Pith. sign in

REVIEW 2 major objections 5 minor 96 references

A quantum-corrected wormhole in a dark matter halo can match the Galactic center shadow size.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-04 08:53 UTC pith:XYP6MVSZ

load-bearing objection Solid wormhole construction with an inverted shadow formula that breaks the EHT claim as stated. the 2 major comments →

arxiv 2510.18264 v1 pith:XYP6MVSZ submitted 2025-10-21 gr-qc quant-ph

Quantum improved wormholes in the Dekel-Zhao dark matter halo

Jonathan A. Rebou\c{c}as , Celio R. Muniz , Francisco Bento Lustosa , Edson Otoniel This is my paper
classification gr-qc quant-ph MSC 83C1583C57 PACS 04.50.Kd04.70.Bw
keywords asymptotically safe gravitytraversable wormholesDekel-Zhao dark matter profilescale-dependent gravitational couplingquantum-improved Einstein equationsnull energy conditionshadow radiusenergy conditions
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper argues that incorporating the scale-dependent gravitational coupling of asymptotically safe gravity directly into Einstein's equations — with the identification k = ξ/r — produces traversable wormhole solutions when the source is a Dekel–Zhao dark matter halo. The wormhole satisfies flare-out and asymptotic flatness only for restricted halo parameters, and the null energy condition is necessarily violated at the throat, so exotic matter remains required. The paper claims the ASG corrections act as a repulsive quantum force that stabilizes the throat against the destabilizing pull of dark matter. Phenomenologically, the predicted shadow radius grows almost linearly with ξ and falls inside the observed Sgr A* shadow window for ξ/M ≈ 0.8–0.9, which would make ASG-corrected wormholes observable signatures of quantum gravity.

Core claim

The central discovery is that a scale-dependent Newton constant G(r) = G0 r²/(r²+ξ²), substituted into G_μν = 8πG(r)T_μν and sourced by the Dekel–Zhao density profile, yields a Morris–Thorne wormhole whose shape function is expressed through hypergeometric functions. For the NFW-like case (a = 1), the throat geometry, the violation of the radial NEC, the sound-speed stability window, and the modified TOV balance with an extra quantum force F_Q = −G′(r)P_r are all computed in closed form. The shadow of the wormhole is purely geometric: the photon sphere coincides with the throat for the chosen redshift function, and when the ASG scale is tied to the Ricci curvature at the throat, the shadow r

What carries the argument

The machinery is the 'quantum improvement' of Einstein's equations: the ASG running coupling G(k) = G0/(1 + ωG0k²) is converted to a position-dependent coupling G(r) = G0 r²/(r²+ξ²) via the cutoff identification k = ξ/r, then inserted directly into the field equations. Consistency requires the modified conservation law ∇_μ(G T^μ_ν) = 0, which produces an extra force term F_Q = −G′(r)P_r in the TOV balance. The other central object is the Morris–Thorne shape function built from integrating G(r)ρ(r)r², with the Dekel–Zhao density profile; the chosen redshift function Φ = 2 ln(r/(r+r0)) makes the photon sphere coincide with the throat, so the shadow radius is determined by the throat geometry a

Load-bearing premise

The entire construction rests on treating k = ξ/r as a faithful translation of the renormalization-group scale into a spacetime position and on substituting the resulting G(r) back into Einstein's equations; if that improvement step is not physically valid, the wormhole solutions are mathematical exercises and the shadow comparison loses its quantum-gravity meaning.

What would settle it

A future high-precision measurement of the Galactic-center shadow that excludes Rsh/M between 4.55 and 5.22 would rule out the claimed ξ/M ≈ 0.8–0.92 window; alternatively, recomputing the shadow without the assumption r_ph = r0 (e.g., with a different redshift function) and finding no ξ that matches the observed bounds would falsify the central phenomenological claim.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • If correct, ASG corrections do not remove the need for exotic matter; radial NEC is always violated at the throat, and more strongly for larger ξ.
  • Dark matter concentration (ρ0, rc, a) suppresses wormhole formation and stability; the NFW-like profile a = 1 is the most favorable, and the ASG parameter ξ counteracts this.
  • The wormhole's shadow is indistinguishable in size from a black hole shadow for ξ/M ≈ 0.8–0.92, so shadow observations alone cannot discriminate; lensing or gravitational-wave signatures would be needed.
  • The near-linear relation between ξ and Rsh/M means the observed shadow bounds translate into a numerical constraint on the quantum scale, not just a qualitative statement.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Because the improvement prescription is non-unique, the same G(k) could be inserted at the action level or into known solutions; comparing those outcomes against this direct insertion would test whether the ξ window is an artifact of the scheme.
  • The fit uses only a static, spherical shadow; a rotating wormhole model would shift the shadow and likely change the ξ window, so the ξ/M ≈ 0.8–0.9 range should be re-derived for spinning geometries before taking it as a firm prediction.
  • The paper's force-balance picture suggests a testable extension: calculating the quasinormal-mode spectrum or tidal Love numbers of these wormholes could yield observable differences from black holes with the same shadow.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. This paper constructs traversable wormhole solutions in the asymptotically safe gravity (ASG) framework, using the scale-dependent Newton constant G(r)=G0 r^2/(r^2+xi^2) in the modified Einstein equations, with a Dekel-Zhao dark matter halo as the matter source. The authors derive an analytic shape function from the t-t field equation, adopt the redshift function Phi(r)=2 ln(r/(r+r0)), and check the flare-out and asymptotic-flatness conditions for a range of halo parameters. They then analyze the null, weak, strong, and dominant energy conditions (with NEC violated at the throat), the adiabatic sound speed, and a modified TOV equation containing a quantum force F_Q=-G'(r)P_r. Finally, they compute the wormhole shadow radius and claim that for xi/M approximately 0.8-0.9 the result falls inside the EHT bounds for Sgr A*.

Significance. If the construction is valid, the paper provides a concrete example of quantum-improved wormhole supported by a realistic dark matter profile, and the shadow analysis offers a potential observational discriminator. The analytic nature of the shape function and the systematic parameter exploration are strengths. However, the central observational claim rests on the shadow calculation, which contains an apparent inversion of the angular-radius formula, and on an ad hoc identification of the ASG scale with throat curvature. These issues must be resolved before the EHT comparison can be assessed.

major comments (2)
  1. [§V, Eqs. (32)–(34)] Eq. (33) is inverted. For a static spherically symmetric metric, the angular radius of the shadow is sin α_sh = γ(R_o)/γ(r_ph), i.e. R_sh = b_cr = r_ph e^{-Φ(r_ph)} for a distant observer, not γ(r_ph)/γ(R_o). With the chosen Φ(r), r_ph = r0, so the correct shadow radius is R_sh = 4 r0. Using Eq. (33) as written gives R_sh ≈ R_o^2/(4 r0), which diverges as R_o → ∞. Therefore Fig. 12 and the claimed EHT overlap cannot be derived from the displayed formula. Please correct Eq. (33) and recompute, or clarify if the reciprocal relation was used in the numerics.
  2. [§V, Eqs. (37)–(38) and Fig. 12] The shadow comparison relies on two additional, unstated choices: the identification ξ ∼ 1/√R(r0) in Eq. (37) (with Eq. (38)) and the mass M used to normalize Fig. 12. The paper does not define M (e.g., ADM mass from S(r) at infinity) nor derive Eq. (37) from the ASG running. Since the overlap with the EHT band is obtained by varying ξ/M, it is a fit to a free parameter plus an ad hoc scale identification rather than a prediction. Please derive or justify Eq. (37), define M, and show the sensitivity of the overlap to alternative cutoff identifications (e.g., k ∼ r^{-p}) before drawing the claimed observational conclusion.
minor comments (5)
  1. [§IV.A, Eq. (25)] The factor [1+(ξ/r0)^2] should be [1+(ξ/r)^2] if the expression is valid for arbitrary r; the r0 version is the throat limit and should be indicated as such.
  2. [§IV.A, text after Eq. (26)] The phrase 'for construction' should read 'by construction'.
  3. [§V, Fig. 12] Axes are not labeled. Please label the horizontal axis ξ/M and the vertical axis R_sh/M, and state the value of the mass M used in the normalization.
  4. [§V, Eq. (38)] The right-hand side carries a leading minus sign; since ξ^{-2}>0, the authors should discuss the sign conditions under which a real positive ξ exists.
  5. [§IV.B, Eq. (28)] The use of ⟨P⟩ = (Pr + 2Pt)/3 for the anisotropic fluid should be motivated, and the stability/causality conditions should be discussed in terms of directional sound speeds.

Circularity Check

0 steps flagged

No significant circularity: geometry and stability follow from stated equations; the EHT match is a one-parameter constraint, and Eq. (33) is a correctness issue, not a circular reduction.

full rationale

The derivation is not circular. The shape function follows from integrating Eq. (7) with the assumed running coupling G(r) and Dekel–Zhao density; the redshift function is an explicit ansatz; the energy conditions are evaluated from the resulting metric, and the NEC violation at the throat is a consequence of the flare-out condition, not an input. The modified TOV equation (30) follows from the divergence of the improved field equations (Bianchi), so the 'quantum force' FQ is a derived term, not a fitted one. The shadow section is the only place where the stated derivation is suspect: Eq. (33) gives sinα_sh = γ(rph)/γ(Ro), the reciprocal of the standard relation for this metric, so taken literally it would make R_sh diverge as R_o→∞ and Fig. 12 cannot be derived from it as written. That is a mathematical error/missing support, not a circular reduction: R_sh is not an input to the model. The EHT overlap is obtained by scanning the free parameter ξ/M and reading where the curve crosses the observed band, which the paper describes as establishing 'preliminary bounds on the free parameters'; this is a parameter constraint, not a fitted input renamed as a prediction. The identification ξ∼1/√R(r0) is an additional ansatz, and the paper itself states 'There is no generally agreed upon definition for these last identification'; that is a validity caveat, not circularity. The only self-citation with a current author (ref. [8], Muniz) is background, not load-bearing. Given the stated assumptions, the geometric and physical derivations are self-contained.

Axiom & Free-Parameter Ledger

4 free parameters · 7 axioms · 1 invented entities

The paper's central claims rest on a chain of modelling choices: an RG-flow form for G(k), a cutoff identification k = ξ/r, insertion of G(r) directly into the field equations, a hand-picked redshift function, and an ad hoc scale-curvature identification for the shadow. None of these is independently verified, and the final EHT match is a free-parameter selection.

free parameters (4)
  • ξ (ASG running scale) = ξ/M ≈ 0.8–0.9 (EHT-compatible range)
    Free parameter of the model; the shadow analysis selects this range to match Sgr A*.
  • r0 (throat radius) = r0 = 1 in most figures; in the shadow section determined by Eq. (38) for chosen ξ
    Sets the wormhole scale; arbitrary in the analytic solution, and in the shadow comparison fixed by the ad hoc scale-curvature relation rather than by data.
  • ρ0, rc, a (halo parameters) = a = 1, rc = 8 kpc, ρ0 = 0.5 GeV/cm³ for the shadow comparison; varied in the figures
    Astrophysical inputs chosen for the shadow comparison; not constrained by the model itself, but the Rsh curve depends on them.
  • b, γ in the Dekel–Zhao profile = b = 1, γ = 3
    Fixed by hand to keep the NFW-like regime; not varied.
axioms (7)
  • domain assumption The ASG running coupling has the form G(k) = G0/(1 + ωG0 k²), with ω = 4/π (1 − π²/144).
    Taken from the ASG literature (Bonanno–Reuter); the paper does not re-derive it.
  • ad hoc to paper The cutoff identification k = ξ/r is adopted in the infrared regime.
    The paper states this is a 'simple' choice and acknowledges the cutoff identification is not unique (Sec. IIA).
  • ad hoc to paper Position-dependent G(r) is inserted directly into the Einstein equations as G_μν = 8πG(r)T_μν, and the conservation law is replaced by ∇_μ(G T^μ_ν) = 0.
    This is an effective 'quantum improvement' prescription; no action or systematic truncation is given, and backreaction is neglected.
  • ad hoc to paper The redshift function is chosen by hand as Φ(r) = 2 ln(r/(r+r0)).
    Chosen for analytical convenience and to avoid horizons, not derived from the field equations.
  • ad hoc to paper The ASG scale is identified with the curvature at the throat via ξ ∼ 1/√R(r0).
    This identification, Eq. (37), is imposed to relate ξ to the geometry and directly shapes the shadow-radius curve.
  • domain assumption The Dekel–Zhao dark matter profile is used with b = 1 and γ = 3.
    A standard empirical dark matter profile; the paper fixes two of its parameters to remain in the NFW-like regime.
  • standard math The Morris–Thorne metric and standard wormhole conditions (flare-out, asymptotic flatness, traversability) are assumed.
    Standard framework for traversable wormholes; not in question.
invented entities (1)
  • Quantum force F_Q = −G′(r)P_r no independent evidence
    purpose: A new force term in the modified TOV equation, interpreted as an effective repulsive quantum correction from the running of G(r).
    It is a bookkeeping term arising from the position-dependent G(r); it has no independent observational handle and its sign and magnitude are set by the assumed G(r).

pith-pipeline@v1.3.0-alltime-deepseek · 22474 in / 18539 out tokens · 156021 ms · 2026-08-04T08:53:08.498625+00:00 · methodology

0 comments
read the original abstract

This work presents and investigates novel traversable wormhole solutions within the framework of Asymptotically Safe Gravity (ASG), sourced by a dark matter halo modeled by the Dekel--Zhao density profile. The scale-dependent gravitational coupling $G(k)$, derived from the ASG renormalization group flow in the infrared regime, is incorporated directly into the field equations, providing a consistent description of quantum gravitational corrections even at astrophysical scales. The combined effects of the running coupling (parameterized by $\xi$) and the dark matter characteristics determine the geometric structure and physical viability of the wormhole. The solutions satisfy the flare-out and asymptotic flatness conditions within restricted parameter domains, exhibiting enhanced curvature near the throat due to ASG corrections. Null Energy Conditions are necessarily violated at the throat, and stability analysis based on the adiabatic sound speed as well as the modified Tolman--Oppenheimer--Volkoff equation reveal that quantum effects from ASG counteract the destabilizing influence of dark matter. Phenomenologically, the wormhole shadow radius increases nearly linearly with $\xi$, lying within the Event Horizon Telescope bounds for Sgr~A$^*$ when $\xi/M \simeq 0.8--0.9$, thus suggesting that ASG-corrected wormholes may represent observable signatures of quantum gravity in the strong-field regime.

Figures

Figures reproduced from arXiv: 2510.18264 by Celio R. Muniz, Edson Otoniel, Francisco Bento Lustosa, Jonathan A. Rebou\c{c}as.

Figure 1
Figure 1. Figure 1: FIG. 1. The Dekel-Zhao’s dark matter density profile, [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The flare-out, [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The flare-out, [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Ricci’s scalar as a function of the radial coordinate, produced for Dekel-Zhao’s dark matter density profile: (a) [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Embedding diagrams of a wormhole produced for Dekel-Zhao’s dark matter density profile. (a) [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The illustrations of radial NEC, [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The illustrations of tangential NEC, [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. The illustrations of SEC, [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. The illustrations of tangential DEC, [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Average squared adiabatic sound speed curves of a wormhole as a function of the radial coordinate, produced [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Profiles of the combined hydrostatic ( [PITH_FULL_IMAGE:figures/full_fig_p019_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Shadow radius [PITH_FULL_IMAGE:figures/full_fig_p021_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Visual representation of the wormhole shadow in ASG with Dekel-Zhao dark matter ( [PITH_FULL_IMAGE:figures/full_fig_p021_13.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

96 extracted references · 7 canonical work pages

  1. [1]

    Flamm,Beiträge zur Einsteinschen gravitationstheorie(Hirzel, 1916)

    L. Flamm,Beiträge zur Einsteinschen gravitationstheorie(Hirzel, 1916)

    1916

  2. [2]

    Einstein and N

    A. Einstein and N. Rosen, Phys. Rev.48, 73 (1935)

    1935

  3. [3]

    ordinary

    it was shown that some form of “exotic” matter is required to stabilize these solutions to make them traversable wormholes (TWs). Dark energy or Casimir vacuum energy have been used as possible sources of this exotic matter in multiple wormhole solutions studied in the literature [4, 5] and modified gravity theories have been used to construct wormhole so...

    Pith/arXiv arXiv 2025

  4. [4]

    J. P. S. Lemos, F. S. N. Lobo, and S. Q. de Oliveira, Phys. Rev. D68, 064004 (2003)

    2003

  5. [5]

    M. S. Morris and K. S. Thorne, American Journal of Physics56, 395 (1988)

    1988

  6. [6]

    Capozziello and N

    S. Capozziello and N. Godani, Phys. Lett. B835, 137572 (2022), arXiv:2211.06481 [gr-qc]

    Pith/arXiv arXiv 2022

  7. [7]

    Garattini, European Physical Journal C79(2019), 10.1140/epjc/s10052-019-7468-y

    R. Garattini, European Physical Journal C79(2019), 10.1140/epjc/s10052-019-7468-y

    work page doi:10.1140/epjc/s10052-019-7468-y 2019

  8. [8]

    Alencar, V

    G. Alencar, V. B. Bezerra, C. R. Muniz, and H. S. Vieira, Universe7(2021), 10.3390/universe7070238

    work page doi:10.3390/universe7070238 2021

  9. [9]

    M. Cruz, R. Neves, and C. R. Muniz, Journal of Cosmology and Astroparticle Physics2024, 016 (2024)

    2024

  10. [10]

    Nilton, J

    M. Nilton, J. Furtado, and G. Alencar, Physical Review D105(2022), 10.1103/PhysRevD.105.084048

    work page doi:10.1103/physrevd.105.084048 2022

  11. [11]

    Alencar and M

    G. Alencar and M. Nilton, Universe7(2021), 10.3390/universe7090332

    work page doi:10.3390/universe7090332 2021

  12. [12]

    Maldacena and L

    J. Maldacena and L. Susskind, Fortschritte der Physik61, 781 (2013)

    2013

  13. [13]

    F. S. N. Lobo and M. Visser, Classical and Quantum Gravity21, 5871 (2004)

    2004

  14. [14]

    Li and C

    Z. Li and C. Bambi, Phys. Rev. D90, 024071 (2014)

    2014

  15. [15]

    F. S. N. Lobo, G. J. Olmo, and D. Rubiera-Garcia, The European Physical Journal C74, 2924 (2014)

    2014

  16. [16]

    Akiyamaet al.(Event Horizon Telescope), Astrophys

    K. Akiyamaet al.(Event Horizon Telescope), Astrophys. J. Lett.930, L12 (2022), arXiv:2311.08680 [astro-ph.HE]

    Pith/arXiv arXiv 2022

  17. [17]

    Deliyski, G

    V. Deliyski, G. Gyulchev, P. Nedkova, and S. Yazadjiev, Phys. Rev. D106, 104024 (2022)

    2022

  18. [18]

    Planck Collaboration, A&A641, A1 (2020)

    2020

  19. [19]

    Abbottet al.(LIGO Scientific, Virgo), Phys

    R. Abbottet al.(LIGO Scientific, Virgo), Phys. Rev. X11, 021053 (2021), arXiv:2010.14527 [gr-qc]

    Pith/arXiv arXiv 2021

  20. [20]

    Bertiet al., Classical and Quantum Gravity32, 243001 (2015)

    E. Bertiet al., Classical and Quantum Gravity32, 243001 (2015)

    2015

  21. [21]

    M. S. Turner, Annual Review of Nuclear and Particle Science72, 1 (2022)

    2022

  22. [22]

    Vagnozzi, R

    S. Vagnozzi, R. Roy, Y.-D. Tsai, L. Visinelli, M. Afrin, A. Allahyari, P. Bambhaniya, D. Dey, S. G. Ghosh, P. S. Joshi, K. Jusufi, M. Khodadi, R. K. Walia, A. Övgün, and C. Bambi, Classical and Quantum Gravity40, 165007 (2023)

    2023

  23. [23]

    Ashtekar, A

    A. Ashtekar, A. del Río, and M. Schneider, Gen. Rel. Grav.54, 45 (2022), arXiv:2205.00298 [gr-qc]

    Pith/arXiv arXiv 2022

  24. [24]

    Adameet al.(DESI Collaboration), Journal of Cosmology and Astroparticle Physics2025, 021 (2025)

    A. Adameet al.(DESI Collaboration), Journal of Cosmology and Astroparticle Physics2025, 021 (2025)

    2025

  25. [25]

    Adameet al.(DESI Collaboration), The Astronomical Journal168, 58 (2024)

    A. Adameet al.(DESI Collaboration), The Astronomical Journal168, 58 (2024)

    2024

  26. [26]

    Silket al.,Particle Dark Matter: Observations, Models and Searches, edited by G

    J. Silket al.,Particle Dark Matter: Observations, Models and Searches, edited by G. Bertone (Cambridge Univ. Press, Cambridge, 2010)

    2010

  27. [27]

    Andrade, E

    U. Andrade, E. Paillas, J. Mena-Fernández, Q. Li, A. J. Ross, S. Nadathur, M. Rashkovetskyi, A. Pérez-Fernández, H. Seo, N. Sanders, O. Alves, X. Chen, N. Deiosso, A. de Mattia, M. White, M. A. Karim, S. Ahlen, E. Armengaud, A. Aviles, P. Bansal, J. Behera, D. Bianchi, S. Brieden, A. Brodzeller, D. Brooks, E. Burtin, R. Calderon, R. Canning, A. C. Rosell,...

    2025

  28. [28]

    Capozziello, V

    S. Capozziello, V. F. Cardone, and A. Troisi, Journal of Cosmology and Astroparticle Physics2006, 001 (2006)

    2006

  29. [29]

    Dark matter,

    M. Cirelli, A. Strumia, and J. Zupan, “Dark matter,” (2024), arXiv:2406.01705 [hep-ph]

    Pith/arXiv arXiv 2024

  30. [30]

    G. J. Olmo and P. Singh, Journal of Cosmology and Astroparticle Physics2009, 030 (2009)

    2009

  31. [31]

    Harko, F

    T. Harko, F. S. N. Lobo, S. Nojiri, and S. D. Odintsov, Phys. Rev. D84, 024020 (2011)

    2011

  32. [32]

    S. E. Perez Bergliaffa and Y. E. C. de Oliveira Nunes, Phys. Rev. D84, 084006 (2011), arXiv:1107.5727 [gr-qc]

    Pith/arXiv arXiv 2011

  33. [33]

    R. V. Lobato, G. A. Carvalho, A. G. Martins,et al., European Physical Journal Plus134, 132 (2019)

    2019

  34. [34]

    Bonanno and M

    A. Bonanno and M. Reuter, Phys. Rev. D62, 043008 (2000)

    2000

  35. [35]

    G. J. Olmo and D. Rubiera-Garcia, Universe1, 173 (2015)

    2015

  36. [36]

    Ishibashi, N

    A. Ishibashi, N. Ohta, and D. Yamaguchi, Physical Review D104(2021), 10.1103/PhysRevD.104.066016

    work page doi:10.1103/physrevd.104.066016 2021

  37. [37]

    Bonanno and M

    A. Bonanno and M. Reuter, Phys. Rev. D73, 083005 (2006)

    2006

  38. [38]

    Bambi, D

    C. Bambi, D. Malafarina, and L. Modesto, Phys. Rev. D88, 044009 (2013)

    2013

  39. [39]

    Modesto, Class

    L. Modesto, Class. and Quantum Grav.23, 5587 (2006)

    2006

  40. [40]

    K. M. Belotsky, A. E. Dmitriev, E. A. Esipova, V. A. Gani, A. V. Grobov, M. Y. Khlopov, A. A. Kirillov, S. G. Rubin, and I. V. Svadkovsky, Modern Physics Letters A29, 1440005 (2014), https://doi.org/10.1142/S0217732314400057

    doi:10.1142/s0217732314400057 2014

  41. [41]

    A. Akil, M. Cadoni, L. Modesto, M. Oi, and A. P. Sanna, Phys. Rev. D108, 044051 (2023)

    2023

  42. [42]

    K. S. Croker, K. A. Nishimura, and D. Farrah, The Astrophysical Journal889, 115 (2020)

    2020

  43. [43]

    Bai and N

    Y. Bai and N. Orlofsky, Phys. Rev. D101, 055006 (2020), arXiv:1906.04858 [hep-th]

    Pith/arXiv arXiv 2020

  44. [44]

    Cadoni, A

    M. Cadoni, A. Sanna, M. Pitzalis, B. Banerjee, R. Murgia, N. Hazra, and M. Branchesi, Journal of Cosmology and Astroparticle Physics2023, 007 (2023)

    2023

  45. [45]

    Farrahet al., The Astrophysical Journal Letters944, L31 (2023)

    D. Farrahet al., The Astrophysical Journal Letters944, L31 (2023)

    2023

  46. [46]

    Mitra, Foundations of Physics Letters13, 543 (2000)

    A. Mitra, Foundations of Physics Letters13, 543 (2000)

    2000

  47. [47]

    S. P. Ahlenet al.(DESI Collaboration), Phys. Rev. Lett.135, 081003 (2025)

    2025

  48. [48]

    Akiyamaet al.(Event Horizon Telescope), The Astrophysical Journal Letters875, L1 (2019)

    K. Akiyamaet al.(Event Horizon Telescope), The Astrophysical Journal Letters875, L1 (2019)

    2019

  49. [49]

    R. E. Schild, D. J. Leiter, and S. L. Robertson, The Astronomical Journal132, 420 (2006)

    2006

  50. [50]

    Abdujabbarov, M

    A. Abdujabbarov, M. Amir, B. Ahmedov, and S. G. Ghosh, Phys. Rev. D93, 104004 (2016)

    2016

  51. [51]

    Simpson and M

    A. Simpson and M. Visser, J. Cosmol. Astropart. Phys.2019, 042 (2019), arXiv:1812.07114 [gr-qc]

    Pith/arXiv arXiv 2019

  52. [52]

    Carballo-Rubio, F

    R. Carballo-Rubio, F. Di Filippo, S. Liberati, and M. Visser, Journal of Cosmology and Astroparticle Physics2022, 055 (2022)

    2022

  53. [53]

    Annulli, V

    L. Annulli, V. Cardoso, and L. Gualtieri, Classical and Quantum Gravity39, 105005 (2022)

    2022

  54. [54]

    Facchinetti, M

    G. Facchinetti, M. Lucca, and S. Clesse, Phys. Rev. D107, 043537 (2023)

    2023

  55. [55]

    Loeb, The Astrophysical Journal Letters975, L15 (2024)

    A. Loeb, The Astrophysical Journal Letters975, L15 (2024)

    2024

  56. [56]

    Figueiredo, A

    E. Figueiredo, A. Maselli, and V. Cardoso, Phys. Rev. D107, 104033 (2023)

    2023

  57. [57]

    Jangra, D

    P. Jangra, D. Gaggero, B. J. Kavanagh, and J. Diego, Journal of Cosmology and Astroparticle Physics2025, 006 (2025)

    2025

  58. [58]

    S. L. Jung, I. H. Whittam, M. J. Jarvis, C. L. Hale, M. N. Tudorache, and T. Yasin, Monthly Notices of the Royal Astronomical Society539, 2362 (2025)

    2025

  59. [59]

    Övgün and R

    A. Övgün and R. C. Pantig, Physics Letters B864, 139398 (2025)

    2025

  60. [60]

    J. F. Navarro, C. S. Frenk, and S. D. M. White, Astrophys. J.462, 563 (1996), arXiv:astro-ph/9508025 [astro-ph]

    Pith/arXiv arXiv 1996

  61. [61]

    Mattheeet al., The Astrophysical Journal963, 129 (2024)

    J. Mattheeet al., The Astrophysical Journal963, 129 (2024)

    2024

  62. [62]

    Hassan and P

    Z. Hassan and P. Sahoo, Annalen der Physik536, 2400114 (2024)

    2024

  63. [63]

    Castignani, N

    G. Castignani, N. Frusciante, D. Vernieri, and P. Salucci, Natural Science4, 265 (2012), arXiv:1201.3998 [astro-ph.CO]

    Pith/arXiv arXiv 2012

  64. [64]

    Zhao, Monthly Notices of the Royal Astronomical Society287, 525 (1997)

    H. Zhao, Monthly Notices of the Royal Astronomical Society287, 525 (1997)

    1997

  65. [65]

    Zhao, Monthly Notices of the Royal Astronomical Society278, 488 (1996)

    H. Zhao, Monthly Notices of the Royal Astronomical Society278, 488 (1996)

    1996

  66. [66]

    Khatri and P

    M. Khatri and P. K. Sahoo, Physics of the Dark Universe49(2025), 10.1016/j.dark.2025.102042

    arXiv 2025

  67. [67]

    Freundlich, F

    J. Freundlich, F. Jiang, A. Dekel, N. Cornuault, O. Ginzburg, R. Koskas, S. Lapiner, A. Dutton, and A. V. Mac- ciò, Monthly Notices of the Royal Astronomical Society499, 2912 (2020), https://academic.oup.com/mnras/article- pdf/499/2/2912/33995419/staa2790.pdf

    2020

  68. [68]

    Bojowald, Universe6(2020), 10.3390/universe6080125

    M. Bojowald, Universe6(2020), 10.3390/universe6080125

    doi:10.3390/universe6080125 2020

  69. [69]

    Bambi, L

    C. Bambi, L. Modesto, and I. Shapiro, eds.,Handbook of Quantum Gravity(Springer, 2024)

    2024

  70. [70]

    Huggett and T

    N. Huggett and T. Vistarini, Philosophy of Science82, 1163–1174 (2015)

    2015

  71. [71]

    Space and time in loop quantum gravity,

    C. Rovelli, “Space and time in loop quantum gravity,” inBeyond Spacetime: The Foundations of Quantum Gravity, edited by N. Huggett, K. Matsubara, and C. Wüthrich (Cambridge University Press, 2020) p. 117–132

    2020

  72. [72]

    Reuter and F

    M. Reuter and F. Saueressig, Phys. Rev. D65, 065016 (2002)

    2002

  73. [73]

    M. M. Anber and J. F. Donoghue, Phys. Rev. D85, 104016 (2012), arXiv:1111.2875 [hep-th]

    Pith/arXiv arXiv 2012

  74. [74]

    B. L. Giacchini, T. de Paula Netto, and I. L. Shapiro, Journal of High Energy Physics2020(2020), 10.1007/JHEP10(2020)011

    work page doi:10.1007/jhep10(2020)011 2020

  75. [75]

    Modesto, Phys

    L. Modesto, Phys. Rev. D86, 044005 (2012)

    2012

  76. [76]

    Reuter, Phys

    M. Reuter, Phys. Rev. D57, 971 (1998)

    1998

  77. [77]

    Asorey, G

    M. Asorey, G. Krein, M. Pardina, and I. L. Shapiro, JHEP01, 113 (2025), arXiv:2408.16514 [gr-qc]

    arXiv 2025

  78. [78]

    Bosma, B

    L. Bosma, B. Knorr, and F. Saueressig, Phys. Rev. Lett.123, 101301 (2019)

    2019

  79. [79]

    Asymptotic safety of gravity with matter,

    A. Eichhorn and M. Schiffer, “Asymptotic safety of gravity with matter,” inHandbook of Quantum Gravity, edited by C. Bambi, L. Modesto, and I. Shapiro (Springer Nature Singapore, Singapore, 2024) pp. 915–1001. 25

    2024

  80. [80]

    A. M. Sultan, A. Batool, G. Abbas, A. Jawad, and S. Shaymatov, Nuclear Physics B1013(2025), 10.1016/j.nuclphysb.2025.116838

    arXiv 2025

Showing first 80 references.