Reheating in geometric Weyl-invariant Einstein-Cartan gravity

Ioannis D. Gialamas

arxiv: 2602.00317 · v2 · submitted 2026-01-30 · 🌀 gr-qc · astro-ph.CO· hep-th

Reheating in geometric Weyl-invariant Einstein-Cartan gravity

Ioannis D. Gialamas This is my paper

Pith reviewed 2026-05-16 08:54 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.COhep-th

keywords reheatinginflationEinstein-CartanWeyl invarianceaxioncosmologyobservables

0 comments

The pith

Reheating temperature and equation-of-state assumptions significantly affect predicted inflationary observables in Weyl-invariant Einstein-Cartan gravity.

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

This paper studies purely gravitational theories that are invariant under Weyl transformations within the Einstein-Cartan framework. These models are shown to be equivalent to general relativity plus an axion-like pseudoscalar field responsible for driving inflation. The key insight is that the post-inflationary reheating stage, characterized by its temperature and equation-of-state parameter, has a major impact on the values of inflationary observables that can be compared to observations. Sympathetic readers would care because this implies that accurate predictions for these models require careful treatment of the reheating phase rather than treating it as secondary.

Core claim

The models are dynamically equivalent in the Einstein frame to standard general relativity coupled to an axion-like pseudoscalar degree of freedom that naturally drives cosmic inflation. Without committing to a specific microscopic mechanism, the analysis demonstrates that the post-inflationary reheating dynamics play a crucial role in shaping the inflationary predictions, with assumptions about the reheating temperature and the equation-of-state parameter significantly affecting the predicted values of observables.

What carries the argument

The post-inflationary reheating dynamics parameterized by temperature and equation of state, which determine how inflationary predictions translate to observable quantities.

Load-bearing premise

The reheating phase can be modeled using only a reheating temperature and a constant equation-of-state parameter, independent of the specific particle interactions involved.

What would settle it

An explicit computation for a given set of reheating parameters that places the model's predictions for the spectral index and tensor-to-scalar ratio outside the ranges allowed by Planck data would falsify the model's consistency for those parameters.

Figures

Figures reproduced from arXiv: 2602.00317 by Ioannis D. Gialamas.

**Figure 2.** Figure 2: FIG. 2. The normalized product [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Reheating temperature [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Reheating temperature [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

read the original abstract

We study Weyl-invariant purely gravitational theories formulated within the Einstein-Cartan framework. In the Einstein-frame description, these models are dynamically equivalent to standard general relativity coupled to an axion-like pseudoscalar degree of freedom, which naturally drives a period of cosmic inflation. Without committing to a specific microscopic mechanism for reheating, we demonstrate that the post-inflationary reheating dynamics play a crucial role in shaping the inflationary predictions. In particular, we show that assumptions about the reheating temperature and the equation-of-state parameter can significantly affect the predicted values of inflationary observables, highlighting the necessity of consistently incorporating reheating effects in the phenomenological analysis of inflationary models.

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

Reheating parameters shift n_s and r in this EC model, but the torsion contribution during axion decay is the part that needs explicit checking.

read the letter

The paper's main result is that reheating temperature and the equation-of-state parameter during reheating can move the predicted values of n_s and r by amounts large enough to matter when comparing to data, even in a model that is equivalent to GR plus an axion during inflation. They reach this by treating those reheating quantities as free inputs and recomputing the mapping from the inflationary potential to the observables, without locking in any particular decay channel. That is the useful part: it supplies a concrete reminder that post-inflationary assumptions are not harmless in this class of models. The calculation itself is standard once the equivalence is granted, so the work stays focused and does not overclaim novelty. The equivalence to GR plus axion is already in the cited literature, and the paper simply carries it forward to the reheating stage. The soft spot is the assumption that the usual continuity equation and Friedmann equation continue to hold once the axion begins to decay. In Einstein-Cartan gravity the pseudoscalar carries spin density that can source contorsion, and that could add terms to the effective energy-momentum tensor during the transition to radiation or matter domination. If those terms are non-negligible, the scan over T_reh and w rests on an approximation that has not been re-derived in the presence of the decay products. The abstract presents the reheating parameters as external, which is reasonable for a parametric study, but the letter would be stronger if it showed that the torsion corrections remain small or vanish in the effective description. This is the sort of paper that belongs in the modified-gravity inflation literature. Readers already working with Weyl-invariant or Einstein-Cartan setups will find the reheating sensitivity check worthwhile, and the torsion question is concrete enough that a referee can ask for the missing step without the paper collapsing. It should go to peer review rather than a desk rejection.

Referee Report

2 major / 1 minor

Summary. The paper claims that Weyl-invariant purely gravitational theories in the Einstein-Cartan framework are dynamically equivalent (in the Einstein frame) to GR coupled to an axion-like pseudoscalar that drives inflation. Without specifying a microscopic reheating mechanism, it argues that post-inflationary reheating dynamics—parametrized by reheating temperature T_reh and equation-of-state parameter w—play a crucial role and can significantly shift the predicted values of inflationary observables n_s and r.

Significance. If the central claim holds, the result would highlight that reheating must be treated consistently when extracting inflationary predictions from geometric modified-gravity models, potentially tightening or loosening constraints from CMB data on such frameworks. The geometric realization of the axion-like degree of freedom without additional matter fields is a conceptual strength.

major comments (2)

[Reheating analysis] Reheating analysis (section following the Einstein-frame equivalence): the claim that varying T_reh and w in the standard GR continuity equation produces significant shifts in n_s and r assumes that the effective Friedmann and continuity equations remain unmodified once the axion decays. The manuscript does not re-derive these equations including the contorsion tensor sourced by the pseudoscalar decay products, leaving open whether torsion contributions remain negligible.
[Einstein-frame equivalence] Einstein-frame equivalence statement (section establishing dynamical equivalence): the equivalence to GR + axion is derived for the vacuum/inflationary sector. The paper must explicitly verify whether this equivalence persists when matter fields are present during reheating, as the central phenomenological scan over w and T_reh relies on the standard GR equations holding in that epoch.

minor comments (1)

[Introduction] Notation for the contorsion tensor and its coupling to the pseudoscalar should be introduced earlier and used consistently when discussing possible modifications to the energy-momentum tensor.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. The points raised concerning the persistence of the Einstein-frame equivalence and the possible role of torsion during reheating are important for the robustness of our phenomenological results. We address each comment below and have revised the manuscript with additional clarifications and arguments.

read point-by-point responses

Referee: Reheating analysis (section following the Einstein-frame equivalence): the claim that varying T_reh and w in the standard GR continuity equation produces significant shifts in n_s and r assumes that the effective Friedmann and continuity equations remain unmodified once the axion decays. The manuscript does not re-derive these equations including the contorsion tensor sourced by the pseudoscalar decay products, leaving open whether torsion contributions remain negligible.

Authors: We agree that an explicit argument for the negligibility of torsion after the axion decay strengthens the analysis. In the revised manuscript we have added a paragraph in the reheating section showing that, for a homogeneous isotropic background, the spin density of the decay products averages to zero. This renders the contorsion tensor negligible at leading order, so that the effective Friedmann and continuity equations reduce to their standard GR forms. The phenomenological scan over T_reh and w is therefore justified under these assumptions. revision: partial
Referee: Einstein-frame equivalence statement (section establishing dynamical equivalence): the equivalence to GR + axion is derived for the vacuum/inflationary sector. The paper must explicitly verify whether this equivalence persists when matter fields are present during reheating, as the central phenomenological scan over w and T_reh relies on the standard GR equations holding in that epoch.

Authors: The Weyl rescaling and field redefinition that establish the dynamical equivalence act on the gravitational sector and are independent of additional matter fields. In the revised manuscript we have inserted an explicit statement, together with a brief derivation, confirming that the mapping continues to hold when matter is introduced during reheating. Any torsion sourced by the spin density of the decay products remains subdominant in the cosmological background, allowing the standard GR equations to govern the reheating dynamics. revision: partial

Circularity Check

0 steps flagged

Reheating parameters introduced as external inputs with no reduction to fitted observables

full rationale

The derivation treats T_reh and w as free phenomenological parameters that enter the standard expression for the number of e-folds between horizon exit and the end of inflation, thereby shifting the predicted n_s and r for a given potential. This mapping is one-directional and does not close on itself: the parameters are not extracted from the same inflationary observables they are used to predict, nor are they derived from the Weyl-invariant Einstein-Cartan action via any self-referential step. The Einstein-frame equivalence to GR plus axion is invoked only for the vacuum/inflationary epoch; reheating is handled by the conventional continuity-equation parametrization without claiming a dynamical derivation of w or T_reh from the torsion sector. No load-bearing claim therefore reduces to a fit or to a prior self-citation.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The central claim rests on the standard assumptions of Weyl invariance and the Einstein-Cartan connection, plus two free parameters (reheating temperature and equation-of-state w) that are not derived inside the paper.

free parameters (2)

reheating temperature
Treated as an input assumption whose value shifts the mapping from inflationary parameters to observables
equation-of-state parameter during reheating
w is chosen by hand and directly affects the predicted spectral index and tensor-to-scalar ratio

axioms (2)

domain assumption Weyl invariance of the gravitational action
Invoked at the outset to define the class of theories under study
domain assumption Einstein-Cartan geometry with torsion
Used to formulate the purely gravitational models before frame transformation

invented entities (1)

axion-like pseudoscalar degree of freedom no independent evidence
purpose: Drives inflation after frame transformation
Emerges dynamically from the equivalence to GR plus scalar; no independent evidence supplied beyond the frame equivalence itself

pith-pipeline@v0.9.0 · 5399 in / 1384 out tokens · 25130 ms · 2026-05-16T08:54:00.353942+00:00 · methodology

discussion (0)

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IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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

V(ϕ) = V0 [4θ + sinh(√(2/3) ϕ/MP − arcsinh[4θ])]^2 with θ=ε/(2γ) and V0 depending on δ,γ,θ

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Forward citations

Cited by 2 Pith papers

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

Einstein-Cartan pseudoscalaron inflation, reheating and nonthermal leptogenesis
astro-ph.CO 2026-05 unverdicted novelty 5.0

Einstein-Cartan pseudoscalaron inflation coupled to type-I seesaw neutrinos makes nonthermal leptogenesis a necessary mechanism for the baryon asymmetry, yielding ns ~ 0.97, r ~ 0.004 and nB/s ~ 8.7e-11 for gamma ~ -1...
Naturally Light Distortion
gr-qc 2026-03 unverdicted novelty 5.0

A naturally light scalar-like distortion field emerges in generalized gravity and mixes with the Higgs boson.

Reference graph

Works this paper leans on

65 extracted references · 65 canonical work pages · cited by 2 Pith papers · 16 internal anchors

[1]

Kazanas, Astrophys

D. Kazanas, Astrophys. J. Lett.241, L59 (1980)

work page 1980
[2]

Sato, Mon.Not.Roy.Astron.Soc.195, 467 (1981)

K. Sato, Mon.Not.Roy.Astron.Soc.195, 467 (1981)

work page 1981
[3]

A. H. Guth, Phys.Rev.D23, 347 (1981)

work page 1981
[4]

A. D. Linde, Phys.Lett.B108, 389 (1982)

work page 1982
[5]

A. A. Starobinsky, JETP Lett.30, 682 (1979)

work page 1979
[6]

V. F. Mukhanov and G. V. Chibisov, JETP Lett.33, 532 (1981)

work page 1981
[7]

S. W. Hawking, Phys. Lett. B115, 295 (1982)

work page 1982
[8]

A. A. Starobinsky, Phys. Lett. B117, 175 (1982)

work page 1982
[9]

A. H. Guth and S. Y. Pi, Phys. Rev. Lett.49, 1110 (1982)

work page 1982
[10]

J. M. Bardeen, P. J. Steinhardt, and M. S. Turner, Phys. Rev. D28, 679 (1983)

work page 1983
[11]

Planck 2018 results. X. Constraints on inflation

Y. Akrami et al. (Planck), Astron. Astrophys.641, A10 (2020), arXiv:1807.06211 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2020
[12]

P. A. R. Ade et al. (BICEP, Keck), Phys. Rev. Lett.127, 151301 (2021), arXiv:2110.00483 [astro-ph.CO]

work page arXiv 2021
[13]

The Atacama Cosmology Telescope: DR6 Constraints on Extended Cosmological Models

E. Calabrese et al. (Atacama Cosmology Telescope), JCAP11, 063 (2025), arXiv:2503.14454 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2025
[14]

L˚ angvik, J.-M

M. Langvik, J.-M. Ojanpera, S. Raatikainen, and S. Rasanen, Phys. Rev. D103, 083514 (2021), arXiv:2007.12595 [astro-ph.CO]

work page arXiv 2021
[15]

Shaposhnikov, A

M. Shaposhnikov, A. Shkerin, I. Timiryasov, and S. Zell, JCAP02, 008 (2021), [Erratum: JCAP 10, E01 (2021)], arXiv:2007.14978 [hep-ph]

work page arXiv 2021
[16]

Piani and J

M. Piani and J. Rubio, JCAP05, 009 (2022), arXiv:2202.04665 [gr-qc]

work page arXiv 2022
[17]

Pradisi and A

G. Pradisi and A. Salvio, Eur. Phys. J. C82, 840 (2022), arXiv:2206.15041 [hep-th]

work page arXiv 2022
[18]

Salvio,Inflating and reheating the Universe with an independent affine connection,Phys

A. Salvio, Phys. Rev. D106, 103510 (2022), arXiv:2207.08830 [hep-ph]. 5 Recent developments suggest that artificial intelligence based ap- proaches can also play a role in systematically exploring the land- scape of inflationary models and identifying viable scenarios con- sistent with observational data, see e.g. [62]

work page arXiv 2022
[19]

I. D. Gialamas and K. Tamvakis, JCAP03, 042 (2023), arXiv:2212.09896 [gr-qc]

work page arXiv 2023
[20]

Piani and J

M. Piani and J. Rubio, JCAP12, 002 (2023), arXiv:2304.13056 [hep-ph]

work page arXiv 2023
[21]

I. D. Gialamas and H. Veerm¨ ae, Phys. Lett. B844, 138109 (2023), arXiv:2305.07693 [hep-th]

work page arXiv 2023
[22]

Di Marco, E

A. Di Marco, E. Orazi, and G. Pradisi, Eur. Phys. J. C 84, 146 (2024), arXiv:2309.11345 [hep-th]

work page arXiv 2024
[23]

M. He, M. Hong, and K. Mukaida, JCAP05, 107 (2024), arXiv:2402.05358 [gr-qc]

work page arXiv 2024
[24]

Racioppi and A

A. Racioppi and A. Salvio, JCAP06, 033 (2024), arXiv:2403.18004 [hep-ph]

work page arXiv 2024
[25]

Inagaki and N

T. Inagaki and N. Yoshioka, Phys. Rev. D110, 103537 (2024), arXiv:2406.14982 [gr-qc]

work page arXiv 2024
[26]

I. D. Gialamas and K. Tamvakis, Phys. Rev. D111, 044007 (2025), arXiv:2410.16364 [gr-qc]

work page arXiv 2025
[27]

Racioppi, ˜ξ-attractors in metric-affine gravity,JCAP04(2025) 084 [2411.08031]

A. Racioppi, JCAP04, 084 (2025), [Erratum: JCAP 08, E01 (2025)], arXiv:2411.08031 [gr-qc]

work page arXiv 2025
[28]

I. D. Gialamas and A. Racioppi, JCAP05, 072 (2025), arXiv:2412.17738 [gr-qc]

work page arXiv 2025
[29]

G. K. Karananas, Phys. Lett. B862, 139343 (2025), arXiv:2501.16416 [gr-qc]

work page arXiv 2025
[30]

Katsoulas and K

T. Katsoulas and K. Tamvakis, JCAP06, 022 (2025), arXiv:2502.16980 [gr-qc]

work page arXiv 2025
[31]

I. D. Gialamas and K. Tamvakis, Phys. Rev. D112, 084051 (2025), arXiv:2503.16598 [hep-th]

work page arXiv 2025
[32]

Salvio, (2025), arXiv:2504.10488 [hep-ph]

A. Salvio, Phys. Rev. D112, L061301 (2025), arXiv:2504.10488 [hep-ph]

work page arXiv 2025
[33]

I. D. Gialamas, T. Katsoulas, and K. Tamvakis, Phys. Rev. D112, 9 (2025), arXiv:2506.02159 [hep-th]

work page arXiv 2025
[34]

Iosifidis, Phys

D. Iosifidis, Phys. Lett. B868, 139705 (2025), arXiv:2506.04738 [gr-qc]

work page arXiv 2025
[35]

G. K. Karananas, M. Shaposhnikov, and S. Zell, Phys. Lett. B873, 140151 (2026), arXiv:2507.15927 [hep-ph]

work page arXiv 2026
[36]

G. K. Karananas and M. Shaposhnikov, (2025), arXiv:2511.04732 [hep-ph]

work page arXiv 2025
[37]

Katsoulas and K

T. Katsoulas and K. Tamvakis, (2025), arXiv:2512.02847 [gr-qc]. 9

work page internal anchor Pith review arXiv 2025
[38]

Inﬂation in light of ACT/SPT: a new perspective from Weyl grav- ity, 12 2025

Q.-Y. Wang, (2025), arXiv:2512.10862 [astro-ph.CO]

work page arXiv 2025
[39]

Quasi-pole inflation in metric-affine gravity

A. Racioppi, (2025), arXiv:2512.16815 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2025
[40]

A. R. Liddle and S. M. Leach, Phys. Rev. D68, 103503 (2003), arXiv:astro-ph/0305263

work page internal anchor Pith review Pith/arXiv arXiv 2003
[41]

A Horizon Ratio Bound for Inflationary Fluctuations

S. Dodelson and L. Hui, Phys. Rev. Lett.91, 131301 (2003), arXiv:astro-ph/0305113

work page internal anchor Pith review Pith/arXiv arXiv 2003
[42]

First CMB Constraints on the Inflationary Reheating Temperature

J. Martin and C. Ringeval, Phys. Rev. D82, 023511 (2010), arXiv:1004.5525 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2010
[43]

L. Dai, M. Kamionkowski, and J. Wang, Phys. Rev. Lett. 113, 041302 (2014), arXiv:1404.6704 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[44]

J. B. Munoz and M. Kamionkowski, Phys. Rev. D91, 043521 (2015), arXiv:1412.0656 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[45]

J. L. Cook, E. Dimastrogiovanni, D. A. Easson, and L. M. Krauss, JCAP04, 047 (2015), arXiv:1502.04673 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[46]

K. D. Lozanov and M. A. Amin, Phys. Rev. D97, 023533 (2018), arXiv:1710.06851 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[47]

I. D. Gialamas and A. B. Lahanas, Phys. Rev. D101, 084007 (2020), arXiv:1911.11513 [gr-qc]

work page arXiv 2020
[48]

A. B. Lahanas, Phys. Rev. D106, 123530 (2022), arXiv:2210.00837 [gr-qc]

work page arXiv 2022
[49]

A. A. Starobinsky, Phys. Lett.B91, 99 (1980)

work page 1980
[50]

K. S. Stelle, Phys. Rev. D16, 953 (1977)

work page 1977
[51]

A universal attractor for inflation at strong coupling

R. Kallosh, A. Linde, and D. Roest, Phys. Rev. Lett. 112, 011303 (2014), arXiv:1310.3950 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[52]

The Unity of Cosmological Attractors

M. Galante, R. Kallosh, A. Linde, and D. Roest, Phys. Rev. Lett.114, 141302 (2015), arXiv:1412.3797 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[53]

Drees and Y

M. Drees and Y. Xu, Phys. Lett. B867, 139612 (2025), arXiv:2504.20757 [astro-ph.CO]

work page arXiv 2025
[54]

D. S. Zharov, O. O. Sobol, and S. I. Vilchinskii, Phys. Rev. D112, 023544 (2025)

work page 2025
[55]

Antoniadis, J

I. Antoniadis, J. Ellis, W. Ke, D. V. Nanopoulos, and K. A. Olive, JCAP08, 090 (2025), arXiv:2504.12283 [hep-ph]

work page arXiv 2025
[56]

In: 2025

J. Ellis, M. A. G. Garcia, K. A. Olive, and S. Verner, Phys. Rev. D113, 063571 (2026), arXiv:2510.18656 [hep- ph]

work page arXiv 2026
[57]

J. Kim, X. Wang, Y.-l. Zhang, and Z. Ren, JCAP09, 011 (2025), arXiv:2504.12035 [astro-ph.CO]

work page arXiv 2025
[58]

I. D. Gialamas, T. Katsoulas, and K. Tamvakis, JCAP 09, 060 (2025), arXiv:2505.03608 [gr-qc]

work page arXiv 2025
[59]

Curvature corrections to Starobinsky inflation can explain the ACT results,

A. Addazi, Y. Aldabergenov, and S. V. Ketov, Phys. Lett. B869, 139883 (2025), arXiv:2505.10305 [gr-qc]

work page arXiv 2025
[60]

S. V. Ketov, E. O. Pozdeeva, and S. Y. Vernov, JCAP 12, 040 (2025), arXiv:2508.08927 [gr-qc]

work page arXiv 2025
[61]

Effects of Radiative Corrections on Starobinsky Inflation,

J. Ellis, T. Gherghetta, K. Kaneta, W. Ke, and K. A. Olive, Phys. Rev. D112, 123530 (2025), arXiv:2510.15137 [hep-ph]

work page arXiv 2025
[62]

Peng, H.-S

Z.-Y. Peng, H.-S. Yuan, Q. Lai, J.-Q. Jiang, G. Ye, J. Zhang, and Y.-S. Piao, (2026), arXiv:2601.14288 [astro-ph.CO]

work page arXiv 2026
[63]

SPIDER: CMB polarimetry from the edge of space

R. Gualtieri et al. (SPIDER), J. Low Temp. Phys.193, 1112 (2018), arXiv:1711.10596 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[64]

The Simons Observatory: Science goals and forecasts

P. Ade et al. (Simons Observatory), JCAP02, 056 (2019), arXiv:1808.07445 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[65]

Mission design of LiteBIRD

T. Matsumura et al., (2013), 10.1007/s10909-013-0996- 1, [J. Low. Temp. Phys.176,733(2014)], arXiv:1311.2847 [astro-ph.IM]

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/s10909-013-0996- 2013

[1] [1]

Kazanas, Astrophys

D. Kazanas, Astrophys. J. Lett.241, L59 (1980)

work page 1980

[2] [2]

Sato, Mon.Not.Roy.Astron.Soc.195, 467 (1981)

K. Sato, Mon.Not.Roy.Astron.Soc.195, 467 (1981)

work page 1981

[3] [3]

A. H. Guth, Phys.Rev.D23, 347 (1981)

work page 1981

[4] [4]

A. D. Linde, Phys.Lett.B108, 389 (1982)

work page 1982

[5] [5]

A. A. Starobinsky, JETP Lett.30, 682 (1979)

work page 1979

[6] [6]

V. F. Mukhanov and G. V. Chibisov, JETP Lett.33, 532 (1981)

work page 1981

[7] [7]

S. W. Hawking, Phys. Lett. B115, 295 (1982)

work page 1982

[8] [8]

A. A. Starobinsky, Phys. Lett. B117, 175 (1982)

work page 1982

[9] [9]

A. H. Guth and S. Y. Pi, Phys. Rev. Lett.49, 1110 (1982)

work page 1982

[10] [10]

J. M. Bardeen, P. J. Steinhardt, and M. S. Turner, Phys. Rev. D28, 679 (1983)

work page 1983

[11] [11]

Planck 2018 results. X. Constraints on inflation

Y. Akrami et al. (Planck), Astron. Astrophys.641, A10 (2020), arXiv:1807.06211 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2020

[12] [12]

P. A. R. Ade et al. (BICEP, Keck), Phys. Rev. Lett.127, 151301 (2021), arXiv:2110.00483 [astro-ph.CO]

work page arXiv 2021

[13] [13]

The Atacama Cosmology Telescope: DR6 Constraints on Extended Cosmological Models

E. Calabrese et al. (Atacama Cosmology Telescope), JCAP11, 063 (2025), arXiv:2503.14454 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2025

[14] [14]

L˚ angvik, J.-M

M. Langvik, J.-M. Ojanpera, S. Raatikainen, and S. Rasanen, Phys. Rev. D103, 083514 (2021), arXiv:2007.12595 [astro-ph.CO]

work page arXiv 2021

[15] [15]

Shaposhnikov, A

M. Shaposhnikov, A. Shkerin, I. Timiryasov, and S. Zell, JCAP02, 008 (2021), [Erratum: JCAP 10, E01 (2021)], arXiv:2007.14978 [hep-ph]

work page arXiv 2021

[16] [16]

Piani and J

M. Piani and J. Rubio, JCAP05, 009 (2022), arXiv:2202.04665 [gr-qc]

work page arXiv 2022

[17] [17]

Pradisi and A

G. Pradisi and A. Salvio, Eur. Phys. J. C82, 840 (2022), arXiv:2206.15041 [hep-th]

work page arXiv 2022

[18] [18]

Salvio,Inflating and reheating the Universe with an independent affine connection,Phys

A. Salvio, Phys. Rev. D106, 103510 (2022), arXiv:2207.08830 [hep-ph]. 5 Recent developments suggest that artificial intelligence based ap- proaches can also play a role in systematically exploring the land- scape of inflationary models and identifying viable scenarios con- sistent with observational data, see e.g. [62]

work page arXiv 2022

[19] [19]

I. D. Gialamas and K. Tamvakis, JCAP03, 042 (2023), arXiv:2212.09896 [gr-qc]

work page arXiv 2023

[20] [20]

Piani and J

M. Piani and J. Rubio, JCAP12, 002 (2023), arXiv:2304.13056 [hep-ph]

work page arXiv 2023

[21] [21]

I. D. Gialamas and H. Veerm¨ ae, Phys. Lett. B844, 138109 (2023), arXiv:2305.07693 [hep-th]

work page arXiv 2023

[22] [22]

Di Marco, E

A. Di Marco, E. Orazi, and G. Pradisi, Eur. Phys. J. C 84, 146 (2024), arXiv:2309.11345 [hep-th]

work page arXiv 2024

[23] [23]

M. He, M. Hong, and K. Mukaida, JCAP05, 107 (2024), arXiv:2402.05358 [gr-qc]

work page arXiv 2024

[24] [24]

Racioppi and A

A. Racioppi and A. Salvio, JCAP06, 033 (2024), arXiv:2403.18004 [hep-ph]

work page arXiv 2024

[25] [25]

Inagaki and N

T. Inagaki and N. Yoshioka, Phys. Rev. D110, 103537 (2024), arXiv:2406.14982 [gr-qc]

work page arXiv 2024

[26] [26]

I. D. Gialamas and K. Tamvakis, Phys. Rev. D111, 044007 (2025), arXiv:2410.16364 [gr-qc]

work page arXiv 2025

[27] [27]

Racioppi, ˜ξ-attractors in metric-affine gravity,JCAP04(2025) 084 [2411.08031]

A. Racioppi, JCAP04, 084 (2025), [Erratum: JCAP 08, E01 (2025)], arXiv:2411.08031 [gr-qc]

work page arXiv 2025

[28] [28]

I. D. Gialamas and A. Racioppi, JCAP05, 072 (2025), arXiv:2412.17738 [gr-qc]

work page arXiv 2025

[29] [29]

G. K. Karananas, Phys. Lett. B862, 139343 (2025), arXiv:2501.16416 [gr-qc]

work page arXiv 2025

[30] [30]

Katsoulas and K

T. Katsoulas and K. Tamvakis, JCAP06, 022 (2025), arXiv:2502.16980 [gr-qc]

work page arXiv 2025

[31] [31]

I. D. Gialamas and K. Tamvakis, Phys. Rev. D112, 084051 (2025), arXiv:2503.16598 [hep-th]

work page arXiv 2025

[32] [32]

Salvio, (2025), arXiv:2504.10488 [hep-ph]

A. Salvio, Phys. Rev. D112, L061301 (2025), arXiv:2504.10488 [hep-ph]

work page arXiv 2025

[33] [33]

I. D. Gialamas, T. Katsoulas, and K. Tamvakis, Phys. Rev. D112, 9 (2025), arXiv:2506.02159 [hep-th]

work page arXiv 2025

[34] [34]

Iosifidis, Phys

D. Iosifidis, Phys. Lett. B868, 139705 (2025), arXiv:2506.04738 [gr-qc]

work page arXiv 2025

[35] [35]

G. K. Karananas, M. Shaposhnikov, and S. Zell, Phys. Lett. B873, 140151 (2026), arXiv:2507.15927 [hep-ph]

work page arXiv 2026

[36] [36]

G. K. Karananas and M. Shaposhnikov, (2025), arXiv:2511.04732 [hep-ph]

work page arXiv 2025

[37] [37]

Katsoulas and K

T. Katsoulas and K. Tamvakis, (2025), arXiv:2512.02847 [gr-qc]. 9

work page internal anchor Pith review arXiv 2025

[38] [38]

Inﬂation in light of ACT/SPT: a new perspective from Weyl grav- ity, 12 2025

Q.-Y. Wang, (2025), arXiv:2512.10862 [astro-ph.CO]

work page arXiv 2025

[39] [39]

Quasi-pole inflation in metric-affine gravity

A. Racioppi, (2025), arXiv:2512.16815 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2025

[40] [40]

A. R. Liddle and S. M. Leach, Phys. Rev. D68, 103503 (2003), arXiv:astro-ph/0305263

work page internal anchor Pith review Pith/arXiv arXiv 2003

[41] [41]

A Horizon Ratio Bound for Inflationary Fluctuations

S. Dodelson and L. Hui, Phys. Rev. Lett.91, 131301 (2003), arXiv:astro-ph/0305113

work page internal anchor Pith review Pith/arXiv arXiv 2003

[42] [42]

First CMB Constraints on the Inflationary Reheating Temperature

J. Martin and C. Ringeval, Phys. Rev. D82, 023511 (2010), arXiv:1004.5525 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2010

[43] [43]

L. Dai, M. Kamionkowski, and J. Wang, Phys. Rev. Lett. 113, 041302 (2014), arXiv:1404.6704 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2014

[44] [44]

J. B. Munoz and M. Kamionkowski, Phys. Rev. D91, 043521 (2015), arXiv:1412.0656 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2015

[45] [45]

J. L. Cook, E. Dimastrogiovanni, D. A. Easson, and L. M. Krauss, JCAP04, 047 (2015), arXiv:1502.04673 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2015

[46] [46]

K. D. Lozanov and M. A. Amin, Phys. Rev. D97, 023533 (2018), arXiv:1710.06851 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2018

[47] [47]

I. D. Gialamas and A. B. Lahanas, Phys. Rev. D101, 084007 (2020), arXiv:1911.11513 [gr-qc]

work page arXiv 2020

[48] [48]

A. B. Lahanas, Phys. Rev. D106, 123530 (2022), arXiv:2210.00837 [gr-qc]

work page arXiv 2022

[49] [49]

A. A. Starobinsky, Phys. Lett.B91, 99 (1980)

work page 1980

[50] [50]

K. S. Stelle, Phys. Rev. D16, 953 (1977)

work page 1977

[51] [51]

A universal attractor for inflation at strong coupling

R. Kallosh, A. Linde, and D. Roest, Phys. Rev. Lett. 112, 011303 (2014), arXiv:1310.3950 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 2014

[52] [52]

The Unity of Cosmological Attractors

M. Galante, R. Kallosh, A. Linde, and D. Roest, Phys. Rev. Lett.114, 141302 (2015), arXiv:1412.3797 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 2015

[53] [53]

Drees and Y

M. Drees and Y. Xu, Phys. Lett. B867, 139612 (2025), arXiv:2504.20757 [astro-ph.CO]

work page arXiv 2025

[54] [54]

D. S. Zharov, O. O. Sobol, and S. I. Vilchinskii, Phys. Rev. D112, 023544 (2025)

work page 2025

[55] [55]

Antoniadis, J

I. Antoniadis, J. Ellis, W. Ke, D. V. Nanopoulos, and K. A. Olive, JCAP08, 090 (2025), arXiv:2504.12283 [hep-ph]

work page arXiv 2025

[56] [56]

In: 2025

J. Ellis, M. A. G. Garcia, K. A. Olive, and S. Verner, Phys. Rev. D113, 063571 (2026), arXiv:2510.18656 [hep- ph]

work page arXiv 2026

[57] [57]

J. Kim, X. Wang, Y.-l. Zhang, and Z. Ren, JCAP09, 011 (2025), arXiv:2504.12035 [astro-ph.CO]

work page arXiv 2025

[58] [58]

I. D. Gialamas, T. Katsoulas, and K. Tamvakis, JCAP 09, 060 (2025), arXiv:2505.03608 [gr-qc]

work page arXiv 2025

[59] [59]

Curvature corrections to Starobinsky inflation can explain the ACT results,

A. Addazi, Y. Aldabergenov, and S. V. Ketov, Phys. Lett. B869, 139883 (2025), arXiv:2505.10305 [gr-qc]

work page arXiv 2025

[60] [60]

S. V. Ketov, E. O. Pozdeeva, and S. Y. Vernov, JCAP 12, 040 (2025), arXiv:2508.08927 [gr-qc]

work page arXiv 2025

[61] [61]

Effects of Radiative Corrections on Starobinsky Inflation,

J. Ellis, T. Gherghetta, K. Kaneta, W. Ke, and K. A. Olive, Phys. Rev. D112, 123530 (2025), arXiv:2510.15137 [hep-ph]

work page arXiv 2025

[62] [62]

Peng, H.-S

Z.-Y. Peng, H.-S. Yuan, Q. Lai, J.-Q. Jiang, G. Ye, J. Zhang, and Y.-S. Piao, (2026), arXiv:2601.14288 [astro-ph.CO]

work page arXiv 2026

[63] [63]

SPIDER: CMB polarimetry from the edge of space

R. Gualtieri et al. (SPIDER), J. Low Temp. Phys.193, 1112 (2018), arXiv:1711.10596 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2018

[64] [64]

The Simons Observatory: Science goals and forecasts

P. Ade et al. (Simons Observatory), JCAP02, 056 (2019), arXiv:1808.07445 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2019

[65] [65]

Mission design of LiteBIRD

T. Matsumura et al., (2013), 10.1007/s10909-013-0996- 1, [J. Low. Temp. Phys.176,733(2014)], arXiv:1311.2847 [astro-ph.IM]

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/s10909-013-0996- 2013