alice d-3 brane is allowed inside the thermofield-double Hilbert space and the underlying quantum mechanics is time-independent; in realistic Big Bang cosmologies the symmetry is simply absent because initial conditions force small uncorrelated causal diamonds.
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We show analytically that, in the large N limit, the quantum magic of pure Kourkoulou-Maldacena (KM) states, dual to a quantum black hole with an end-of-world particle behind the horizon, is linear in N with a slope, depending on the black hole temperature, that can be tuned between zero and 1/2.
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We prove that Lubkin-Page typicality bounds, which demonstrate vanishing mutual information for generic states in Type I algebras, survive for all Type II von Neumann factors. In the hyperfinite Type II₁ case with R ≅ A ⊗ B ⊗ E, the mutual information I(A:B) vanishes as O((d_A d_B / d_E)^2) when d_A d_B ≤ d_E in finite-dimensional approximations. For Type II_∞ factors including crossed-product gravitational algebras, the bound includes additional exponential suppression governed by the Bekenstein-Hawking entropy.
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The central claim is that the hybrid ITE-TR-FALQON protocol, formed by merging the imaginary-time evolution of ITE-FALQON with the time-rescaling mechanism of TR-FALQON, is both necessary and sufficient to prepare the thermofield double ground state of the Maldacena-Qi model from simple initial states, yielding fidelities near unity and reproducing the exact entropy spectra of the target state.
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The canonical equivalence among their standard characterizations - as eigenstates of the annihilation operator, displaced vacuum states and minimum-uncertainty wave packets - is generically lost in the presence of a minimal length. Minimal-length effects induce nontrivial deformations of phase-space trajectories and give rise to an intrinsic squeezing mechanism with no counterpart in ordinary quantum mechanics.
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The dynamics of canonically quantized JT gravity with finite Dirichlet boundaries is exactly equivalent to the scattering problem of a nonrelativistic particle in a repulsive Pöschl-Teller potential, yielding exact wavefunctions of the universe and a disk partition function interpreted as a transition matrix element between vanishing bare-length states; at finite cutoff the spectral measure exhibits genuinely nonperturbative corrections absent in T Tbar treatments.
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In models obeying the Covariant Entropy Bound, the favored initial states are those without localized excitations or consisting of one large black hole. To obtain a long radiation-dominated era, most horizon volumes must contain tiny black holes that decay into radiation, while a random population of horizon-sized black holes supplies dark matter. A suitable distribution of these primordial black holes accounts for all dark matter and seeds the early galaxies seen by the James Webb Space Telescope, with possible additional dark matter in Planck-scale remnants. The construction uses both approximate solutions to general relativity and a speculative quantum-gravity model whose hydrodynamics re
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Both the Schrödinger evolution under the quantized Lense-Thirring Hamiltonian and the on-shell action of linearized quantum gravity in the stationary-phase approximation yield identical entanglement phases for the rotational degrees of freedom of the source and the paths of the test particle; this common phase equals the proper-time difference between the arms and is modified by gravitational retardation, thereby furnishing an explicit, relativistically causal description within linearized gravity.
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The analysis of how spacetime emerges from quantum gravity is incomplete because it fails to interpret the dynamical and quantum aspects of these theories, which differ from standard quantum theory; without showing how these aspects can fulfill spacetime roles, spacetime functionalism provides no help and the emergentist position remains unsupported by any successful reduction example.
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This paper presents a curated selection of research questions at the intersection of quantum gravity and quantum information, chosen to highlight issues that we regard as particularly important for researchers in both fields. We organize the discussion into four main themes: the operational characterization of observables, the role of observers, quantum error correction, and the infinite-dimensionality of Hilbert spaces. We hope that addressing these questions will engage researchers across both communities and further strengthen the profound interplay between the two disciplines.
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We provide a field-theoretic construction of Padmanabhan's duality-invariant Feynman propagator for a massive point particle in Euclidean space R^D. Padmanabhan's propagator includes quantum-gravity effects due to the existence of a quantum of length ℓ. Including O(ℓ²) corrections, the corresponding field-theory model turns out to be a free, massive scalar defined in R^{D+2}. The two additional dimensions with respect to the original R^D provide the necessary room for quantum-gravity fluctuations.
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We adapt the extended Anderson-Candelas-Christensen-DeWitt approach to compute the scalar vacuum polarization ⟨φ²⟩ exterior to the quantum-corrected LQG black hole geometry. The quantum-gravity exponent ε enhances the near-horizon polarization and induces, farther out, a small negative tail that we identify through a parameter-free DeWitt-Schwinger comparison with the field's response to the nonzero curvature of the background. The correction scales linearly with ε.
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The Euclidean action evaluated on the bounce solution that mediates false-vacuum decay yields the same numerical value for the tunneling exponent in TEGR and STEGR as it does in GR, so the decay rate is formulation-independent.
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There exist background independent representations of Fock type within the manifestly non-perturbative, canonical approach to quantum gravity. Mandatory for their existence is the presence of suitable matter fields next to the geometry field. In particular, the excitations of the corresponding Fock vacuum necessarily entangle matter and geometry. The Fock quantum gravity Hilbert space, in contrast to the loop quantum gravity Hilbert space, is separable, allowing the Hamiltonian constraint to be implemented as a densely defined quadratic form.
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Scalar leptoquarks in the SU(5) grand unified theory, forced to be superheavy by proton decay bounds, produce a stochastic gravitational wave background through graviton bremsstrahlung induced by quantum gravity. Solving the Boltzmann equation for the leptoquark number density evolution allows computation of the gravitational wave spectrum, which high-frequency resonant cavity detectors could probe.
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We propose a definition of the quantum width by a physical experiment involving the last moment a signal emitted from an ingoing light ray can escape to infinity. Calculations of this observable for spherically symmetric black holes in perturbative quantum gravity reveal that the quantum width depends on the resolution of the probe, and is often much larger than the Planck scale. For example, for Schwarzschild black holes in four dimensions in a particular regime of parameters, a piece of the horizon of size σ_⊥ has quantum width roughly √(l_P r_s²/σ_⊥).
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In perturbative quantum gravity, the quantum width of the BTZ horizon, defined by a precise protocol that maps bulk fluctuations to boundary correlators, is typically of order (G_N L_AdS^3)^{1/4} and diverges logarithmically in the UV.
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For the LQG heat trace on a bounded domain driven by the whole-plane Gaussian free field, the expected value admits an asymptotic expansion in which the second term as t to 0 is governed by the KPZ exponent; an almost-sure version holds for the associated heat content. The same analysis yields the conjectured annealed short-time asymptotics of the heat kernel together with finiteness of all moments after proper rescaling.
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In models with temporal diffeomorphism invariance, the standard definition of observables as phase space functions with vanishing Poisson brackets with the constraints does not cover all trajectories. Correlations can be shown to be invariant only in a generalized sense that does not yield smooth phase space functions. Spatiotemporal relations are also invariant. Spatiotemporal structures are therefore indispensable for defining the invariant content. These formal results are expected to extend to models invariant under d-dimensional diffeomorphisms.
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Contrary to common intuition, there exist rigorous, background independent Fock representations available for a non-perturbative canonical quantisation of geometry and suitable matter fields. The Fock Hilbert space is separable while the Hilbert space of other manifestly background independent and non-perturbative canonical quantisation programmes is not. Since non-separability is a source for quantisation ambiguities, such a Fock representation may help to arrive at a significantly more predictive theory. As a simple application the cosmological truncation and mechanisms for quantum bounces are discussed.
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The graviton field generated by an axion cloud around a Kerr black hole is expressed, via the Takagi decomposition of its complex symmetric squeezing kernel, as a set of independent squeezed supermodes possessing anomalous correlators. These correlators survive tracing over the inaccessible graviton degrees of freedom and, together with the weak-interaction flavour-mixing matrix element, induce transitions between the antisymmetric and symmetric two-meson sectors. This produces a small exchange-symmetric admixture, parametrized by ω, in the otherwise antisymmetric EPR state, where ω is given by a sum over the Takagi supermodes weighted by their squeezing amplitudes and phases together with t
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The paper states that focusing on the bottom-up approach reveals symmetries, key elements of celestial CFT, interplay with twistor theory, and connections to AdS/CFT as central components in the ongoing effort to construct a celestial dual for quantum gravity in flat spacetimes.
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On flat half-space with the fixed conformal bosonic boundary rows — trace-free metric perturbation zero, the mean-curvature combination zero, and the gauge-fixing rows zero — in the gauge-fixed N=1 supergravity model, the paper proves that no completion which leaves half of the gravitino boundary data free (local differential, nonlocal spectral, or pseudodifferential, with any ghost boundary condition compatible with BRST at highest-derivative order) can preserve the full half-supersymmetry P^⊥_+ ε = ε. The forward variation of the conformal-class row forces the kept tangential gravitino datum to be the chiral projection P^⊥_- ψ_a = 0; the reverse variation of that datum produces the normal–
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The central claim is that quantized irreversible null-geometry, formulated through statistics of discrete Poisson point processes, supplies a double-exponential probability functional that regularizes amplitudes and enables a bifurcation of the stochastic action; the macroscopic mean defines classical spacetime while residual ultraviolet noise produces quantum kinematics and, after linear separation from the nonlinear action, a rectified drift identified with dark energy, yielding a UV-finite synthesis that predicts a 6 TeV cutoff and derives Standard Model hierarchies, CMB power suppression, and quantum axioms as statistical effects.
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The classical spectral curve of the seven-vertex matrix model is given in closed parametric form by a pair of elliptic functions built from Jacobi theta functions whose three free coefficients are fixed by the large-x asymptotics of the resolvent; the A- and B-cycle integrals of the one-form equal the cosmological constant and the derivative of the free energy, respectively, and the critical curve consists of three analytic branches that realise the massive, dense and dilute phases.
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Gol'fand's discrete evolution equation, when written as a CPTP quantum channel, coarse-grains to a Lindblad master equation governed by a fundamental time scale τ. This equation produces decoherence in both the energy basis and the operator basis W and yields a strictly positive entropy production rate driven solely by the decay of quantum coherences, thereby furnishing a microscopic foundation for the arrow of time that is independent of environmental coupling.
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In Calabi-Yau compactifications of Type IIB string theory the bound Λ_QG ≲ 2π √S f holds for both C2 and C4 axions throughout the Kähler moduli space, including near boundaries where the co-scaling relationship for axion strings fails, as demonstrated by a combination of analytic arguments and numerical landscape scans.
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The central claim is that compelling evidence for quantum scale symmetry exists in four-dimensional Euclidean pure gravity via the Reuter fixed point, with increasingly conclusive evidence when matter fields are included and when Lorentzian spacetime signature is accounted for, making the approach predictive at all scales.
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Concentration of measure on the Fubini-Study geometry of pure states forces any finite random sample to an equidistant dust whose thresholded metric graph is the complete graph; a diffusion probe then reads this dust as two-dimensional in the large-sample limit at the dust's single relaxation scale, a value fixed by the eigenvalue density near zero rather than by any structural dimension, so the convergence on two is not evidence that spacetime is two-dimensional.
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We compute spectral functions of graviton modes in Lorentzian quantum gravity, interpolating between classical general relativity and an asymptotically safe ultraviolet fixed point. Using functional renormalisation adapted for theories in Lorentzian signature, and enhanced by new symmetry conditions to account for underlying Ward identities, we derive and solve flow equations directly for the Källén-Lehmann representation of propagators. Consistent results are found for several sets of renormalisation conditions yielding normalisable spectral functions for the graviton and the scalar graviton mode, in agreement with effective theory in the infrared. We further calculate the full quantum effe
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Simulations of accretion onto regular loop-quantum black holes show that quantum-gravity corrections can modify photon-ring size, polarization structure, and jet power, leading to observational constraints from Event Horizon Telescope data.
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The volume operator is realized matrix-free by replacing the spectral fourth-root step with a shifted-resolvent quadrature drawn from the Balakrishnan-Stieltjes integral representation of (Q_v²)^{1/4}; the resulting operator requires only repeated applications of the locally computable Q_v together with solves against shifted positive operators and therefore never materializes the full recoupling matrix.
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We derive an analytical approximation for the graviton propagator from Asymptotic Safety. We find neither extra poles nor indications of unitarity or causality violations in the spin-two sector. Our results strengthen the case that Asymptotic Safety does not introduce new degrees of freedom, and thus propagates the same field content as General Relativity. We also identify the underlying mechanism: the residues of spurious poles in finite-order derivative expansions approach zero as the order is increased.
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θ and η induce the entanglement. The bipartite Gaussian state is almost always entangled in deformed space. The Peres-Horodecki separability condition leads to a constraint equation for the parameter values of the oscillator in NC space.
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When the running scale of quantum gravity is defined by a spectral shell on the eigenvalues of the scalar Laplace-Beltrami operator, the one-loop Einstein-Hilbert beta functions for the dimensionless Newton and cosmological constants exhibit a non-Gaussian UV-attractive fixed point, both for a smooth proper-time cutoff and for a hard spectral cutoff.
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Non-isometric encoding arises in finite-energy, non-ideal codewords of continuous-variable codes and in holographic quantum gravity. A systematic theory of non-isometric quantum error-correcting codes employs the approximate quantum error correction framework to quantify the fundamental limitations that non-isometric encodings place on error-correction accuracy and on the implementation of logical operations. The theory is applied to GKP and tiger codes under energy constraints and yields implications for holography.
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A complete recovery of general relativity requires an effective metric, a continuum limit, or Einstein-like dynamics together with the physical conditions under which relational geometrical quantities can be objectively determined. These conditions concern the dynamical stability of measuring devices and reference systems, causal accessibility among physical systems, record formation, and invariance under admissible descriptions.
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The background graviton propagator, obtained by flowing the non-local form factors to k=0 and continuing to Minkowski space, exhibits a single pole at q²=0 with positive residue and no additional ghost poles at this level of approximation. The corresponding Newtonian potential is found to be regular at r=0.
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In the model, the interaction between the propagating modes of the quantized gravitational field and the two particles produces entanglement whose strength is fixed by the graviton commutation relations inside the Feynman-Vernon influence functional. Entanglement does not appear at once; a delay proportional to the particle separation must elapse first, reflecting the causal character of gravitational propagation. The effect remains tiny for ordinary initial states but can be increased by preparing the particles in squeezed states.
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The central claim is that loop quantum corrections produce only moderate changes to the quasinormal spectrum of massless scalar perturbations while the number of spacetime dimensions exerts a stronger influence on both oscillation frequencies and damping rates; all modes display negative imaginary parts, establishing dynamical stability within the explored parameter range; the shadow radius depends sensitively on the loop quantum parameter, the cosmological constant, and dimensionality, and comparison with Event Horizon Telescope constraints for M87* supplies concrete bounds on the model parameters.
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The central claim is that after choosing an admissible flux quantization law A — a classifying space whose real Whitehead-bracket L∞-algebra lA is equivalent to the characteristic L∞-algebra a encoding the theory's Bianchi identities and Gauss laws — the globally completed on-shell phase space of any Maxwell-type higher gauge theory is the homotopy fiber product Phs(X^d;A) = Ω^1_cl(X^d;a) ×_{SΩ^1_cl(X^d;a)} Map(X^d,A). The maps being completed are the nonabelian character map, which sends charge configurations to their flux shadows, and the shape unit, which regards flux densities as homotopical data. The homotopy filling the square is the gauge potential. The paper shows this construction r
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In the spacetime of a charged LQG black hole with polymerization parameter fixed by the area-gap condition, the effective potential admits innermost stable circular orbits and marginally bound orbits. Periodic orbits are labeled by integers (z, w, v) according to the rational ratio of azimuthal to radial frequencies, and the gravitational waveforms they produce in the quadrupole approximation display a zoom-whirl structure whose amplitude and phase vary with the charge parameter Q and the LQG correction. The resulting characteristic strains lie in the millihertz band and surpass the projected sensitivities of LISA, Taiji, and TianQin for all examined values of Q.
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The Brownian sphere is quasisymmetrically rigid, meaning that, almost surely, it has no nontrivial quasisymmetric automorphisms. Two independent Brownian spheres are almost surely not quasisymmetrically equivalent. The argument also gives a new proof that the conformal structure of the Brownian sphere is almost surely determined by its metric structure, using its equivalence to the √(8/3)-Liouville quantum gravity sphere.
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We prove that the set of 3-star points has Hausdorff dimension at least two with respect to the LQG metric, which is conjectured to be optimal. Our proof works for a general class of planar length metrics which also includes, e.g., Kendall's Poisson roads metric. We additionally prove a dimension lower bound of one for the set of 2-star points intersected with the boundary and for the metric net intersected with the boundary, as well as a dimension lower bound of two for the intersection of two metric nets. In the particular setting of LQG, we obtain sharper lower bounds for the Hausdorff dimensions of the set of 2-star points and the LQG metric net, with respect to both the Euclidean metric
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The path integral calculation over classical cosmologies that differ only in their rms relative rotation rate, weighted by the Einstein-Hilbert action, shows that the action is an extremum at zero rms relative rotation rate. Phase interference then limits the cosmologies that contribute significantly to those with relative rms rotation rates less than about 10^{-51} rad/year after 50 e-foldings during inflation. The result is insensitive to the specific details of the quantum gravity theory.
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The authors distinguish C_BPS-B, the cone generated by BPS branes, from C_BPS-BB, the subcone of charges that admit BPS black-brane attractor solutions. They conjecture that every integrally charged state lying in C_BPS-BB is realized by a BPS state in the spectrum. They further conjecture that when C_BPS-B is moduli independent, it can be determined as the dual to C_BPS-BB under the electric-magnetic pairing.
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The virtual exchange of a graviton provides entanglement between the photon degrees of freedom and the spatial position of the quantum rotor, with the rotational state affecting its magnitude. We analyze the case of a high spinning rotor, in an approximately classical state of angular momentum, and quantify its effect on the gravitationally induced entanglement between the photon and the position of the quantum rotor. We show that the difference in the linear entanglement entropies, of prograde-and-retrograde motion of the photon with respect to the quantum rotor, provide tangible observable consequences.
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The coframe/spin-connection pair provides an alternative and geometrically refined description of gravitational variables, which may serve as a useful starting point for future investigations of quantum gravity by encoding gravity in torsion rather than curvature.
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Quantum reference fields, defined as four dynamical scalar fields entering the constraints, permit reduced descriptions of relational observables in each perspective. The unitary transformations connecting these perspectives act on the linearized gravitational field in a manner structurally analogous to a linearized diffeomorphism, except that the classical gauge parameter is replaced by a physical quantum field.
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When leading order post-Newtonian corrections are included in the Hamiltonian of the quantum gravity model interacting with a Bose-Einstein condensate in a harmonic trap, the non-quadratic operators responsible for non-Gaussianity persist from the quantum gravity sector, but the overall signal to noise ratio of the detection gets slightly damped.
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The central claim is that Planck-scale perturbations induced by the unique gauge-invariant dimension-5 operator can partially compensate matter-induced biases when specific Majorana phases are chosen. For quasi-degenerate neutrino masses near 2 eV the solar mass-squared splitting receives a correction of order (1.0 ± 0.5)×10^{-5} eV² while the atmospheric splitting remains essentially unchanged. Around L ≈ 7000 km this compensation reduces the combined bias by about 30%, demonstrating that the two effects must be propagated together rather than independently.
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The gravitational Hamiltonian acts on the black hole interior through a pair of pants interaction, mapping between a single interior sector and a connected two interior sector. Evolution over a Page time causes the connected two interior branch to dominate. One of these is the naive semiclassical interior, which carries a nontrivial one sided boost upon gluing the interior back to the exterior, and hence a firewall. The other interior is a zero mode of the one sided boost generator. Gluing the interior back to the exterior quotients by the gravitational constraints, which annihilates the firewall branch. On the surviving branch, the horizon vacuum measurement and the early radiation purity m
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Starting from the phase space of a stretched horizon inside a Minkowski causal diamond, the Poisson algebra generated by the fields averaged over stretched-horizon time is quantized. Fluctuations of the averaged area density are then computed in a thermal state analogous to the black-body thermal state. In the null limit, the thermal fluctuation formula of the boundary area operator contains a linear term with Verlinde-Zurek scaling characteristic of independent microscopic constituents, which is interpreted as a statistical signature of discrete quanta of geometry.
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Spatial subregions in quantum gravity can be assigned pure states prepared by a partially frozen gravitational path integral, in which a spacetime subregion containing the spatial subregion is fixed while the field configurations and ambient geometry are summed over. In the semiclassical regime a holographic prescription for the entanglement entropy of bipartitions of this state, with a frozen-region analogue of the homology constraint, satisfies strong subadditivity, complementarity, and entanglement wedge nesting while reproducing known entropy formulas in holography and gravity as special cases.
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The paper claims that gravitational interactions among mechanical oscillators enable the teleportation of arbitrary quantum states and that framing these interactions as imitation games supplies a concrete route to fundamental tests of gravity's quantum character in laboratory settings.
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In the spacetime whose geometry is the Newtonian potential sourced by a non-relativistic quantum particle, a propagating massless scalar field experiences an operator-valued Shapiro delay. Consequently, causal-boundary shifts become noncommuting observables that endow the causal structure with irreducible quantum uncertainty; the causal relation between any two fixed events can exist in a superposition of timelike and spacelike configurations; and tracing over the source state smears the light-cone singularity of the Wightman function, yielding an effective ultraviolet cutoff.
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The central claim is that the gravitational path integral computing the supersymmetric index contains |G| degenerate saddle points for the Euclidean AdS5 black hole, related by the action of the discrete electric one-form symmetry of the boundary theory. This yields Z = |G| e^{-I_BH} + ... and can be rewritten as a universal log|G| correction to the on-shell action. In the infinite-volume (Cardy-like) limit the degeneracy is realized as |G| distinct vacua of a 3d effective theory obtained by reducing on the cigar; the count is fixed by the level N of the BF coupling N/(2π) ∫ b2 ∧ dc2, which is quantized by the internal flux, and is independent of the black hole's charge parameters and rotati
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In the period 1962-1967 the Wheeler-DeWitt equation moved from a semi-formal constraint to a usable model once an expression for the inner product on the space of wave functionals was supplied; that step, rather than the writing of the equation alone, constituted the rigorisation that removed barriers to calculation and thereby fixed credit attribution between Wheeler and DeWitt.
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The paper claims that the dual Hamiltonian to the IHO governs the additional spin-2 sector of the unique unitary perturbatively renormalizable theory of quantum gravity in four dimensions, with that sector remaining purely virtual and regularizing gravitational interactions at the Planck scale. This universal physics of the saddle point course-corrects the history of quantum gravity approaches that abandoned renormalizability, uniqueness, and predictivity.
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Within the proper-time formalism at quadratic order in the curvature expansion, the flow equations for gravitational form factors integrate to k equals zero. Asymptotic safety alone leaves a logarithmic divergence in the Lambda to infinity limit, requiring an additional renormalization condition. Only the non-Gaussian fixed point as ultraviolet boundary condition removes these divergences, yielding finite dimensionful form factors that are independent of the renormalization scale mu, decay as one over q squared in the ultraviolet, and exhibit the expected logarithmic structure in the infrared with the Planck scale in place of mu.
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We propose that any compact d-manifold with elliptic data, J, prepares a quantum state |J> on its (d-1)-boundary σ. No asymptotic structure is required. Inner products and traces are evaluated by the gravitational path integral with closed boundary conditions obtained by gluing elliptic data manifolds. We give a prescription for the Rényi entropies S_n of a subregion of σ. In examples, S_n is nonnegative and nonincreasing with n. The von Neumann entropy by analytic continuation agrees with the minimal surface prescription.
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A PBH mass around 10^3 kg allows Hawking evaporation to reheat the Universe while the remnants entirely constitute the present-day DM. This scenario does not require fine-tuning the initial abundance of PBHs of this mass, which could range from 10^{-10} to order one. These early-Universe cosmologies produce distinct observational signatures through scalar-induced gravitational waves sourced by primordial or Poisson fluctuations amplified by the early PBH-dominated era, and through constraints on the effective number of relativistic degrees of freedom.