Cosmology of the Planck Era from a Renormalization Group for Quantum Gravity

A. Bonanno; M. Reuter

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Cosmology of the Planck Era from a Renormalization Group for Quantum Gravity

A. Bonanno, M. Reuter

High Energy Physics - Theory · Submitted 15 Jun 2001 · 28 references

Pith's verdict: A genuine, carefully derived attractor solution from the asymptotic-safety fixed point, with the qualitative scaling robust but the quantitative claims resting on an unpublished R² truncation.

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arXiv IDhep-th/0106133 (version 1)

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CitationA. Bonanno, M. Reuter. "Cosmology of the Planck Era from a Renormalization Group for Quantum Gravity." arXiv:hep-th/0106133 (2001). https://pith.science/paper/CKUS7EWA

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Editor's note

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Bonanno and Reuter take the asymptotic-safety fixed point seriously and push it into early-universe cosmology. The core result is worth your time: for a flat FRW background with cutoff k = ξ/t, the RG-improved equations have an attractor as t → 0 with a ∝ t^{4/(3+3w)}, G ∝ t², Λ ∝ t⁻², and ρ = ρ_Λ = ρ_crit/2. For w = 1/3 that gives a ∝ t, so no particle horizon, and Ω_tot = 1 comes out automatically. The step beyond Kalligas–Wesson–Everitt [21] is real: there G ∝ t² was postulated to close an underdetermined system; here it follows from the fixed point. The algebra in Sections III–IV is clean and I rechecked the w = 1/3 case without trouble. The scale-free argument is the nicest part — with w = 1/3, M is dimensionless and G_0, Λ_0 drop out at the fixed point, so t is the only scale and the exponents are fixed by canonical dimensions. That is a structural statement, not a fit. Where it is soft: the stress-test concern lands. At the fixed point R/k² ~ λ* ≈ 0.36, so the curvature expansion is not parametrically controlled; asymptotic freedom makes G small but leaves GΛ = g*λ* finite. The paper's defense is that an R² truncation confirms the picture, but that is [13], Lauscher and Reuter, in preparation. The same unpublished reference backs the 'g*λ* is universal' claim in Section IV.B. So both load-bearing robustness statements rest on work not yet in the literature. The qualitative scaling survives; the numerical coefficients may not. Second, ξ is fixed by consistency conditions (4.7, 4.21, 4.29), not predicted. The paper is candid that the system is 'seemingly overdetermined' and treats this as a virtue. Fair enough, but it means the predictions are partly consistency requirements on R(0) and ξ. Third, Section VI is the weakest: δρ ∝ δR with the log propagator from [13] gives n = 1, but the chain is heuristic and again leans on unpublished work. The horizon discussion is illustrative — the toy model (5.7) is fine, but the paper admits broadening only matters for τ < t_class. Credit where due: the Conclusions list assumptions (i)–(iii) explicitly, and the K = ±1 failures are reported rather than buried. Anyone working on asymptotic safety or on alternatives to inflation should read this. It deserves a serious referee.

Referee report

Significance

If correct, this is an economical proposal: no new fields, no additional cosmological epochs, only the quantization of the metric already present. The dimensional argument of Sec. IV.B — that for w = 1/3 the only dimensionful scale is the cosmological time, so the exponents of (4.27) are fixed by canonical dimensions — is elegant and makes the qualitative scaling robust against details of the truncation. The paper deserves explicit credit for checking the cutoff dependence in Appendix A and showing that the 1/t and 1/a identifications agree in the fixed-point regime for w = 1/3 (Eqs. A.9 versus 4.27 and 4.30); this is the strongest evidence in the manuscript that the radiation attractor is not an artifact of the cutoff choice. The authors are also candid about the truncation assumptions in the Conclusions, which is appropriate.

Major objections (4)

[Sec. V.A] The existence of the complete interpolating solution is asserted rather than demonstrated. The text states that a continuous interpolation between the fixed-point solution (4.22) and the perturbative solution (4.8) 'should exist, because we have considerable freedom in adjusting the functions R(0) and k(t, a(t), ···)'. But the interpolation must carry Ω_Λ from 1/2 (Eq. 4.24) to 0 (Eq. 4.10) while keeping Ω_tot = 1, and must connect the two different power laws for a(t) and ρ(t). No such solution is constructed, and the central 'no fine tuning' conclusion of Sec. V.B depends on it: the argument that the attractor 'automatically prepares' ρ_tot = ρ_crit for the classical era presupposes that a complete solution exists and is generic. The authors should either exhibit a monotonic interpolation or give a concrete argument that the transition in Ω_Λ is guaranteed and not itself fine-tuned.
[Sec. II and Sec. IV.B] The truncation is not under parametric control at the UV fixed point. At k → ∞ the dimensionful couplings are G = g*/k² and Λ = λ*k², so the dimensionless curvature is R/k² ~ λ* ≈ 0.36, which is O(1) rather than small; higher-curvature operators such as R² and R_μνR^μν therefore contribute at the same order as the Einstein–Hilbert terms that are retained. The asymptotic-freedom argument controls the gravitational coupling G, not the curvature expansion, and the combination GΛ = g*λ* ≈ 0.1 remains finite. The load-bearing support for truncation-independence is Ref. [13] (Lauscher and Reuter, in preparation), which is not yet available in the literature. A concrete test would be to compare g*, λ* and the coefficients of (4.22) between the Einstein–Hilbert and R² truncations. I note that the qualitative scaling survives by the dimensional argument of Sec. IV.B, so the horizon and flatness claims are robust; it is the numerical coefficients of the attractor that are at risk, and the manuscript should say so explicitly.
[Sec. IV.B] The statement that 'This product is universal (scheme-independent) in the sense that it does not depend on the function R(0) [13]' conflates two different notions. Independence of the cutoff shape R(0) is a statement within a fixed truncation; it is weaker than independence of the truncation itself (Einstein–Hilbert versus R², for instance). The subsequent claim that (4.22) is 'free from any numerical ambiguities' is therefore too strong as written. Either the claim should be softened to R(0)-independence, or a truncation-independence argument should be supplied.
[Sec. VI] The derivation of the n = 1 spectrum rests on two steps that are not established within the manuscript. First, the fixed-point graviton propagator ∝ 1/p⁴, and hence the anomalous dimension η = −2, is taken from Ref. [13], which is in preparation. Second, the identification 8πG δρ = −δG₀₀ uses the classical Einstein equation inside the regime where G is running and the curvature is Planckian. The equal-time curvature correlator (6.3) is then converted directly into a primordial spectrum without addressing horizon crossing or the gauge issue, which the authors acknowledge at the end of the section. A useful addition would be a statement of how n shifts if the anomalous dimension changes in a wider truncation, so that the reader can judge how robust the Harrison–Zeldovich prediction is.

Minor objections (7)

[Sec. II, below Eq. (2.12)] The restriction to Λ_0 = 0 is acknowledged as a way of avoiding the infrared singularity of the Einstein–Hilbert trajectory, but it means that the flatness discussion of Sec. V.B is tied to that special trajectory. This should be stated once more in Sec. V.B where the conclusion is drawn.
[Sec. IV.A, Eq. (4.11) and Sec. IV.B, Eq. (4.28)] The K = ±1 cases require w = −1/3 in the perturbative regime and w = +1/3 in the fixed-point regime, so no constant-w interpolation exists. The authors say this is likely an artifact of the approximation, which is fair, but the abstract's 'might provide a resolution to the horizon and flatness problem' should be read with that caveat in mind.
[Sec. III, Eq. (3.20)] The consistency condition assumes that T_μν is separately conserved, Eq. (3.16). This is an assumption rather than a consequence of the improved equations, and it would help to restate it at the point where (3.20) is used to close the system.
[Figs. 1 and 2] Both figures are qualitative, and the captions refer to solid and dashed lines that are difficult to distinguish in the reproduction. Labelling the curves directly in the figure would make the comparison between R(t, τ) and R_class(t, τ) easier to follow.
[Sec. V.C, Eq. (5.7)] The interpolating toy model a(t) = At/(1 + √(t/t_class)) is ad hoc. It would be worth stating explicitly that the horizon conclusion depends only on the t → 0 exponent and not on the details of the interpolation.
[Sec. VII] There are a few typographical slips, for example 'the the Universe' in the Conclusion, and the spelling of 'pseudospherical' should be checked throughout.
[References] Ref. [13] is cited three times (Secs. II, IV.B and VI) and is listed as 'in preparation'. Since it carries a substantial part of the truncation and propagator arguments, the editor may wish to note its status.

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The paper

The paper claims

Running Newton's constant and running cosmological constant may replace the big bang singularity with an attractor that leaves the early universe flat, horizon-free and scale-free.

The reading

The paper asks whether the first few Planck times of the universe can be described by Einstein's equations with the constants promoted to scale-dependent quantities, $G(k)$ and $Λ(k)$, taken from a renormalization-group flow for gravity. Identifying the cutoff with cosmological time, $k = ξ/t$, the authors find that the improved equations admit a consistent solution near $t = 0$ in which $G ∝ t^2$, $Λ ∝ 1/t^2$ and the scale factor grows as $t^{4/(3+3w)}$, with the matter density and vacuum energy each equal to half the critical density. Because this solution is an attractor tied to an ultraviolet fixed point, it does not need finely tuned initial data: any solution with the right equation of state is funnelled into it as $t → 0$. For a radiation-like Planck era ($w = 1/3$) the scale factor grows linearly, so the spacetime has no particle horizon, and the light cones of the Planck epoch are wide enough to put regions of the last-scattering surface in causal contact. The authors also argue that metric fluctuations at the fixed point give a curvature two-point function falling as $1/d^4$, which Fourier transforms to a Harrison–Zeldovich spectrum with spectral index $n = 1$.

What carries the argument

The machinery is the renormalization-group improvement of the cosmological equations: replace the constants in Einstein's equations by $G(k)$ and $Λ(k)$ taken from the flow equation of the effective average action for gravity in the Einstein–Hilbert truncation, then close the system with the cutoff identification $k = ξ/t$, the conservation law $D_νT^{μν} = 0$, an equation of state $p = wρ$, and a new consistency condition $dΛ/dt + 8πρ dG/dt = 0$ that follows from the Bianchi identity when $G$ and $Λ$ depend on time. That consistency condition is what makes the system predictive: it fixes $ρ$ as $-dΛ/dt$ divided by $8π dG/dt$, then fixes $a$ from $ρ a^{3+3w} = $ const, and finally the Friedmann equation becomes an overdetermined check that selects allowed cutoffs and equations of state. The ultraviolet fixed point $(g_*, λ_*)$ of the flow, with $g = k^2G$ and $λ = Λ/k^2$, supplies the power laws $G ∝ t^2$ and $Λ ∝ 1/t^2$ that drive the attractor.

Extended reading notes

Core claim

The central claim is that the renormalization-group improved Friedmann–Robertson–Walker equations, with $G$ and $Λ$ running according to the flow of the effective average action and with the cutoff set by $k = ξ/t$, possess a consistent attractor solution immediately after the initial singularity. In the fixed-point regime the solution is $a(t) ∝ t^{4/(3+3w)}$, $ρ(t) ∝ t^{-4}$, $G(t) = (3/8)(1+w)^2 (g_*λ_*) t^2$ and $Λ(t) = (8/3)(1+w)^2 t^{-2}$, with $ρ = ρ_Λ = ρ_{crit}/2$ so that $Ω_M = Ω_Λ = 1/2$ and $Ω_{tot} = 1$. The consistency of the Friedmann equation fixes the otherwise unknown cutoff constant $ξ$ in terms of the fixed-point values, $ξ^2 = 8/[3(1+w)^2 λ_*]$; the authors stress that after this elimination the solution depends on the renormalization-group data only through the product $g_*λ_*$, which they describe as scheme independent. Because the fixed point is ultraviolet attractive, the solution is universal: all trajectories with arbitrary infrared values $G_0$, $Λ_0$ and integration constant $M$ look like it as $t → 0$, so the flatness condition $ρ_{tot} = ρ_{crit}$ is imposed automatically rather than by fine tuning. For $w = 1/3$ the expansion is linear, $a ∝ t$, which removes the particle horizon, and the authors exhibit an interpolating toy scale factor to show how the backward light cones of two separated points overlap at sufficiently early times. The same fixed-point propagator, falling as $1/p^4$, yields $⟨δR(x)δR(y)⟩ ∝ 1/d(x,y)^4$ and hence a scale-free spectrum of density fluctuations. The authors are explicit that for spatially curved geometries they find a fixed-point solution only for $w = +1/3$ and a perturbative solution only for $w = -1/3$, so no interpolating solution with constant $w$ exists in that case, and they say it would be premature to read this as a prediction that the universe is flat.

Load-bearing premise

The load-bearing premise is that substituting $G(t)$ and $Λ(t)$ into the classical Einstein equations, with no extra higher-curvature or nonlocal terms, still captures the leading quantum gravitational effects all the way down to $t = 0$.

Editorial extensions

If this is right

For a radiation-like Planck era the scale factor grows linearly with time, so the improved spacetime has no particle horizon and the horizon problem of standard cosmology is removed without invoking an inflationary epoch.
For a spatially flat universe the total density equals the critical density automatically at all $t > 0$, so the flatness problem becomes an artifact of imposing initial conditions at a time when the classical equations were never valid.
The early universe is scale free: with $w = 1/3$ the only dimensionful quantity available is $t$ itself, so the exponents of $t$ in $a$, $ρ$, $G$ and $Λ$ are fixed by their mass dimensions rather than by parameters.
Metric fluctuations at the fixed point produce a curvature correlator falling as $1/d^4$, giving a Harrison–Zeldovich spectrum with $n = 1$ as the initial condition for standard cosmological perturbation theory.
For $t$ well above the Planck time the improved solutions reduce to the classical radiation-dominated Friedmann–Robertson–Walker behaviour, so the quantum era hands over a conventional cosmology.

Reading between the lines

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

The same cutoff constant $ξ$ must serve both regimes: the perturbative fit demands $ξ^2 = 2ω/[3ν(1+w)^2]$ while the fixed-point fit demands $ξ^2 = 8/[3(1+w)^2λ_*]$. Together these imply $λ_* = 4ν/ω$, an internal relation between the ultraviolet fixed point and the infrared coefficients that the paper does not check numerically; if it fails, the two ends of the Planck era cannot be joined by a sing
Because the attractor depends on the renormalization-group data only through $g_*λ_*$, any independent determination of that product, for example from a truncation extended to include $R^2$ or higher-curvature terms, would sharpen or break the scenario without needing to reproduce the full flow.
The removal of the horizon is confined to $t \lesssim t_{Pl}$, which means any causal mechanism explaining microwave background isotropy would have to operate within the Planck era itself; this makes the proposal testable in principle against any observable that survives from that epoch.
The linear expansion $a ∝ t$ changes the relation between comoving and physical scales at early times, so the matching of the $n = 1$ spectrum onto standard perturbation evolution should be checked for modes that cross the Planck length during the transition.

Original abstract

Homogeneous and isotropic cosmologies of the Planck era before the classical Einstein equations become valid are studied taking quantum gravitational effects into account. The cosmological evolution equations are renormalization group improved by including the scale dependence of Newton's constant and of the cosmological constant as it is given by the flow equation of the effective average action for gravity. It is argued that the Planck regime can be treated reliably in this framework because gravity is found to become asymptotically free at short distances. The epoch immediately after the initial singularity of the Universe is described by an attractor solution of the improved equations which is a direct manifestation of an ultraviolet attractive renormalization group fixed point. It is shown that quantum gravity effects in the very early Universe might provide a resolution to the horizon and flatness problem of standard cosmology, and could generate a scale-free spectrum of primordial density fluctuations.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.30 · mentions code or data availability 0.01.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Homogeneous and isotropic cosmologies of the Planck era before the classical Einstein equations become valid are studied taking quantum gravitational effects into account. The cosmological evolution equations are renormalization group improved by including the scale dependence of Newton's constant and of the cosmological constant as it is given by the flow equation of the effective average action for gravity. It is argued that the Planck regime can be treated reliably in this framework because gravity is found to become asymptotically free at short distances. The epoch immediately after the initial singularity of the Universe is described by an attractor solution of the improved equations which is a direct manifestation of an ultraviolet attractive renormalization group fixed point. It is shown that quantum gravity effects in the very early Universe might provide a resolution to the horizon and flatness problem of standard cosmology, and could generate a scale-free spectrum of primordial density fluctuations.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Homogeneous and isotropic cosmologies of the Planck era before the classical Einstein equations become valid are studied taking quantum gravitational effects into account.	contribution 0.83	0.75	0.05	asserted 0.92
s1	The cosmological evolution equations are renormalization group improved by including the scale dependence of Newton's constant and of the cosmological constant as it is given by the flow equation of the effective average action for gravity.	method 0.97	0.85	0.06	asserted 0.99
s2	It is argued that the Planck regime can be treated reliably in this framework because gravity is found to become asymptotically free at short distances.	interpretation 0.80	0.78	0.13	asserted 0.90
s3	The epoch immediately after the initial singularity of the Universe is described by an attractor solution of the improved equations which is a direct manifestation of an ultraviolet attractive renormalization group fixed point.	result 0.91	0.86	0.23	asserted 1.00
s4	It is shown that quantum gravity effects in the very early Universe might provide a resolution to the horizon and flatness problem of standard cosmology, and could generate a scale-free spectrum of primordial density fluctuations.	interpretation 0.53	0.86	0.64	hedged possibility 0.90

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.89.

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sources read

arXiv listing abstract v1

not examined

full text
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references and citing sentences
relations to other papers

levels run

P abstract

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** FIG. 1. Graphical representation of the proper distance

Figures reproduced from arXiv:hep-th/0106133 by the authors.

References

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hep-th 2010-03 conditional novelty 6.0 of 10

A bimetric truncation of the gravitational average action, driven by scalar matter in the large-N limit, still possesses a non-Gaussian fixed point, so the enlargement of theory space does not by itself destroy asympt...
Bimetric Truncations for Quantum Einstein Gravity and Asymptotic Safety
gr-qc 2009-07 conditional novelty 6.0 of 10

A first bimetric truncation of the gravitational average action, in a conformally reduced toy model, retains a non-Gaussian UV fixed point and moves the k^4 vacuum-energy running into the background cosmological constant.
Cosmology of the Lifshitz universe
hep-th 2009-04 conditional novelty 6.0 of 10

A Lifshitz scalar coupled to Horava gravity produces bouncing vacuum cosmologies but, under detailed balance, an inflationary spectrum that is exponentially scale-dependent and observationally unviable.
Background Independence and Asymptotic Safety in Conformally Reduced Gravity
hep-th 2008-01 conditional novelty 6.0 of 10

Quantizing only the conformal factor of the metric, with the coarse-graining scale set by that factor itself, reproduces the non-Gaussian fixed point required for asymptotic safety.
On the renormalization group flow of f(R)-gravity
hep-th 2007-12 conditional novelty 6.0 of 10

Including ln(R) and R^{-n} terms in the gravitational effective action removes the infrared singularity at lambda = 1/2 and, for the ln(R) case, produces an infrared fixed point that drives the cosmological constant to zero.
Fractal Spacetime Structure in Asymptotically Safe Gravity
hep-th 2005-08 conditional novelty 6.0 of 10

Asymptotically safe quantum gravity predicts a spectral dimension of 2 at sub-Planckian scales and 4 at macroscopic scales, matching causal dynamical triangulation simulations.
Renormalization Group Flow of Quantum Gravity in the Einstein-Hilbert Truncation
hep-th 2001-10 accept novelty 6.0 of 10

With a sharp cutoff, the Einstein-Hilbert truncation of quantum gravity yields closed-form beta functions, a complete four-dimensional phase portrait, and a UV-attractive non-Gaussian fixed point at (lambda*, g*) = (0...
Ultraviolet Fixed Point and Generalized Flow Equation of Quantum Gravity
hep-th 2001-08 conditional novelty 6.0 of 10

A new transverse-traceless exact renormalization group equation confirms that the non-Gaussian fixed point of the Einstein-Hilbert truncation exists for all admissible cutoffs, with the product g*λ* scheme-independent...
From thermogravity to thermocosmology with a running non-conservation scale
gr-qc 2026-10 conditional novelty 5.0 of 10

Running thermocosmology, with a Hubble-dependent non-conservation scale acting on cold dark matter, reproduces late-time cosmological data at ΛCDM-comparable fit quality, with the simpler standard model preferred by t...
Aspects of asymptotic safety for quantum gravity
gr-qc 2018-10 conditional novelty 5.0 of 10

Removing regulator-induced curvature poles from the f(R) renormalisation group flow leaves the asymptotic-safety fixed point intact and turns a pair of complex de Sitter solutions into two real ones.
Inflation in an effective gravitational model & asymptotic safety
gr-qc 2018-06 conditional novelty 5.0 of 10

Adding a resummed logarithmic correction to Starobinsky's R-squared inflation raises the predicted tensor-to-scalar ratio from about 0.003 to as much as 0.01, while the scalar spectral index stays within current bounds.
The R^2 phase-diagram of QEG and its spectral dimension
hep-th 2012-06 conditional novelty 5.0 of 10

Including an R² term in the gravitational average action preserves the multi-plateau spectral dimension of asymptotically safe quantum gravity, and reveals that some intermediate plateaus are caused by singular loci i...
Exact renormalization group with optimal scale and its application to cosmology
gr-qc 2010-10 conditional novelty 5.0 of 10

Requiring the renormalization-group cutoff to respect diffeomorphism invariance and stress-energy conservation yields a cosmology that matches observation only if the ultraviolet fixed-point product is about 10^-122, ...
Quantum Gravity Effects in the Kerr Spacetime
hep-th 2010-09 conditional novelty 5.0 of 10

Renormalization-group improving the Kerr metric with a running Newton constant deforms but does not add horizons, and forces the black hole temperature to depart from surface gravity over two pi.
Inflationary solutions in asymptotically safe f(R) theories
gr-qc 2010-06 conditional novelty 5.0 of 10

Polynomial f(R) truncations of asymptotically safe gravity admit de Sitter and power-law inflationary solutions, with the power-law exponent exceeding one only when the cutoff-to-Hubble ratio lies roughly between 2.7 and 3.9.
Running Gauge Coupling in Asymptotically Safe Quantum Gravity
hep-th 2009-10 conditional novelty 5.0 of 10

Virtual gravitons add a correction to the Yang-Mills beta function with the same sign as the gauge boson term, driving the gauge coupling to zero at the Quantum Einstein Gravity fixed point.
Distinguishing scale-dependent Planck stars from renormalization group improved Schwarzschild black holes by Gravitational waves
gr-qc 2025-06 conditional novelty 4.0 of 10

Gravitational-wave strains from analytic-kludge EMRI models can distinguish scale-dependent Planck stars from renormalization-group improved Schwarzschild black holes, at least for the chosen orbit parameters.
Asymptotically safe inflation from quadratic gravity
gr-qc 2015-07 conditional novelty 4.0 of 10

An asymptotically safe quadratic-gravity inflation model with an R^{3/2}-type operator reproduces Planck 2015 values of the spectral index and tensor-to-scalar ratio for a narrow hand-picked range of couplings.
Horava-Lifshitz Dark Energy
hep-th 2009-05 conditional novelty 4.0 of 10

Grouping a second scalar field with the Horava-Lifshitz dark radiation and cosmological constant terms yields an effective dark energy that is phantom in a non-flat universe and can cross minus one.
Running Vacuum in the expanding Universe: a unified QFT paradigm for Inflation and Dark Energy
gr-qc 2026-06 unverdicted novelty 3.0 of 10

The running vacuum model derives dynamical vacuum energy from QFT in curved spacetime, using H^4 terms for inflation and H^2 terms for dark energy while G evolves logarithmically.
The inflationary mechanism in Asymptotically Safe Gravity
gr-qc 2019-08 conditional novelty 3.0 of 10

Departure from the asymptotically safe gravity fixed point generates a plateau inflaton potential with a nearly scale-invariant spectrum, and the Starobinsky model is recovered for critical exponents θ1=θ2=2.
Dimension and Dimensional Reduction in Quantum Gravity
gr-qc 2017-05 accept novelty 3.0 of 10

Multiple quantum gravity programs independently suggest that spacetime's effective dimension falls toward two at the Planck scale, though no approach yet proves it.
Black holes within Asymptotic Safety
hep-th 2014-01 conditional novelty 3.0 of 10

Applying the same scale-dependent-coupling improvement to empty space produces a conical singularity, indicating that the singularity in improved black hole models is a scheme artifact rather than a black hole prediction.
Black Holes in Asymptotically Safe Gravity
gr-qc 2023-02 accept novelty 2.0 of 10

The chapter surveys asymptotically safe black-hole models and argues that requiring a local effective action sharply limits power-law corrections to Schwarzschild at large radii.
Renormalisation group and the Planck scale
hep-th 2011-02 accept novelty 2.0 of 10

A review argues that functional renormalisation group calculations give growing evidence for a non-trivial ultraviolet fixed point in four-dimensional quantum gravity, the asymptotic safety scenario.

How later papers used it

57 later papers cite it

Evidence: substantial. 48 of the citing papers share no author with it, and 7 of those carry a confident label from Pith's citation classifier.

Pith read 18 of the 113 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 later paper by other authors is listed below: 1 cited it as support.

Cites it as support 1 of 4 papers with this label

This conclusion is in line with the arguments presented in [ref] .

Renormalization group improved cosmology in the presence of a stiff matter era (2024) · Stiff matter, radiation, and dark matter · 0.95

How the literature uses it

49 arXiv papers cite this in 103 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 65 sentences without a confident label

Contests it 1 paper

We conclude that the consistency approach of [ref] the vanishing entropy production rate is an artifact of the requirement that $T_μν$ should be conserved independently of the scale (time)-dependence of $G$ and $Λ$.

Cosmology with modified continuity equation in asymptotically safe gravity · Summary and Conclusions · contest 0.82

Uses its method or tool 2 papers

Following [ref] we will take $R^(0)(z)$ to be of the form

Cosmology of Bianchi type-I metric using renormalization group approach for quantum gravity · Flow of $G$ and $Λ$ · 0.96
Following [ref] , we will take $R^(0)(z)$ to be of the form

Cosmology with modified continuity equation in asymptotically safe gravity · Flow of $G$ and $Λ$ · 0.97

Uses its data or values 1 paper

One can use the values of $g_*$ and $λ_*$ as $g_*≃0.27$, and $λ_*≃0.36$ [ref] .

Renormalization group improved cosmology in the presence of a stiff matter era · Stiff matter, radiation, and dark matter era after the Planck time · 1.00

Compares with it 2 papers

The key difference between this model [ref] and the one analyzed in the previous subsections [ref] lies in the presence of an additional term, $Δ=-η_NH^2$, in the modified Friedmann equation.

From renormalization group flows to cosmology · Cosmological singularities and bouncing cosmologies in ASG · 0.98
This is the same value of $ξ$ that one gets from the consistency approach [ref] in which the energy momentum tensor is taken to be covariantly conserved, independent of the scale(time)-dependence of $G$ and $Λ$.

Cosmology with modified continuity equation in asymptotically safe gravity · Cosmological expansion and entropy generation · 0.97

Cites it as support 2 papers

The prospect that Asymptotic Safety could be capable of describing gravitational force at all length scales makes the theory quite attractive for cosmological model building [ref] .

Asymptotically safe cosmology - a status report · Asymptotic Safety: a brief introduction · 0.97
Moreover, the existence of a regime where gravity is approximately scale-invariant could be relevant in cosmology to provide a natural explanation for the nearly-scale-invariant distribution of temperature anisotropies in the Cosmic Microwave Background (CMB) radiation [ref] (see also [ref] for a recent review).

From renormalization group flows to cosmology · Gravitational antiscreening: a historical perspective · 0.97

Cites it as background 27 papers

As our main focus is to investigate a stiff-matter dominated cosmology where renormalization group flows plays an important role, we shall start by briefly discussing the renormalization group approach to quantum gravity and cosmology developed in [ref] .

Renormalization group improved cosmology in the presence of a stiff matter era · Renormalization group improved cosmology and the Friedmann equations · 0.97
That is, whether running $G$ and $Λ$ should bring additional contributions to the stress energy tensor as shown in the last term of Eq. ([ref]) [ref] or not [ref] .

Asymptotically safe gravity as a scalar-tensor theory and its cosmological implications · Cosmological implications of running gravitational constant · 0.84
A detailed discussion of this mechanism is beyond the scope of the present review; the reader it referred to [ref] .

Astrophysical implications of the Asymptotic Safety Scenario in Quantum Gravity · Primordial density fluctuations · 0.96

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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