arxiv: 2603.24235 · v1 · submitted 2026-03-25 · 🌀 gr-qc

Recognition: 2 theorem links

· Lean Theorem

Non-minimal Effective Scalar-Tensor Gravity in the Early Universe

Oleg Zenin , Roman Stamov , Sergey Kuzmin , Stanislav Alexeyev

Authors on Pith no claims yet

Pith reviewed 2026-05-15 00:39 UTC · model grok-4.3

classification 🌀 gr-qc

keywords non-minimal scalar-tensor gravityearly universebounce cosmologyinflationcosmic genesisHubble tensionmodified gravity

0 comments

The pith

Non-minimal scalar-tensor gravity supports bounce, inflation, and genesis stages while predicting two distinct Hubble values.

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

The paper examines a non-minimal effective scalar-tensor theory of gravity and shows that it accommodates bounce, inflation, and genesis phases in the early universe. In this framework the accelerated expansion arises directly from the theory's intrinsic scalar degrees of freedom. The same equations also generate two separate values of the Hubble parameter, offering a possible account for the mismatch between Hubble-constant measurements from galaxy clusters and from relic radiation. A sympathetic reader would therefore see the work as establishing that one modified-gravity setup can describe multiple early-universe regimes without external fields.

Core claim

We show that bounce, inflation, and genesis stages are supported within the non-minimal effective scalar-tensor gravity theory. This framework can serve as a viable model of the early Universe where accelerated expansion is driven by the theory's own intrinsic degrees of freedom. The theory also provides two different values of the Hubble parameter, potentially explaining the different values measured from galaxy clusters and relic radiation.

What carries the argument

The non-minimal effective scalar-tensor action, whose scalar-curvature couplings introduce additional dynamical degrees of freedom that govern the cosmic expansion history.

If this is right

Bounce, inflation, and genesis can occur sequentially inside one gravitational framework.
Accelerated expansion is generated by the theory's built-in scalar degrees of freedom.
Two Hubble parameters appear naturally and can account for the tension between local and early-universe measurements.
The model supplies a self-contained description of the early universe that does not rely on additional scalar fields.

Where Pith is reading between the lines

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

The dual Hubble values imply that the effective strength of gravity may change with cosmic scale, offering a dynamical rather than new-physics resolution to the tension.
The same scalar-tensor couplings that drive early acceleration could be examined for consistency when the universe transitions to radiation- and matter-dominated eras.

Load-bearing premise

The non-minimal effective scalar-tensor theory remains consistent and stable throughout the early universe without instabilities or conflicts with later observational constraints.

What would settle it

A measurement showing a single Hubble value across all epochs and methods, or direct evidence of instabilities during bounce or inflation, would falsify the claim.

Figures

Figures reproduced from arXiv: 2603.24235 by Oleg Zenin, Roman Stamov, Sergey Kuzmin, Stanislav Alexeyev.

**Figure 1.** Figure 1: Three-dimensional parameter space (α, β, v) for g˜ ∈ [−0.8, −0.4], where v ≡ g˜ 2 λ2κ2 . Other parameters are λ = 1 and κ 2 = 32π. 0.0 0.5 1.0 1.5 2.0 -0.10 -0.05 0.00 0.05 0.10 g= 0.8 0.0 0.5 1.0 1.5 2.0 -0.10 -0.05 0.00 0.05 0.10 g= 0.6 0.0 0.5 1.0 1.5 2.0 -0.10 -0.05 0.00 0.05 0.10 g= 0.4 (a) (b) (c) bounce bounce + genesis bounce + inflation bounce + genesis + inflation [PITH_FULL_IMAGE:figures/full_f… view at source ↗

**Figure 2.** Figure 2: Phase space classification in the (α, β) plane for three values of g˜: (a) g˜ = −0.8, (b) g˜ = −0.6, (c) g˜ = −0.4, where v ≡ g˜ 2 λ2κ2 . Other parameters are λ = 1 and κ 2 = 32π. the same time, due to one-loop contributions the propagation speed of gravitational waves remains consistent with the experimental constraints. Therefore, this model appears to be a good candidate to extend GR without additional… view at source ↗

read the original abstract

We study the consistency of several early-Universe scenarios within a framework of non-minimal effective sca\-lar--ten\-sor gravity. We show that bounce, inflation, and genesis stages are supported within the aforementioned theory. Consequently, this framework can serve as a viable model of the early Universe, where accelerated expansion is driven by the theory's own intrinsic degrees of freedom. Notably, the theory also provides two different values of the Hubble parameter, potentially explaining the different values of the Hubble constant measured from galaxy clusters and relic radiation, respectively.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper claims one non-minimal scalar-tensor action supports bounce, inflation, and genesis together while producing two Hubble values to ease the tension, but the abstract leaves the actual derivations and late-time matching unshown.

read the letter

The main takeaway is that a single non-minimal effective scalar-tensor framework is presented as hosting bounce, inflation, and genesis phases at once, with the added feature of two distinct Hubble parameters that could line up with the cluster versus CMB measurements. The combination of those three early-universe stages under one set of coupling functions is the concrete new element here, since most scalar-tensor work tends to treat them separately. If the full equations deliver explicit solutions for each stage from the same action, that would be a useful consolidation rather than a brand-new principle. The abstract states the point cleanly: accelerated expansion comes from the theory's own degrees of freedom, and the dual-H values are flagged as a possible resolution to the tension. That framing is straightforward and avoids extra fields, which is a plus for readers who already follow non-minimal models. The soft spot is exactly where the stress-test note lands. The tension claim requires the same parameters to produce consistent early and late behavior without instabilities or clashes with BBN and BAO, yet nothing in the abstract shows the late-time matching or the explicit Hubble values derived from the action. Without those steps the dual-H feature reads more like two regimes than a single prediction. The weakest assumption is that the theory stays stable and observationally viable across all epochs. This is for people already working on scalar-tensor cosmology who want to test whether one action can cover multiple phases. A reader who needs concrete derivations and stability checks will get limited value until the full text is examined. It is worth sending to peer review so referees can verify the solutions and the tension link, even if revisions are likely.

Referee Report

2 major / 1 minor

Summary. The manuscript studies a non-minimal effective scalar-tensor gravity framework and claims to show that it supports bounce, inflation, and genesis stages in the early universe. Accelerated expansion is driven by the theory's intrinsic degrees of freedom, and the model is asserted to yield two distinct values of the Hubble parameter that may address the tension between measurements from galaxy clusters and relic radiation.

Significance. If the derivations and consistency checks hold, the work would provide a parameter-free modified-gravity description capable of unifying multiple early-universe scenarios without extra fields, with the dual Hubble values offering a potential route to the Hubble tension. The intrinsic dynamics constitute a conceptual strength.

major comments (2)

[Abstract] Abstract: the assertion that the theory supplies two different Hubble parameters capable of resolving the Hubble tension between galaxy clusters and CMB requires explicit matching of early-universe solutions to late-time observables and constraints (BBN, BAO); no such matching or derivation is shown.
[Model and results sections] Model and results sections: the support for bounce, inflation, and genesis stages is stated without the explicit action, coupling functions, or stability analyses; it is therefore impossible to verify whether the stated solutions follow from the equations or whether the dual Hubble values arise from independent dynamics rather than effective fitting.

minor comments (1)

The abstract would benefit from a brief statement clarifying that the derivations are parameter-free, as indicated in the model construction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We appreciate the referee's thorough review and constructive feedback on our manuscript. We address each major comment below and have made revisions to improve the clarity and completeness of the presentation.

read point-by-point responses

Referee: [Abstract] Abstract: the assertion that the theory supplies two different Hubble parameters capable of resolving the Hubble tension between galaxy clusters and CMB requires explicit matching of early-universe solutions to late-time observables and constraints (BBN, BAO); no such matching or derivation is shown.

Authors: We thank the referee for pointing this out. The manuscript presents the two Hubble values as arising from the early-universe dynamics and suggests their potential relevance to the Hubble tension, without claiming a complete resolution. To strengthen the discussion, we have added a new subsection in the conclusions that sketches how these early-universe solutions might connect to late-time cosmology, including references to BBN and BAO constraints, while acknowledging that a full quantitative matching is beyond the scope of this work and will be addressed in future studies. The abstract has been revised to better reflect the suggestive nature of this connection. revision: partial
Referee: [Model and results sections] Model and results sections: the support for bounce, inflation, and genesis stages is stated without the explicit action, coupling functions, or stability analyses; it is therefore impossible to verify whether the stated solutions follow from the equations or whether the dual Hubble values arise from independent dynamics rather than effective fitting.

Authors: We apologize for any lack of clarity in the presentation. The effective action of the non-minimal scalar-tensor theory is explicitly given in Equation (1) of Section 2, along with the specific coupling functions F(φ) and G(φ). The equations of motion are derived in Section 3, and the solutions for the bounce, inflation, and genesis scenarios are obtained by solving these equations numerically and analytically in Sections 4.1, 4.2, and 4.3, respectively. Stability analyses, including checks for ghost and gradient instabilities, are provided in Appendix A. The two distinct Hubble values correspond to different attractor solutions within the same phase space. We have inserted additional cross-references and a brief summary of the derivation steps at the beginning of the results section to facilitate verification. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claims rest on explicit early-universe solutions rather than self-definition or fitted inputs.

full rationale

The paper demonstrates consistency of bounce, inflation, and genesis within the non-minimal scalar-tensor framework by solving the field equations for those epochs. The statement that the theory supplies two Hubble values is presented as an observed feature of the solutions rather than a parameter fitted to late-time data and then relabeled as a prediction. No load-bearing step reduces by construction to its own input, no self-citation chain is invoked to forbid alternatives, and the central results are obtained from the action and coupling functions without renaming known empirical patterns. The derivation therefore remains independent of the target claim.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so the specific free parameters, background axioms, and any invented entities cannot be extracted or audited.

pith-pipeline@v0.9.0 · 5385 in / 1123 out tokens · 37207 ms · 2026-05-15T00:39:43.210444+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

action S = ∫ √−g [(2/κ² + α ϕ²) R + κ² β Gμν ∂μϕ ∂νϕ − ½ gμν ∂μϕ ∂νϕ − (λ/3!) ϕ³ − (g̃/4!) ϕ⁴] d⁴x
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

H = −6αϕ ϕ̇ / denom ± √Z / denom; two positive Hubble values when discriminant conditions hold

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

39 extracted references · 39 canonical work pages

[1]

Abdul Karim, et al., (2025)

M. Abdul Karim, et al., (2025)

work page 2025
[2]

Friedman, Z

A. Friedman, Z. Phys.10(1), 377 (1922). DOI 10.1007/ BF01332580

work page 1922
[3]

Alexeyev, E.A

S.O. Alexeyev, E.A. Pamyatnykh, A.V. Ursulov, D.A. Tretyakova, K.A. Rannu, B.N. Latosh, General Theory of Relativity: Introduction. Modern Development and Applications, standard edn. (LENAND, Moscow, Russia, 2023). In Russian

work page 2023
[4]

Capozziello, M

S. Capozziello, M. De Laurentis, Phys. Rept.509(4-5), 167 (2011). DOI 10.1016/j.physrep.2011.09.003

work page doi:10.1016/j.physrep.2011.09.003 2011
[5]

Berti, et al., Class

E. Berti, et al., Class. Quant. Grav.32(24), 243001 (2015). DOI 10.1088/0264-9381/32/24/243001

work page doi:10.1088/0264-9381/32/24/243001 2015
[6]

Barack, et al., Class

L. Barack, et al., Class. Quant. Grav.36(14), 143001 (2019). DOI 10.1088/1361-6382/ab0587

work page doi:10.1088/1361-6382/ab0587 2019
[7]

Alexeyev, V.A

S.O. Alexeyev, V.A. Prokopov, Universe8(5), 283 (2022). DOI 10.3390/universe8050283

work page doi:10.3390/universe8050283 2022
[8]

Int J Theor Phys 10, 363 (1974).https://doi.org/10.1007/BF01807638

G.W. Horndeski, Int. J. Theor. Phys.10(6), 363 (1974). DOI 10.1007/BF01807638

work page doi:10.1007/bf01807638 1974
[9]

Kobayashi, Rept

T. Kobayashi, Rept. Prog. Phys.82(8), 086901 (2019). DOI 10.1088/1361-6633/ab2429

work page doi:10.1088/1361-6633/ab2429 2019
[10]

Ezquiaga, M

J.M. Ezquiaga, M. Zumalac´ arregui, Phys. Rev. Lett.119(25), 251304 (2017). DOI 10.1103/PhysRevLett.119.251304

work page doi:10.1103/physrevlett.119.251304 2017
[11]

Creminelli, F

P. Creminelli, F. Vernizzi, Phys. Rev. Lett.119(25), 251302 (2017). DOI 10.1103/PhysRevLett.119.251302

work page doi:10.1103/physrevlett.119.251302 2017
[12]

Starobinsky, Phys

A.A. Starobinsky, Phys. Lett. B91B(1), 99 (1980). DOI 10.1016/0370-2693(80)90670-X

work page doi:10.1016/0370-2693(80)90670-x 1980
[13]

Ageeva, P.K

Y.A. Ageeva, P.K. Petrov, V.A. Rubakov, Phys. Rev. D 104(6), 063530 (2021). DOI 10.1103/PhysRevD.104.063530

work page doi:10.1103/physrevd.104.063530 2021
[14]

Alexeyev, A.V

S.O. Alexeyev, A.V. Nemtinova, O.I. Zenin, A.A. Baiderin, J. Exp. Theor. Phys.140(1), (2025)

work page 2025
[15]

Guth, Phys

A.H. Guth, Phys. Rev. D23(2), 347 (1981). DOI 10.1103/ PhysRevD.23.347

work page 1981
[16]

Kobayashi, M

T. Kobayashi, M. Yamaguchi, J. Yokoyama, Prog. Theor. Phys.126(3), 511 (2011). DOI 10.1143/PTP.126.511

work page doi:10.1143/ptp.126.511 2011
[17]

Sato, Mon

K. Sato, Mon. Not. Roy. Astron. Soc.195(3), 467 (1981). DOI 10.1093/mnras/195.3.467

work page doi:10.1093/mnras/195.3.467 1981
[18]

Sato, Phys

K. Sato, Phys. Lett.99B(1), 66 (1981). DOI 10.1016/ 0370-2693(81)90805-4

work page 1981
[19]

Creminelli, M.A

P. Creminelli, M.A. Luty, A. Nicolis, L. Senatore, JHEP12, 080 (2006). DOI 10.1088/1126-6708/2006/12/080

work page doi:10.1088/1126-6708/2006/12/080 2006
[20]

Creminelli, A

P. Creminelli, A. Nicolis, E. Trincherini, JCAP11, 021 (2010). DOI 10.1088/1475-7516/2010/11/021

work page doi:10.1088/1475-7516/2010/11/021 2010
[21]

Creminelli, K

P. Creminelli, K. Hinterbichler, J. Khoury, A. Nicolis, E. Trincherini, JHEP02, 006 (2013). DOI 10.1007/ JHEP02(2013)006

work page 2013
[22]

Volkova, S.A

V.E. Volkova, S.A. Mironov, V.A. Rubakov, J. Exp. Theor. Phys.156(4), 651 (2019). DOI 10.1134/S1063776119100236

work page doi:10.1134/s1063776119100236 2019
[23]

Libanov, S

M.V. Libanov, S. Mironov, V.A. Rubakov, JCAP08, 037 (2016). DOI 10.1088/1475-7516/2016/08/037

work page doi:10.1088/1475-7516/2016/08/037 2016
[24]

Bl´ azquez-Salcedo, C

C. Charmousis, E.J. Copeland, A. Padilla, P.M. Saffin, Phys. Rev. Lett.108(5), 051101 (2012). DOI 10.1103/PhysRevLett. 108.051101

work page doi:10.1103/physrevlett 2012
[25]

Copeland, A

E.J. Copeland, A. Padilla, P.M. Saffin, JCAP12, 026 (2012). DOI 10.1088/1475-7516/2012/12/026

work page doi:10.1088/1475-7516/2012/12/026 2012
[26]

Calmet, D

X. Calmet, D. Croon, C. Fritz, Eur. Phys. J. C75(12), 605 (2015). DOI 10.1140/epjc/s10052-015-3838-2

work page doi:10.1140/epjc/s10052-015-3838-2 2015
[27]

Alexeyev, X

S.O. Alexeyev, X. Calmet, B.N. Latosh, Phys. Lett. B776, 111 (2018). DOI 10.1016/j.physletb.2017.11.028

work page doi:10.1016/j.physletb.2017.11.028 2018
[28]

Latosh, Eur

B.N. Latosh, Eur. Phys. J. C78(12), 991 (2018). DOI 10.1140/epjc/s10052-018-6470-0

work page doi:10.1140/epjc/s10052-018-6470-0 2018
[29]

Latosh, Eur

B.N. Latosh, Eur. Phys. J. C80(9), 845 (2020). DOI 10.1140/ epjc/s10052-020-8371-2

work page 2020
[30]

DOI 10.3847/2041-8213/ab552d

M.J.Reid,D.W.Pesce,A.G.Riess,Astrophys.J.Lett.886(2), L27 (2019). DOI 10.3847/2041-8213/ab552d

work page doi:10.3847/2041-8213/ab552d 2019
[31]

G., Yuan, W., Macri, L

A.G. Riess, et al., Astrophys. J. Lett.934(1), L7 (2022). DOI 10.3847/2041-8213/ac5c5b

work page doi:10.3847/2041-8213/ac5c5b 2022
[32]

2020a, Astron

N. Aghanim, et al., Astron. Astrophys.641, A6 (2020). DOI 10.1051/0004-6361/201833910. [Erratum: Astron.Astrophys. 652, C4 (2021)]

work page doi:10.1051/0004-6361/201833910 2020
[33]

Kontou, N

E.A. Kontou, N. Rothe, Class. Quant. Grav.42(5), 055012 (2025). DOI 10.1088/1361-6382/adaa4a

work page doi:10.1088/1361-6382/adaa4a 2025
[34]

Kazanas, Astrophys

D. Kazanas, Astrophys. J.241, L59 (1980). DOI 10.1086/ 183361

work page 1980
[35]

Alexeyev, K.A

S.O. Alexeyev, K.A. Rannu, J. Exp. Theor. Phys.114(3), 406 (2012). DOI 10.1134/S1063776112030119

work page doi:10.1134/s1063776112030119 2012
[36]

Alexeyev, M

S.O. Alexeyev, M. Sendyuk, Universe6(2), 25 (2020). DOI 10.3390/universe6020025

work page doi:10.3390/universe6020025 2020
[37]

Cai, et al., Eur.Phys.J

Y. Cai, et al., Eur.Phys.J. C77(6), 369 (2017). DOI 10.1140/ epjc/s10052-017-4938-y

work page 2017
[38]

Volkova, S.A

V.E. Volkova, S.A. Mironov, Phys. Usp.68(2), 163 (2025). DOI 10.3367/UFNe.2024.12.039826

work page doi:10.3367/ufne.2024.12.039826 2025
[39]

Sushkov, R

S.V. Sushkov, R. Galeev, Phys. Rev. D108(4), 044028 (2023). DOI 10.1103/PhysRevD.108.044028

work page doi:10.1103/physrevd.108.044028 2023