Pith. sign in

REVIEW 4 major objections 4 minor 1 cited by

Conformal Cores of Quantum Black Holes in Quadratic Gravity

T0 review · 4 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Pure quadratic gravity has exact complex power-law solutions that sit at the center of black holes, replacing the singularity with a horizonless 'powerball' matched to Schwarzschild about a Planck length above the would-be horizon.

desk verdict New powerball solutions are real; the black-hole-interpretation weight is not yet earned. read the letter →

arxiv 2411.19311 v2 pith:KPXB3PA2 submitted 2024-11-28 hep-th gr-qc

Ruolin Liu , Jerome Quintin , Niayesh Afshordi This is my paper · ORCID
classification hep-thgr-qc MSC 83C5783C4581T20 PACS 04.70.-s04.60.-m04.50.Kd
keywords quadraticgravitypowerballquantumblackholecomplexmetricconformalinvariancegravitationalpathintegralSchwarzschildmatchingKontsevich-Segalcriterion
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Pure quadratic gravity — the renormalizable extension of Einstein gravity with terms quadratic in curvature — admits exact power-law solutions that are complex valued. The paper calls these horizonless 'powerballs' and proposes them as a model for the interior of quantum black holes. A powerball matches the Schwarzschild metric continuously at a radius about a Planck length outside the would-be Schwarzschild horizon, replacing the classical singularity with a spiraling complex geometry that has finite on-shell action. If this picture is correct, black-hole interiors need not be singular, and the gravitational path integral has a well-defined, finite-weight saddle point that reproduces black-hole thermodynamics to leading order. The paper is explicit that the complex contour used to compute the action violates the Kontsevich-Segal admissibility bound, and leaves the resolution of that issue to future work.

What carries the argument

The load-bearing mechanism is the complex power-law ansatz $A(r) = a r^{\alpha}$, $B(r) = b$ with $\alpha_{\mp} = \frac{1}{2}(1 \mp i\sqrt{15})$ and $b_{\mp} = \frac{3}{8}(1 \mp i\sqrt{15})$, which solve the pure quadratic-gravity equations regardless of the couplings. The action is rendered finite by integrating the radial coordinate along a contour that circles the branch cut and the $r=0$ singularity in the complex plane rather than passing through them; the monodromy $e^{2\pi i\alpha} = -e^{\pm\pi\sqrt{15}}$ is what converts the Lorentzian exterior into a Euclidean one and produces the real weight entering the path integral.

What would settle it

Evaluate the path integral of the conformally invariant matter action (6.11) on the powerball background along the contour $r(\vartheta)=r_\star e^{i\vartheta}$; if that matter path integral diverges, the finite on-shell action and the probability weight derived from it lose their justification. A separate observational falsifier is the gravitational-wave ringdown: a horizonless reflective surface at $r_\star \approx r_S + \zeta\ell_P$ would produce echo-like deviations from the standard GR template.

Watch

Extended reading notes

Core claim

The central discovery is a pair of exact, complex, power-law solutions to the vacuum equations of pure quadratic gravity in spherical symmetry: with $A(r)=a r^{\alpha}$ and $B(r)=b$, the equations are solved by $\alpha_{\mp} = \frac{1}{2}(1 \mp i\sqrt{15})$ and $b_{\mp} = \frac{3}{8}(1 \mp i\sqrt{15})$, two complex conjugates independent of the theory's couplings. These 'powerball' metrics are Ricci flat, with Weyl-squared curvature $C^2_{\mu\nu\rho\sigma} = 16/(3r^4)$, which diverges at $r=0$ but more mildly than the $r^{-6}$ of Schwarzschild. Because the exponent $\alpha$ is complex, circling $r=0$ in the complex plane multiplies $g_{tt}$ by $e^{2\pi i\alpha} = -e^{\pm\pi\sqrt{15}}$, taking the geometry from a Lorentzian to a Euclidean signature; the paper assembles the global eternal geometry from a Lorentzian Schwarzschild exterior, a Euclidean Schwarzschild exterior, and the complex powerball between them. Matching $g_{tt}$ at $r_{\star} = r_S + \delta$ fixes the otherwise free coefficient, and extremizing an effective interface action yields a proper horizon offset $\delta \approx \zeta^2/(8M)$, of order the Planck length. The full on-shell action, including all boundary terms, is finite; its real part (the 'weight') controls the semiclassical path-integral probability, while its imaginary part supplies a phase.

Load-bearing premise

The construction depends on treating the complex contour that gives the powerball a finite action as an admissible saddle point of the gravitational path integral, even though the paper itself shows that contour fails the standard Kontsevich-Segal convergence test.

Editorial extensions

If this is right

  • Every Schwarzschild black hole would, if this is right, have a horizonless, singularity-free core appearing about a Planck length above where the horizon would be, with no observable difference at macroscopic distances.
  • The on-shell action is finite, so the semiclassical path integral provides either an exponentially suppressed 'virtual powerball' (standard Wick rotation) or an exponentially enhanced stable endpoint of collapse (anti-Wick rotation), depending on the direction of the complex rotation.
  • The Euclidean-sector partition function gives the Bekenstein-Hawking area law at leading order, with corrections controlled by the interface parameter $\zeta$ and the quadratic-gravity couplings $\sigma$ and $\omega$.
  • The monodromy of the complex exponent means an observer or field passing through the powerball emerges on the other side in a Euclidean Schwarzschild region, with the time-time metric rescaled by $e^{\pm\pi\sqrt{15}}$.
  • Since the exponents $\alpha_{\mp}$ and $b_{\mp}$ are independent of $\sigma$ and $\omega$, the powerball core is a robust prediction of pure quadratic gravity in the conformal (Ricci-flat) regime, insensitive to the running of couplings so long as that running is negligible.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A testable extension is to compute the quasinormal-mode spectrum of the matched Schwarzschild–powerball geometry: the reflective surface at $r_\star$ should produce gravitational-wave echoes that distinguish this model from a horizon-having black hole.
  • The explicit Kontsevich–Segal violation flagged in Sec. 6.2 suggests the semiclassical saddle point may not survive a full path-integral treatment with standard matter; evaluating the conformally invariant scalar path integral (action 6.11) on the powerball contour is the natural next calculation.
  • The complex-conjugate pair of solutions suggests a possible interference term $e^{iS_+}+e^{iS_-}$ in the wave function; the paper notes but does not explore this, and it could yield oscillatory structure in the interior state that a single-saddle approximation misses.
  • For astrophysical relevance, the spherical, stationary powerball must be generalized to rotating configurations; if angular momentum changes the complex exponents, the viability of the matched solution could depend on spin.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper constructs exact complex power-law solutions to pure quadratic gravity under spherical symmetry, with exponents alpha_-+ = (1/2)(1 -+ i sqrt(15)) and b_-+ = (3/8)(1 -+ i sqrt(15)) in Eq. (2.6). It proposes these "powerballs" as the conformal cores of quantum black holes, matched continuously to a Schwarzschild exterior at r_star = r_S + delta. The paper computes the on-shell action on a complex radial contour, identifies a Lorentzian-to-Euclidean transition, and interprets the result as a semiclassical gravitational path integral, obtaining a finite action, a probability weight, and an entropy with a leading-order area law. The derivation of the powerball solution is clean and independent of the quadratic-gravity couplings, but the physical interpretation rests on an ad hoc interface action with a free parameter zeta and on the allowability of a complex contour that the paper itself shows violates the Kontsevich-Segal bound.

Significance. If the construction can be put on a firmer footing, it would provide an explicit, singularity-free model of black-hole interiors in a renormalizable theory of gravity, with exact solutions that are independent of sigma and omega and a finite on-shell action. The paper is commendably explicit about its limitations, including the contour-allowedness problem and the conjectural nature of the conformal-matter rescue. These limitations, however, are precisely the load-bearing elements of the path-integral interpretation, so the significance of the result is currently conditional rather than established.

major comments (4)
  1. [6.2, Eqs. (6.8)-(6.10)] The contour r(vartheta) = r_star e^{i eta vartheta} used in Eq. (5.9) is not Kontsevich-Segal allowed: at vartheta = pi/2, r = i r_star, so 2|Arg(r^2)| = 2 pi and the left-hand side of Eq. (6.10) is at least 2 pi, not less than pi. The paper acknowledges this, but the proposed escape via the conformally invariant scalar action (6.11) is not demonstrated: no convergence criterion for the path integral over phi is given, and the text concedes that there is no reason for it to correspond to the Kontsevich-Segal criterion. Without either an allowable contour or a proven convergence criterion for the relevant matter sector, the weight W in Eq. (5.24a) and the probability in Eq. (6.4) remain formal expressions rather than physical predictions.
  2. [5.3, Eqs. (5.15)-(5.19)] The location of the GR-to-quadratic-gravity interface is not predicted by the theory: Eq. (5.19) gives delta approximately zeta^2/(8M), with zeta a free parameter of the ad hoc interface action (5.15), and the setting c1 = c2 = 0 is imposed rather than derived. The statement that the transition occurs a Planck length above the would-be horizon is therefore a choice zeta ~ O(1), not an output of the model. Since zeta controls the correction terms in Eqs. (5.23), (6.6), and (6.7), the quantitative claims of the paper are conditional on this free parameter.
  3. [6.1, Eq. (6.4)] The probability interpretation depends on the orientation of the complex contour through eta: with eta = -1 the weight is exponentially suppressed with time, while with eta = +1 it is exponentially enhanced, the two weights differing by exp(pi sqrt(15)/2) at leading order. No independent principle is given to select eta. The same on-shell action therefore supports opposite physical conclusions, and the paper must either supply a selection rule or restrict the interpretation to the Euclidean partition function of Eq. (6.5), where eta = -1 is fixed by the Wick rotation.
  4. [6.1, Eq. (6.7)] The entropy result imports the standard Hawking temperature beta = m_P^2/(8 pi M) from the Schwarzschild geometry rather than deriving it for the cutoff spacetime with interface at r_star = r_S + delta. Because the Euclidean time periodicity is an input, the leading-order area law in Eq. (6.7) is recovered by construction rather than as a prediction. The thermodynamic interpretation needs either a derivation of beta for this geometry or a precise justification of the extrapolation from Ref. [124] at the required order.
minor comments (4)
  1. [Section 3, after Eq. (3.3)] There is a typo: "Lorenztian" should be "Lorentzian".
  2. [Sections 3 and 5.3, Eqs. (3.1) and (5.19)] The symbol delta is described as a proper distance in Eq. (3.1) but used as a coordinate-length displacement in Eq. (5.19); the distinction should be stated explicitly.
  3. [Section 5.2, Eq. (5.9)] The text should state explicitly that the contour stays on the chosen Riemann sheet of the multivalued function r^alpha when the limit epsilon to 0 is taken, since the branch-cut structure is essential to the result.
  4. [Figure 2] The caption describes the left region as a "folded trapezoid," but the drawing appears to represent a rectangle; the caption and the figure should be made consistent for clarity.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the powerball solution and action computation are self-contained, and the two externally flavored results (Planck-length offset, area-law entropy) are explicitly input-dependent rather than hidden reductions.

full rationale

The central claim is derived rather than assumed: the powerball exponents and constants in Eq. (2.6) are obtained by direct algebraic solution of the quadratic-gravity equations of motion (2.5) with beta = 0, and the on-shell actions in Sec. 5 are evaluated from the stated metric, boundary terms, and integration contour without reusing the conclusions. The matching condition in Eq. (3.2) fixes a by continuity and is a construction, not a prediction. The two places that involve externally supplied or free inputs are explicitly acknowledged by the authors: the Planck-length offset follows from Eq. (5.19) only after the stated assumption zeta ~ sigma ~ O(1), and the area-law entropy in Eq. (6.7) follows from the explicit choice beta = 1/T_Hawk. Because these inputs are stated openly and are not disguised as derived parameters, they are assumptions rather than circular reductions. The paper also transparently concedes in Sec. 6.2 that the complex contour violates the Kontsevich-Segal bound and that the conformal-matter rescue via Eq. (6.11) is not proven; this is an admitted gap in the path-integral interpretation, not a circular step. The self-citations (notably [103] for the conformal-core postulate) motivate rather than justify the central derivation, so they are not load-bearing. Overall, the core mathematical result is self-contained, and the remaining concerns are about explicit inputs and open questions, not circular reasoning.

Assumptions & free parameters 2 free parameters · 5 assumptions · 1 invented entities

The central mathematical result rests only on the standard action and ansatz, but the physical interpretation relies on an ad hoc interface parameter zeta, a chosen contour orientation eta, and an imported Hawking temperature. The powerball entity is postulated without independent evidence.

free parameters (2)
  • zeta (interface coupling) = not fitted; assumed O(1)
    Introduced in the effective interface action (5.15); it sets delta approximately equal to zeta^2/(8M) via Eq. (5.19) and appears in the total action (5.23) and entropy (6.7). No derivation from the fundamental action is given.
  • eta (contour orientation) = plus or minus 1
    Discrete choice of clockwise or counterclockwise contour around the branch cut. It changes the sign of the weight W in Eq. (5.24a) and flips the interpretation from decaying virtual objects to enhanced solitons.
assumptions (5)
  • domain assumption Pure quadratic gravity action (2.2) with constant couplings sigma and omega accurately describes the interior of quantum black holes.
    Stated as the premise of the work in Sec. 1 and Sec. 2; the running of couplings and the ghost problem are set aside as a first approximation and discussed only in the conclusions.
  • domain assumption The interior metric is spherically symmetric, stationary, and has the power-law form (2.4).
    This restricts the solution space searched in Sec. 2; no uniqueness theorem or general argument is given that the physical interior must take this form.
  • ad hoc to paper The transition between Einstein gravity and pure quadratic gravity at r_star is modeled by the effective boundary action (5.15) with c1 = c2 = 0 and a free parameter zeta.
    This action is not derived from the fundamental quadratic gravity action; it is a delta-function interface model introduced in Sec. 5.3 to localize the transition.
  • domain assumption The gravitational path integral is dominated by the complex powerball saddle point, with the contour chosen around the branch cut as in Fig. 3.
    Standard saddle-point approximation, but the chosen contour violates the Kontsevich-Segal criterion as shown in Sec. 6.2, and the proposed conformal-matter rescue is not proven.
  • domain assumption The standard Hawking temperature beta = 1/T_Hawk = m_P^2/(8 pi M) holds for the horizonless powerball.
    Imported from [124] in Sec. 6.1 to convert the partition function into an entropy; this assumption makes the leading area-law term an input rather than an independent derivation.
invented entities (1)
  • Complex powerball metric
    purpose: Replace the classical Schwarzschild singularity as the interior of quantum black holes
    The metric in Eqs. (2.4)-(2.6) is new, but no falsifiable prediction is derived in the paper. Gravitational wave echoes are mentioned qualitatively in the introduction and conclusions, but no echo waveform or rate is computed.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Conformal Cores of Quantum Black Holes in Quadratic Gravity." pith.science (2026). https://pith.science/paper/KPXB3PA2

@misc{pith2026241119311,
  author       = {Pith},
  title        = {Pith review of: Conformal Cores of Quantum Black Holes in Quadratic Gravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KPXB3PA2}},
  note         = {Machine review of arXiv:2411.19311}
}
read the original abstract

We explore the possibility that quadratic gravity, as a renormalizable theory, describes the interior of quantum black holes. We find new exact power-law solutions to pure quadratic gravity under spherical symmetry, which are complex valued. The resulting solutions, dubbed powerballs, are horizonless compact objects that become Schwarzschild-like a small distance (of the order of the Planck length) outside the would-be Schwarzschild horizon. We present a description of the global eternal geometry, whose right and left exteriors are Lorentzian and Euclidean Schwarzschild-like regions, respectively, while the complex interior is a form of spiraling spacetime. We compute the total on-shell action integral as a saddle point to a gravitational path integral and discuss the Lorentzian and Euclidean interpretations thereof.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Complex Riemannian spacetime and singularity-free black holes and cosmology

    gr-qc 2025-01 reject novelty 2.0 of 10

    The paper claims complex-coordinate contours regularize black-hole and cosmological singularities, but the real projection is never constructed and the bounce is inserted by hand.

Reference graph

Works this paper leans on

148 extracted references · 13 canonical work pages · cited by 1 Pith paper

  1. [124]

    Mathur and M

    S.D. Mathur and M. Mehta,The universal thermodynamic properties of extremely compact objects, Class. Quant. Grav. 41 (2024) 235011 [arXiv:2402.13166]. 23

    arXiv 2024

  2. [1]

    Penrose,Gravitational collapse and space-time singularities, Phys

    R. Penrose,Gravitational collapse and space-time singularities, Phys. Rev. Lett.14 (1965) 57

    1965

  3. [2]

    Donoghue,General relativity as an effective field theory: The leading quantum corrections, Phys

    J.F. Donoghue,General relativity as an effective field theory: The leading quantum corrections, Phys. Rev. D 50 (1994) 3874 [gr-qc/9405057]

    arXiv 1994

  4. [3]

    Donoghue,Introduction to the effective field theory description of gravity, inAdvanced School on Effective Theories, 1995, gr-qc/9512024

    J.F. Donoghue,Introduction to the effective field theory description of gravity, inAdvanced School on Effective Theories, 1995, gr-qc/9512024

    arXiv 1995

  5. [4]

    Burgess,Quantum gravity in everyday life: General relativity as an effective field theory, Living Rev

    C.P. Burgess,Quantum gravity in everyday life: General relativity as an effective field theory, Living Rev. Rel. 7 (2004) 5 [gr-qc/0311082]

    arXiv 2004

  6. [5]

    Donoghue,The effective field theory treatment of quantum gravity, AIP Conf

    J.F. Donoghue,The effective field theory treatment of quantum gravity, AIP Conf. Proc.1483 (2012) 73 [arXiv:1209.3511]

    arXiv 2012

  7. [6]

    Donoghue, M.M

    J.F. Donoghue, M.M. Ivanov and A. Shkerin,EPFL Lectures on General Relativity as a Quantum Field Theory, arXiv:1702.00319

    arXiv

  8. [7]

    Ruhdorfer, J

    M. Ruhdorfer, J. Serra and A. Weiler,Effective Field Theory of Gravity to All Orders, JHEP 05 (2020) 083 [arXiv:1908.08050]

    arXiv 2020

Show all 148 references
  1. [8]

    Donoghue,Quantum General Relativity and Effective Field Theory, inHandbook of Quantum Gravity (C

    J.F. Donoghue,Quantum General Relativity and Effective Field Theory, inHandbook of Quantum Gravity (C. Bambi, L. Modesto and I.L. Shapiro, eds.), 2023,arXiv:2211.09902, DOI

    2023 arXiv

  2. [9]

    ’t Hooft and M.J.G

    G. ’t Hooft and M.J.G. Veltman,One loop divergencies in the theory of gravitation, Ann. Inst. H. Poincare A Phys. Theor.20 (1974) 69, http://www.numdam.org/item/AIHPA_1974__20_1_69_0/

    1974

  3. [10]

    Christensen and M.J

    S.M. Christensen and M.J. Duff,Quantizing Gravity with a Cosmological Constant, Nucl. Phys. B 170 (1980) 480

    1980

  4. [11]

    Goroff and A

    M.H. Goroff and A. Sagnotti,The Ultraviolet Behavior of Einstein Gravity, Nucl. Phys. B 266 (1986) 709

    1986

  5. [12]

    Schwarz,Superstring Theory, Phys

    J.H. Schwarz,Superstring Theory, Phys. Rept. 89 (1982) 223

    1982

  6. [13]

    Ashtekar,New Variables for Classical and Quantum Gravity, Phys

    A. Ashtekar,New Variables for Classical and Quantum Gravity, Phys. Rev. Lett.57 (1986) 2244

    1986

  7. [14]

    Rovelli and L

    C. Rovelli and L. Smolin,Discreteness of area and volume in quantum gravity, Nucl. Phys. B442 (1995) 593 [gr-qc/9411005]

    1995 arXiv

  8. [15]

    Rovelli,Loop quantum gravity, Living Rev

    C. Rovelli,Loop quantum gravity, Living Rev. Rel.1 (1998) 1 [gr-qc/9710008]

    1998 arXiv

  9. [16]

    Ashtekar and J

    A. Ashtekar and J. Lewandowski,Background independent quantum gravity: A Status report, Class. Quant. Grav. 21 (2004) R53 [gr-qc/0404018]

    2004 arXiv

  10. [17]

    Bombelli, J

    L. Bombelli, J. Lee, D. Meyer and R. Sorkin,Space-Time as a Causal Set, Phys. Rev. Lett.59 (1987) 521

    1987

  11. [18]

    Sorkin, Causal sets: Discrete gravity, inSchool on Quantum Gravity, 2003, gr-qc/0309009, DOI

    R.D. Sorkin, Causal sets: Discrete gravity, inSchool on Quantum Gravity, 2003, gr-qc/0309009, DOI

    2003 arXiv

  12. [19]

    Dowker,Causal sets and the deep structure of spacetime, in100 Years Of Relativity: space-time structure: Einstein and beyond(A

    F. Dowker,Causal sets and the deep structure of spacetime, in100 Years Of Relativity: space-time structure: Einstein and beyond(A. Ashtekar, ed.), 2005,gr-qc/0508109

    2005 arXiv

  13. [20]

    Surya,The causal set approach to quantum gravity, Living Rev

    S. Surya,The causal set approach to quantum gravity, Living Rev. Rel.22 (2019) 5 [arXiv:1903.11544]

    2019 arXiv

  14. [21]

    Ambjorn, J

    J. Ambjorn, J. Jurkiewicz and R. Loll,Spectral dimension of the universe, Phys. Rev. Lett.95 (2005) 171301 [hep-th/0505113]

    2005 arXiv

  15. [22]

    Ambjorn and R

    J. Ambjorn and R. Loll,Nonperturbative Lorentzian quantum gravity, causality and topology change, Nucl. Phys. B 536 (1998) 407 [hep-th/9805108]

    1998 arXiv

  16. [23]

    Ambjorn, A

    J. Ambjorn, A. Goerlich, J. Jurkiewicz and R. Loll,Nonperturbative Quantum Gravity, Phys. Rept. 519 (2012) 127 [arXiv:1203.3591]. 19

    2012 arXiv

  17. [24]

    Loll, Quantum Gravity from Causal Dynamical Triangulations: A Review, Class

    R. Loll, Quantum Gravity from Causal Dynamical Triangulations: A Review, Class. Quant. Grav.37 (2020) 013002 [arXiv:1905.08669]

    2020 arXiv

  18. [25]

    Niedermaier and M

    M. Niedermaier and M. Reuter,The Asymptotic Safety Scenario in Quantum Gravity, Living Rev. Rel.9 (2006) 5

    2006

  19. [26]

    Codello, R

    A. Codello, R. Percacci and C. Rahmede,Investigating the Ultraviolet Properties of Gravity with a Wilsonian Renormalization Group Equation, Annals Phys. 324 (2009) 414 [arXiv:0805.2909]

    2009 arXiv

  20. [27]

    Benedetti, P.F

    D. Benedetti, P.F. Machado and F. Saueressig,Asymptotic safety in higher-derivative gravity, Mod. Phys. Lett. A 24 (2009) 2233 [arXiv:0901.2984]

    2009 arXiv

  21. [28]

    Eichhorn,An asymptotically safe guide to quantum gravity and matter, Front

    A. Eichhorn,An asymptotically safe guide to quantum gravity and matter, Front. Astron. Space Sci.5 (2019) 47 [arXiv:1810.07615]

    2019 arXiv

  22. [29]

    Donoghue,A Critique of the Asymptotic Safety Program, Front

    J.F. Donoghue,A Critique of the Asymptotic Safety Program, Front. in Phys.8 (2020) 56 [arXiv:1911.02967]

    2020 arXiv

  23. [30]

    Stelle, Renormalization of Higher Derivative Quantum Gravity, Phys

    K.S. Stelle, Renormalization of Higher Derivative Quantum Gravity, Phys. Rev. D16 (1977) 953

    1977

  24. [31]

    Stelle, Classical Gravity with Higher Derivatives, Gen

    K.S. Stelle, Classical Gravity with Higher Derivatives, Gen. Rel. Grav.9 (1978) 353

    1978

  25. [32]

    Alvarez-Gaume, A

    L. Alvarez-Gaume, A. Kehagias, C. Kounnas, D. Lüst and A. Riotto,Aspects of Quadratic Gravity, Fortsch. Phys. 64 (2016) 176 [arXiv:1505.07657]

    2016 arXiv

  26. [33]

    Salvio, Quadratic Gravity, Front

    A. Salvio, Quadratic Gravity, Front. in Phys.6 (2018) 77 [arXiv:1804.09944]

    2018 arXiv

  27. [34]

    Fradkin and A.A

    E.S. Fradkin and A.A. Tseytlin,Renormalizable asymptotically free quantum theory of gravity, Nucl. Phys. B 201 (1982) 469

    1982

  28. [35]

    Avramidi and A.O

    I.G. Avramidi and A.O. Barvinsky,Asymptotic freedom in higher-derivative quantum gravity, Phys. Lett. B 159 (1985) 269

    1985

  29. [36]

    Codello and R

    A. Codello and R. Percacci,Fixed points of higher derivative gravity, Phys. Rev. Lett.97 (2006) 221301 [hep-th/0607128]

    2006 arXiv

  30. [37]

    Niedermaier,Gravitational Fixed Points from Perturbation Theory, Phys

    M.R. Niedermaier,Gravitational Fixed Points from Perturbation Theory, Phys. Rev. Lett.103 (2009) 101303

    2009

  31. [38]

    Niedermaier, Gravitational fixed points and asymptotic safety from perturbation theory, Nucl

    M. Niedermaier, Gravitational fixed points and asymptotic safety from perturbation theory, Nucl. Phys. B 833 (2010) 226

    2010

  32. [39]

    Ohta and R

    N. Ohta and R. Percacci,Higher Derivative Gravity and Asymptotic Safety in Diverse Dimensions, Class. Quant. Grav. 31 (2014) 015024 [arXiv:1308.3398]

    2014 arXiv

  33. [40]

    Holdom and J

    B. Holdom and J. Ren,QCD analogy for quantum gravity, Phys. Rev. D93 (2016) 124030 [arXiv:1512.05305]

    2016 arXiv

  34. [41]

    Holdom and J

    B. Holdom and J. Ren,Quadratic gravity: from weak to strong, Int. J. Mod. Phys. D25 (2016) 1643004 [arXiv:1605.05006]

    2016 arXiv

  35. [42]

    Buccio, J.F

    D. Buccio, J.F. Donoghue, G. Menezes and R. Percacci,Physical Running of Couplings in Quadratic Gravity, Phys. Rev. Lett.133 (2024) 021604 [arXiv:2403.02397]

    2024 arXiv

  36. [43]

    Buccio, L

    D. Buccio, L. Parente and O. Zanusso,Physical Running in Conformal Gravity and Higher Derivative Scalars, arXiv:2410.21475

    arXiv

  37. [44]

    Kawai and N

    H. Kawai and N. Ohta,An observation on the beta functions in quadratic gravity, Phys. Lett. B855 (2024) 138863 [arXiv:2405.05706]

    2024 arXiv

  38. [45]

    Hinterbichler and M

    K. Hinterbichler and M. Saravani,Stückelberg approach to quadratic curvature gravity and its decoupling limits, Phys. Rev. D93 (2016) 065006 [arXiv:1508.02401]

    2016 arXiv

  39. [46]

    Hawking and T

    S.W. Hawking and T. Hertog,Living with ghosts, Phys. Rev. D65 (2002) 103515 [hep-th/0107088]

    2002 arXiv

  40. [47]

    Mannheim and A

    P.D. Mannheim and A. Davidson,Dirac quantization of the Pais-Uhlenbeck fourth order oscillator, Phys. Rev. A 71 (2005) 042110 [hep-th/0408104]

    2005 arXiv

  41. [48]

    Mannheim,Solution to the ghost problem in fourth order derivative theories, Found

    P.D. Mannheim,Solution to the ghost problem in fourth order derivative theories, Found. Phys. 37 (2007) 532 [hep-th/0608154]. 20

    2007 arXiv

  42. [49]

    Bender and P.D

    C.M. Bender and P.D. Mannheim,No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model, Phys. Rev. Lett.100 (2008) 110402 [arXiv:0706.0207]

    2008 arXiv

  43. [50]

    Donoghue,Quartic propagators, negative norms and the physical spectrum, Phys

    J.F. Donoghue,Quartic propagators, negative norms and the physical spectrum, Phys. Rev. D96 (2017) 044007 [arXiv:1704.01533]

    2017 arXiv

  44. [51]

    Donoghue and G

    J.F. Donoghue and G. Menezes,Gauge Assisted Quadratic Gravity: A Framework for UV Complete Quantum Gravity, Phys. Rev. D97 (2018) 126005 [arXiv:1804.04980]

    2018 arXiv

  45. [52]

    Donoghue and G

    J.F. Donoghue and G. Menezes,Unitarity, stability and loops of unstable ghosts, Phys. Rev. D100 (2019) 105006 [arXiv:1908.02416]

    2019 arXiv

  46. [53]

    Donoghue and G

    J.F. Donoghue and G. Menezes,Arrow of Causality and Quantum Gravity, Phys. Rev. Lett.123 (2019) 171601 [arXiv:1908.04170]

    2019 arXiv

  47. [54]

    Donoghue and G

    J.F. Donoghue and G. Menezes,Quantum causality and the arrows of time and thermodynamics, Prog. Part. Nucl. Phys. 115 (2020) 103812 [arXiv:2003.09047]

    2020 arXiv

  48. [55]

    Donoghue and G

    J.F. Donoghue and G. Menezes,Ostrogradsky instability can be overcome by quantum physics, Phys. Rev. D 104 (2021) 045010 [arXiv:2105.00898]

    2021 arXiv

  49. [56]

    Donoghue and G

    J.F. Donoghue and G. Menezes,Causality and gravity, JHEP 11 (2021) 010 [arXiv:2106.05912]

    2021 arXiv

  50. [57]

    Donoghue and G

    J.F. Donoghue and G. Menezes,On quadratic gravity, Nuovo Cim. C 45 (2022) 26 [arXiv:2112.01974]

    2022 arXiv

  51. [58]

    Holdom, Running couplings and unitarity in a 4-derivative scalar field theory, Phys

    B. Holdom, Running couplings and unitarity in a 4-derivative scalar field theory, Phys. Lett. B843 (2023) 138023 [arXiv:2303.06723]

    2023 arXiv

  52. [59]

    Holdom, UV-complete 4-derivative scalar field theory, Nucl

    B. Holdom, UV-complete 4-derivative scalar field theory, Nucl. Phys. B 1000 (2024) 116472 [arXiv:2402.09223]

    2024 arXiv

  53. [60]

    Holdom, Making sense of ghosts, Nucl

    B. Holdom, Making sense of ghosts, Nucl. Phys. B 1008 (2024) 116696 [arXiv:2408.04089]

    2024 arXiv

  54. [61]

    Clunan and M

    T. Clunan and M. Sasaki,Tensor ghosts in the inflationary cosmology, Class. Quant. Grav.27 (2010) 165014 [arXiv:0907.3868]

    2010 arXiv

  55. [62]

    Deruelle, M

    N. Deruelle, M. Sasaki, Y. Sendouda and A. Youssef,Inflation with a Weyl term, or ghosts at work, JCAP 03 (2011) 040 [arXiv:1012.5202]

    2011 arXiv

  56. [63]

    Deruelle, M

    N. Deruelle, M. Sasaki, Y. Sendouda and A. Youssef,Lorentz-violating vs ghost gravitons: the example of Weyl gravity, JHEP 09 (2012) 009 [arXiv:1202.3131]

    2012 arXiv

  57. [64]

    Anselmi, E

    D. Anselmi, E. Bianchi and M. Piva,Predictions of quantum gravity in inflationary cosmology: effects of the Weyl-squared term, JHEP 07 (2020) 211 [arXiv:2005.10293]

    2020 arXiv

  58. [65]

    Anselmi, Perturbation spectra and renormalization-group techniques in double-field inflation and quantum gravity cosmology, JCAP 07 (2021) 037 [arXiv:2105.05864]

    D. Anselmi, Perturbation spectra and renormalization-group techniques in double-field inflation and quantum gravity cosmology, JCAP 07 (2021) 037 [arXiv:2105.05864]

    2021 arXiv

  59. [66]

    Anselmi, F

    D. Anselmi, F. Fruzza and M. Piva,Renormalization-group techniques for single-field inflation in primordial cosmology and quantum gravity, Class. Quant. Grav.38 (2021) 225011 [arXiv:2103.01653]

    2021 arXiv

  60. [67]

    De Felice, R

    A. De Felice, R. Kawaguchi, K. Mizui and S. Tsujikawa,Starobinsky inflation with a quadratic Weyl tensor, Phys. Rev. D108 (2023) 123524 [arXiv:2309.01835]

    2023 arXiv

  61. [68]

    Salvio, Inflationary Perturbations in No-Scale Theories, Eur

    A. Salvio, Inflationary Perturbations in No-Scale Theories, Eur. Phys. J. C77 (2017) 267 [arXiv:1703.08012]

    2017 arXiv

  62. [69]

    Salvio and A

    A. Salvio and A. Strumia,Agravity up to infinite energy, Eur. Phys. J. C78 (2018) 124 [arXiv:1705.03896]

    2018 arXiv

  63. [70]

    Salvio, Metastability in Quadratic Gravity, Phys

    A. Salvio, Metastability in Quadratic Gravity, Phys. Rev. D99 (2019) 103507 [arXiv:1902.09557]

    2019 arXiv

  64. [71]

    Salvio, A non-perturbative and background-independent formulation of quadratic gravity, JCAP 07 (2024) 092 [arXiv:2404.08034]

    A. Salvio, A non-perturbative and background-independent formulation of quadratic gravity, JCAP 07 (2024) 092 [arXiv:2404.08034]

    2024 arXiv

  65. [72]

    Held and H

    A. Held and H. Lim,Nonlinear evolution of quadratic gravity in 3+1 dimensions, Phys. Rev. D108 (2023) 104025 [arXiv:2306.04725]

    2023 arXiv

  66. [73]

    Lehners and K

    J.L. Lehners and K. Stelle,A Safe Beginning for the Universe?, Phys. Rev. D100 (2019) 083540 [arXiv:1909.01169]. 21

    2019 arXiv

  67. [74]

    Lehners and K.S

    J.L. Lehners and K.S. Stelle,Higher-order gravity, finite action, and a safe beginning for the universe, Eur. Phys. J. Plus 139 (2024) 380 [arXiv:2312.14048]

    2024 arXiv

  68. [75]

    Bonanno and S

    A. Bonanno and S. Silveravalle,Black holes at a crossroads: late-stage evaporation in quadratic gravity, in 17th Marcel Grossmann Meeting: On Recent Developments in Theoretical and Experimental General Relativity, Gravitation, and Relativistic Field Theories, 2024, arXiv:2409.16690

    2024 arXiv

  69. [76]

    Buoninfante, F

    L. Buoninfante, F. Di Filippo, I. Kolář and F. Saueressig,Dust collapse and horizon formation in quadratic gravity, JCAP 01 (2025) 114 [arXiv:2410.05941]

    2025

  70. [77]

    Belokurov and E.T

    V.V. Belokurov and E.T. Shavgulidze,Path integrals in quadratic gravity, JHEP 02 (2022) 112 [arXiv:2110.06041]

    2022 arXiv

  71. [78]

    Belokurov, V.V

    V.V. Belokurov, V.V. Chistiakov and E.T. Shavgulidze,Perturbation Theory for Path Integrals in Quadratic Gravity, arXiv:2410.19457

    arXiv

  72. [79]

    Edelstein, R

    J.D. Edelstein, R. Ghosh, A. Laddha and S. Sarkar,Causality constraints in Quadratic Gravity, JHEP 09 (2021) 150 [arXiv:2107.07424]

    2021 arXiv

  73. [80]

    Edelstein, R

    J.D. Edelstein, R. Ghosh, A. Laddha and S. Sarkar,Restoring Causality in Higher Curvature Gravity, arXiv:2409.16935

    arXiv

  74. [81]

    Berglund, L

    P. Berglund, L. Freidel, T. Hubsch, J. Kowalski-Glikman, R.G. Leigh, D. Mattingly et al.,Infrared Properties of Quantum Gravity: UV/IR Mixing, Gravitizing the Quantum – Theory and Observation, in Snowmass 2021, 2022, arXiv:2202.06890

    2021 arXiv

  75. [82]

    Hawking,Breakdown of Predictability in Gravitational Collapse, Phys

    S.W. Hawking,Breakdown of Predictability in Gravitational Collapse, Phys. Rev. D14 (1976) 2460

    1976

  76. [83]

    Mathur,The Information paradox: A Pedagogical introduction, Class

    S.D. Mathur,The Information paradox: A Pedagogical introduction, Class. Quant. Grav.26 (2009) 224001 [arXiv:0909.1038]

    2009 arXiv

  77. [84]

    Almheiri, D

    A. Almheiri, D. Marolf, J. Polchinski and J. Sully,Black Holes: Complementarity or Firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123]

    2013 arXiv

  78. [85]

    Cardoso, E

    V. Cardoso, E. Franzin and P. Pani,Is the gravitational-wave ringdown a probe of the event horizon?, Phys. Rev. Lett.116 (2016) 171101 [arXiv:1602.07309]

    2016 arXiv

  79. [86]

    Cardoso, S

    V. Cardoso, S. Hopper, C.F.B. Macedo, C. Palenzuela and P. Pani,Gravitational-wave signatures of exotic compact objects and of quantum corrections at the horizon scale, Phys. Rev. D94 (2016) 084031 [arXiv:1608.08637]

    2016 arXiv

  80. [87]

    Abedi, H

    J. Abedi, H. Dykaar and N. Afshordi,Echoes from the Abyss: Tentative evidence for Planck-scale structure at black hole horizons, Phys. Rev. D96 (2017) 082004 [arXiv:1612.00266]

    2017 arXiv

  81. [88]

    Cardoso and P

    V. Cardoso and P. Pani,Tests for the existence of black holes through gravitational wave echoes, Nature Astron. 1 (2017) 586 [arXiv:1709.01525]

    2017 arXiv

  82. [89]

    Wang and N

    Q. Wang and N. Afshordi,Black hole echology: The observer’s manual, Phys. Rev. D97 (2018) 124044 [arXiv:1803.02845]

    2018 arXiv

  83. [90]

    Abedi, N

    J. Abedi, N. Afshordi, N. Oshita and Q. Wang,Quantum Black Holes in the Sky, Universe 6 (2020) 43 [arXiv:2001.09553]

    2020 arXiv

  84. [91]

    H. Lu, A. Perkins, C.N. Pope and K.S. Stelle,Black Holes in Higher-Derivative Gravity, Phys. Rev. Lett. 114 (2015) 171601 [arXiv:1502.01028]

    2015 arXiv

  85. [92]

    H. Lü, A. Perkins, C.N. Pope and K.S. Stelle,Spherically Symmetric Solutions in Higher-Derivative Gravity, Phys. Rev. D92 (2015) 124019 [arXiv:1508.00010]

    2015 arXiv

  86. [93]

    H. Lü, A. Perkins, C.N. Pope and K.S. Stelle,Black holes in D = 4 higher-derivative gravity, Int. J. Mod. Phys. A 30 (2015) 1545016

    2015

  87. [94]

    Stelle, Abdus Salam and Quadratic Curvature Gravity: Classical Solutions, Int

    K.S. Stelle, Abdus Salam and Quadratic Curvature Gravity: Classical Solutions, Int. J. Mod. Phys. A32 (2017) 1741012

    2017

  88. [95]

    H. Lü, A. Perkins, C.N. Pope and K.S. Stelle,Lichnerowicz Modes and Black Hole Families in Ricci 22 Quadratic Gravity, Phys. Rev. D96 (2017) 046006 [arXiv:1704.05493]

    2017 arXiv

  89. [96]

    Holdom and J

    B. Holdom and J. Ren,Not quite a black hole, Phys. Rev. D95 (2017) 084034 [arXiv:1612.04889]

    2017 arXiv

  90. [97]

    Holdom, 2-2-holes simplified, Phys

    B. Holdom, 2-2-holes simplified, Phys. Lett. B830 (2022) 137142 [arXiv:2202.08442]

    2022 arXiv

  91. [98]

    Holdom, Not quite black holes at LIGO, Phys

    B. Holdom, Not quite black holes at LIGO, Phys. Rev. D101 (2020) 064063 [arXiv:1909.11801]

    2020 arXiv

  92. [99]

    Aydemir, B

    U. Aydemir, B. Holdom and J. Ren,Not quite black holes as dark matter, Phys. Rev. D102 (2020) 024058 [arXiv:2003.10682]

    2020 arXiv

  93. [100]

    Holdom, Damping of gravitational waves in 2-2-holes, Phys

    B. Holdom, Damping of gravitational waves in 2-2-holes, Phys. Lett. B813 (2021) 136023 [arXiv:2004.11285]

    2021 arXiv

  94. [101]

    Holdom, UV completion and not quite black holes, Nuovo Cim

    B. Holdom, UV completion and not quite black holes, Nuovo Cim. C 45 (2022) 36

    2022

  95. [102]

    Holdom, Towards rotating 2-2-holes, arXiv:2208.08461

    B. Holdom, Towards rotating 2-2-holes, arXiv:2208.08461

    arXiv

  96. [103]

    Borissova, A

    J.N. Borissova, A. Held and N. Afshordi,Scale-invariance at the core of quantum black holes, Class. Quant. Grav. 40 (2023) 075011 [arXiv:2203.02559]

    2023 arXiv

  97. [104]

    Kazanas and P.D

    D. Kazanas and P.D. Mannheim,General Structure of the Gravitational Equations of Motion in Conformal Weyl Gravity, Astrophys. J. Suppl.76 (1991) 431

    1991

  98. [105]

    Mannheim,Making the Case for Conformal Gravity, Found

    P.D. Mannheim,Making the Case for Conformal Gravity, Found. Phys. 42 (2012) 388 [arXiv:1101.2186]

    2012 arXiv

  99. [106]

    Poisson,A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics, Cambridge University Press (12, 2009), 10.1017/CBO9780511606601

    E. Poisson,A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics, Cambridge University Press (12, 2009), 10.1017/CBO9780511606601

    2009 doi

  100. [107]

    Hawking and J.C

    S.W. Hawking and J.C. Luttrell,Higher Derivatives in Quantum Cosmology. 1. The Isotropic Case, Nucl. Phys. B 247 (1984) 250

    1984

  101. [108]

    Dyer and K

    E. Dyer and K. Hinterbichler,Boundary Terms, Variational Principles and Higher Derivative Modified Gravity, Phys. Rev. D79 (2009) 024028 [arXiv:0809.4033]

    2009 arXiv

  102. [109]

    Deruelle, M

    N. Deruelle, M. Sasaki, Y. Sendouda and D. Yamauchi,Hamiltonian formulation of f(Riemann) theories of gravity, Prog. Theor. Phys.123 (2010) 169 [arXiv:0908.0679]

    2010 arXiv

  103. [110]

    Hohm and E

    O. Hohm and E. Tonni,A boundary stress tensor for higher-derivative gravity in AdS and Lifshitz backgrounds, JHEP 04 (2010) 093 [arXiv:1001.3598]

    2010 arXiv

  104. [111]

    Jonas, J.L

    C. Jonas, J.L. Lehners and J. Quintin,Cosmological consequences of a principle of finite amplitudes, Phys. Rev. D 103 (2021) 103525 [arXiv:2102.05550]

    2021 arXiv

  105. [112]

    Barrow,Finite Action Principle Revisited, Phys

    J.D. Barrow,Finite Action Principle Revisited, Phys. Rev. D101 (2020) 023527 [arXiv:1912.12926]

    2020 arXiv

  106. [113]

    Israel, Singular hypersurfaces and thin shells in general relativity, Nuovo Cim

    W. Israel, Singular hypersurfaces and thin shells in general relativity, Nuovo Cim. B 44S10 (1966) 1

    1966

  107. [114]

    Reina, J.M.M

    B. Reina, J.M.M. Senovilla and R. Vera,Junction conditions in quadratic gravity: thin shells and double layers, Class. Quant. Grav.33 (2016) 105008 [arXiv:1510.05515]

    2016 arXiv

  108. [115]

    Chu and H.S

    C.S. Chu and H.S. Tan,Generalized Darmois–Israel Junction Conditions, Universe 8 (2022) 250 [arXiv:2103.06314]

    2022 arXiv

  109. [116]

    Lehners, Review of the no-boundary wave function, Phys

    J.L. Lehners, Review of the no-boundary wave function, Phys. Rept. 1022 (2023) 1 [arXiv:2303.08802]

    2023 arXiv

  110. [117]

    Hartle and S.W

    J.B. Hartle and S.W. Hawking,Wave Function of the Universe, Phys. Rev. D28 (1983) 2960

    1983

  111. [118]

    Vilenkin, Creation of Universes from Nothing, Phys

    A. Vilenkin, Creation of Universes from Nothing, Phys. Lett. B117 (1982) 25

    1982

  112. [119]

    Vilenkin, The Birth of Inflationary Universes, Phys

    A. Vilenkin, The Birth of Inflationary Universes, Phys. Rev. D27 (1983) 2848

    1983

  113. [120]

    Vilenkin, Quantum Creation of Universes, Phys

    A. Vilenkin, Quantum Creation of Universes, Phys. Rev. D30 (1984) 509

    1984

  114. [121]

    Linde, Quantum Creation of the Inflationary Universe, Lett

    A.D. Linde, Quantum Creation of the Inflationary Universe, Lett. Nuovo Cim.39 (1984) 401

    1984

  115. [122]

    Feldbrugge, J.L

    J. Feldbrugge, J.L. Lehners and N. Turok,No smooth beginning for spacetime, Phys. Rev. Lett.119 (2017) 171301 [arXiv:1705.00192]

    2017 arXiv

  116. [123]

    Gibbons and S.W

    G.W. Gibbons and S.W. Hawking,Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D 15 (1977) 2752

    1977

  117. [125]

    Kontsevich and G

    M. Kontsevich and G. Segal,Wick Rotation and the Positivity of Energy in Quantum Field Theory, Quart. J. Math. Oxford Ser.72 (2021) 673 [arXiv:2105.10161]

    2021 arXiv

  118. [126]

    Louko and R.D

    J. Louko and R.D. Sorkin,Complex actions in two-dimensional topology change, Class. Quant. Grav.14 (1997) 179 [gr-qc/9511023]

    1997 arXiv

  119. [127]

    Witten, A note on complex spacetime metrics, inFrank Wilczek: 50 years of theoretical physics, 2022, arXiv:2111.06514

    E. Witten, A note on complex spacetime metrics, inFrank Wilczek: 50 years of theoretical physics, 2022, arXiv:2111.06514

    2022 arXiv

  120. [128]

    Lehners, Allowable complex metrics in minisuperspace quantum cosmology, Phys

    J.L. Lehners, Allowable complex metrics in minisuperspace quantum cosmology, Phys. Rev. D105 (2022) 026022 [arXiv:2111.07816]

    2022 arXiv

  121. [129]

    Jonas, J.L

    C. Jonas, J.L. Lehners and J. Quintin,Uses of complex metrics in cosmology, JHEP 08 (2022) 284 [arXiv:2205.15332]

    2022 arXiv

  122. [130]

    Lehners, Allowable complex scalars from Kaluza-Klein compactifications and metric rescalings, Phys

    J.L. Lehners, Allowable complex scalars from Kaluza-Klein compactifications and metric rescalings, Phys. Rev. D 107 (2023) 046004 [arXiv:2209.14669]

    2023 arXiv

  123. [131]

    Hertog, O

    T. Hertog, O. Janssen and J. Karlsson,Kontsevich-Segal Criterion in the No-Boundary State Constrains Inflation, Phys. Rev. Lett.131 (2023) 191501 [arXiv:2305.15440]

    2023 arXiv

  124. [132]

    Lehners and J

    J.L. Lehners and J. Quintin,A small Universe, Phys. Lett. B850 (2024) 138488 [arXiv:2309.03272]

    2024 arXiv

  125. [133]

    Maldacena, Comments on the no boundary wavefunction and slow roll inflation, arXiv:2403.10510

    J. Maldacena, Comments on the no boundary wavefunction and slow roll inflation, arXiv:2403.10510

    arXiv

  126. [134]

    Janssen, KSW criterion in large field models, Class

    O. Janssen, KSW criterion in large field models, Class. Quant. Grav.41 (2024) 227001 [arXiv:2406.08422]

    2024 arXiv

  127. [135]

    Chakravarty, A

    J. Chakravarty, A. Maloney, K. Namjou and S.F. Ross,A new observable for holographic cosmology, JHEP 10 (2024) 184 [arXiv:2407.04781]

    2024 arXiv

  128. [136]

    Hertog, O

    T. Hertog, O. Janssen and J. Karlsson,Kontsevich-Segal criterion in the no-boundary state constrains anisotropy, Phys. Rev. D111 (2025) 046008 [arXiv:2408.02652]

    2025 arXiv

  129. [137]

    Feldbrugge, J.L

    J. Feldbrugge, J.L. Lehners and N. Turok,Lorentzian Quantum Cosmology, Phys. Rev. D95 (2017) 103508 [arXiv:1703.02076]

    2017 arXiv

  130. [138]

    Y. Chen, V. Ivo and J. Maldacena,Comments on the double cone wormhole, JHEP 04 (2024) 124 [arXiv:2310.11617]

    2024 arXiv

  131. [139]

    I. Bars, P. Steinhardt and N. Turok,Local Conformal Symmetry in Physics and Cosmology, Phys. Rev. D89 (2014) 043515 [arXiv:1307.1848]

    2014 arXiv

  132. [140]

    Bars, P.J

    I. Bars, P.J. Steinhardt and N. Turok,Cyclic Cosmology, Conformal Symmetry and the Metastability of the Higgs, Phys. Lett. B726 (2013) 50 [arXiv:1307.8106]

    2013 arXiv

  133. [141]

    Boyle, K

    L. Boyle, K. Finn and N. Turok,CPT-Symmetric Universe, Phys. Rev. Lett.121 (2018) 251301 [arXiv:1803.08928]

    2018 arXiv

  134. [142]

    Boyle and N

    L. Boyle and N. Turok,Two-Sheeted Universe, Analyticity and the Arrow of Time, arXiv:2109.06204

    arXiv

  135. [143]

    Boyle and N

    L. Boyle and N. Turok,Cancelling the vacuum energy and Weyl anomaly in the standard model with dimension-zero scalar fields, arXiv:2110.06258

    arXiv

  136. [144]

    Turok and L

    N. Turok and L. Boyle,Gravitational entropy and the flatness, homogeneity and isotropy puzzles, Phys. Lett. B 849 (2024) 138443 [arXiv:2201.07279]

    2024 arXiv

  137. [145]

    Boyle and N

    L. Boyle and N. Turok,Thermodynamic solution of the homogeneity, isotropy and flatness puzzles (and a clue to the cosmological constant), Phys. Lett. B849 (2024) 138442 [arXiv:2210.01142]

    2024 arXiv

  138. [146]

    Turok and L

    N. Turok and L. Boyle,A Minimal Explanation of the Primordial Cosmological Perturbations, arXiv:2302.00344

    arXiv

  139. [147]

    Marolf and H

    D. Marolf and H. Maxfield,Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information, JHEP 08 (2020) 044 [arXiv:2002.08950]

    2020 arXiv

  140. [148]

    Van Raamsdonk,Comments on wormholes, ensembles, and cosmology, JHEP 12 (2021) 156 [arXiv:2008.02259]

    M. Van Raamsdonk,Comments on wormholes, ensembles, and cosmology, JHEP 12 (2021) 156 [arXiv:2008.02259]. 24

    2021 arXiv

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.