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arxiv: 2511.06453 · v2 · pith:FBYFUKY2new · submitted 2025-11-09 · 🌀 gr-qc · hep-th

Inflationary models in a minimally coupled f(R,T) gravity: Constraints from Planck, BICEP/Keck, and ACT

Biswajit Deb , Atri Deshamukhya This is my paper

Pith reviewed 2026-05-25 07:13 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords inflationf(R,T) gravitymodified gravityspectral indextensor-to-scalar ratioPlanck constraintsBICEP/Keck
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0 comments X

The pith

In minimally coupled f(R,T) gravity, mutated hilltop, D-brane and Woods-Saxon inflation models produce ns and r values inside current observational bounds for suitable parameter choices.

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

The paper examines three inflationary potentials inside the specific f(R,T) model f(R,T) = R + 16πG λ T. It computes the scalar spectral index ns, tensor-to-scalar ratio r and running nsk from the slow-roll parameters for each potential and plots their trajectories in the ns-r plane. Comparison with Planck 2018, BICEP/Keck 2018, DESI DR2 and ACT DR6 data shows that intervals of the coupling λ and the potential parameters place the predictions inside the allowed regions. A reader cares because the extra freedom in λ revives models that standard gravity has already ruled out, thereby enlarging the set of observationally consistent early-universe scenarios without adding new scalar fields.

Core claim

For a certain model parameter space, the mutated hilltop, D-brane and Woods-Saxon potentials in the theory f(R,T) = R + 16πG λ T yield values of ns, r and nsk that lie within the joint constraints from Planck, BICEP/Keck, DESI DR2 and ACT DR6.

What carries the argument

The linear minimally coupled term f(R,T) = R + 16πG λ T, which modifies the Friedmann equation and thereby shifts the slow-roll parameters that determine ns and r.

If this is right

  • These three potentials become viable inflationary candidates under present data.
  • The coupling parameter λ supplies an extra tuning knob that moves the predicted (ns, r) points into the observationally allowed region.
  • The running nsk is also predicted and can be tested by future surveys.
  • Tighter upper limits on r from LiteBIRD or CMB-S4 will shrink the allowed intervals of λ for each model.

Where Pith is reading between the lines

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

  • If the f(R,T) term introduces extra corrections to the perturbation equations, the power-spectrum formulas used here would need re-derivation.
  • The same λ-dependent rescue mechanism could be checked for other potentials already excluded in general relativity.
  • Bounds on λ obtained from inflation could be cross-checked against late-time cosmological constraints in the identical f(R,T) theory.

Load-bearing premise

The standard slow-roll formulas for the power spectra and the derived expressions for ns, r and nsk remain unchanged once the f(R,T) coupling is added.

What would settle it

A future measurement of the tensor-to-scalar ratio r that lies below the lowest value any of the three models can reach for any allowed λ would falsify the viability claim.

Figures

Figures reproduced from arXiv: 2511.06453 by Atri Deshamukhya, Biswajit Deb.

Figure 1
Figure 1. Figure 1: The ns − r plot predicted by the mutated hilltop potential. The marginalized joint 68% and 95% C.L. regions for ns and r at k = 0.002Mpc−1 from Planck 2018 data are shown in blue and pink colour where as for Planck+BK18 are shown in orange and green respectively. ηV = M2 P lτ 2 [sech3 (τϕ) − sech (τϕ) tanh2 τϕ] (1 + 2λ)[1 − sech (τϕ)] (3.3) ξ 2 V = M4 P lτ 4 coth2 ( τϕ 2 ) sech4 (τϕ)[cosh (2τϕ) − 1] 2(1 + … view at source ↗
Figure 2
Figure 2. Figure 2: The ns −r trajectory predicted by the KKLT potential at 60 e-folding. The marginalized joint 68% and 95% C.L. regions for ns and r at k = 0.002M pc−1 from Planck 2018 data are shown in blue and pink colour where as for Planck+BK18 are shown in orange and green respectively. 3.3 Woods-Saxon Inflation Wood-Saxon inflation is based on a potential that was originally used to describe the nuclear force experien… view at source ↗
Figure 3
Figure 3. Figure 3: The ns − r trajectory predicted by the Woods-Saxon potential at 60 e-folding. The marginalized joint 68% and 95% C.L. regions for ns and r at k = 0.002M pc−1 from Planck 2018 data are shown in blue and pink colour where as for Planck+BK18 are shown in orange and green respectively. Inflationary Model Fixed Parameter λ ns r nsk KKLT (n = 2) m = 0.5 310 0.9690 0.048 −5.36 × 10−4 KKLT (n = 2) m = 5 3 0.9688 0… view at source ↗
Figure 4
Figure 4. Figure 4: The ns−r trajectory predicted by the mutated hilltop potential, KKLT (n = 2, m = 0.5), KKLT (n = 4, m = 0.5), Woods-Saxon potential (b = 0.001, c = −5) at 60 e-folding are shown in red, black, blue, and green colour respectively. The marginalized joint 68% and 95% C.L. regions for ns and r at k = 0.002M pc−1 from the combined P-ACT-LB-BK18 data are shown in purple and orange colour. 4 Conclusion Its been f… view at source ↗
read the original abstract

The advent of high-precision cosmological observations has challenged many traditional inflationary models. Data from $Planck$ 2018 along with the BICEP/$Keck$ 2018 result have already ruled out most of the established models by placing tight constraints on the tensor-to-scalar ratio $r$. Upcoming missions like LiteBIRD & CMB-S4 are expected to impose an even more stringent bound on $r$, potentially excluding further models from the viable landscape. In this evolving observational context, modified gravity theories offer a promising way to reconcile inflationary models with data. In this work, we explore several inflationary models, namely mutated hilltop inflation, D-brane inflation, and Woods-Saxon inflation, within the framework of $f(R,T)$ gravity. A minimally coupled and linear combination of Ricci scalar and trace of EM tensor is considered as $f(R,T)=R+16\pi G \lambda T$ and the cosmological observable parameters, viz. scalar spectral tilt $n_s$, tensor-to-scalar ratio $r$, and running of scalar spectral index $n_{sk}$ are estimated for the three models, and their trajectories are plotted in the $n_s-r$ plane. The model results are evaluated in light of the $Planck$, BICEP/$Keck$, DESI DR2, and ACT DR6 data. We observe that for a certain model parameter space, these potentials are viable within the current observational bounds.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript examines three inflationary potentials (mutated hilltop, D-brane, and Woods-Saxon) in minimally coupled f(R,T) gravity with the specific form f(R,T)=R+16πGλT. It computes the observables ns, r, and nsk from the chosen potentials, plots the resulting trajectories in the ns-r plane, and reports that certain ranges of the potential parameters and the coupling λ place the models inside the observational windows from Planck 2018, BICEP/Keck 2018, DESI DR2, and ACT DR6.

Significance. If the slow-roll expressions remain unmodified by the trace coupling, the work would show that the linear T term can enlarge the viable parameter space for these potentials relative to general relativity, thereby illustrating one concrete way modified gravity can accommodate models otherwise under pressure from tightening r bounds. The use of the most recent ACT DR6 and DESI data adds timely observational context.

major comments (2)
  1. [results and observables computation] The estimation of ns, r, and nsk (throughout the results section and the ns-r trajectories): the manuscript employs the standard GR slow-roll relations ns=1−6ε+2η, r=16ε, and the usual expression for nsk without deriving the modified background Friedmann equation H²=(8πG/3)[ρ+λ(ρ−3p)] or the corrected Mukhanov-Sasaki equation that arises once the λT term is present. This assumption is load-bearing for the central viability claim.
  2. [discussion of viability] Parameter-space selection for viability: the abstract and results state that the models are viable “for a certain model parameter space,” yet no independent motivation or prior constraints on λ and the potential parameters are supplied before the observational comparison; the reported compatibility therefore reduces to the existence of fitted values inside the data window.
minor comments (2)
  1. Clarify whether the f(R,T) model is minimally coupled in the usual sense or whether the trace term introduces an effective non-minimal coupling at the level of the action.
  2. Explicitly list the functional forms and free parameters of the three potentials (mutated hilltop, D-brane, Woods-Saxon) in a dedicated subsection or table for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review. We respond point-by-point to the major comments below, agreeing where revisions are needed and providing the strongest honest defense of our approach.

read point-by-point responses

  1. Referee: [results and observables computation] The estimation of ns, r, and nsk (throughout the results section and the ns-r trajectories): the manuscript employs the standard GR slow-roll relations ns=1−6ε+2η, r=16ε, and the usual expression for nsk without deriving the modified background Friedmann equation H²=(8πG/3)[ρ+λ(ρ−3p)] or the corrected Mukhanov-Sasaki equation that arises once the λT term is present. This assumption is load-bearing for the central viability claim.

    Authors: We agree that explicit derivation of the modified equations is required to support the central claim. For the specific linear form f(R,T)=R+16πGλT, the background equation is H²=(8πG/3)[ρ+λ(ρ−3p)]. In the slow-roll regime where the inflaton potential dominates and p≈−ρ, this reduces to an overall rescaling of the effective gravitational strength (or equivalently of V), which leaves the definitions of the Hubble slow-roll parameters ε=−Ḣ/H² and η=Ḧ/(2HḢ) unchanged in form when expressed via the potential. Consequently the standard expressions for ns, r and nsk remain valid. We will add a dedicated section (or appendix) deriving both the background and the Mukhanov-Sasaki equations to demonstrate this explicitly and remove any ambiguity. revision: yes

  2. Referee: [discussion of viability] Parameter-space selection for viability: the abstract and results state that the models are viable “for a certain model parameter space,” yet no independent motivation or prior constraints on λ and the potential parameters are supplied before the observational comparison; the reported compatibility therefore reduces to the existence of fitted values inside the data window.

    Authors: We accept that the manuscript would benefit from clearer framing. The coupling λ is a free parameter of the f(R,T) theory, and the potential parameters are varied within their natural ranges. The central result is precisely that the λT term enlarges the viable region relative to GR, allowing these three potentials to satisfy the combined Planck+BICEP/Keck+DESI+ACT constraints for suitable (λ, potential-parameter) choices. We will revise the abstract, introduction and discussion to state this motivation explicitly, note that λ has no a-priori observational prior in the present context, and emphasize that the exercise demonstrates the existence of viable parameter space in the extended theory rather than a unique prediction. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard parameter-space constraints

full rationale

The paper selects potentials, adopts the linear f(R,T) form, and reports ranges of the potential parameters plus λ for which the usual slow-roll expressions for ns, r, and nsk lie inside current observational windows. This is ordinary model fitting against external data; the viability statement does not reduce any derived quantity to its own inputs by construction. No self-citation chain, no fitted parameter relabeled as a prediction, and no uniqueness theorem invoked. The assumption that standard slow-roll formulas remain unmodified is an explicit modeling choice, not an internal loop.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the slow-roll formulas inside the chosen f(R,T) action and on the freedom to adjust λ together with the potential parameters until the observables fall inside the allowed region.

free parameters (2)
  • λ
    Dimensionless coupling strength in the linear f(R,T) term; its value is chosen so that the resulting ns and r satisfy observational bounds.
  • potential parameters
    Shape parameters inside each of the three inflationary potentials; adjusted per model to place trajectories inside the ns-r allowed region.
axioms (2)
  • domain assumption Slow-roll approximation remains valid and unmodified by the f(R,T) term
    Invoked when mapping the potentials to the observables ns, r, nsk.
  • ad hoc to paper f(R,T) = R + 16πG λ T is an adequate effective description
    Chosen as the minimally coupled linear combination without further justification from a fundamental theory.

pith-pipeline@v0.9.0 · 5806 in / 1612 out tokens · 36130 ms · 2026-05-25T07:13:38.491809+00:00 · methodology

discussion (0)

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Forward citations

Cited by 2 Pith papers

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  1. Positive Running of the Spectral Index for Scalar Theory and Modified Gravity

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    Positive running of the spectral index is achievable in Einstein-Gauss-Bonnet gravity with viable inflation, unlike standard scalar field and F(R) models which face challenges.

  2. String-inspired Gauss-Bonnet Gravity Inflation and ACT

    gr-qc 2026-04 unverdicted novelty 4.0

    MCMC analysis of sixteen ghost-free f(R,G) inflation models shows all reproduce ns ≈ 0.97 at 60 e-folds with stable μ ≈ 0.1, preference set by Hubble parametrization.

Reference graph

Works this paper leans on

74 extracted references · 74 canonical work pages · cited by 2 Pith papers · 18 internal anchors

  1. [1]

    Inflationary universe: A possible solution to the horizon and flatness problems

    Alan H Guth. Inflationary universe: A possible solution to the horizon and flatness problems. In:Phys. Rev. D232 1981, p. 347

    work page 1981

  2. [2]

    A new inflationary universe scenario: a possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems

    Andrei D Linde. A new inflationary universe scenario: a possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems. In:Phys. Lett. B1086 1982, pp. 389–393

    work page 1982

  3. [3]

    Generation of density perturbations in inflationary cosmology

    Lev Abramovič Kofman and Andrei D Linde. Generation of density perturbations in inflationary cosmology. In:Nucl. Phys. B282 1987, pp. 555–588

    work page 1987

  4. [4]

    Particle Physics Models of Inflation and the Cosmological Density Perturbation

    David H. Lyth and Antonio Riotto. Particle physics models of inflation and the cosmological density perturbation. In:Phys. Rept.314 1999, pp. 1–146.doi:10.1016/S0370- 1573(98)00128- 8. arXiv: hep-ph/9807278

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/s0370- 1999

  5. [5]

    TASI Lectures on Inflation

    Daniel Baumann. “Inflation”. In:Theoretical Advanced Study Institute in Elementary Particle Physics: Physics of the Large and the Small. 2011, pp. 523–686.doi:10.1142/9789814327183_0010. arXiv: 0907.5424 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1142/9789814327183_0010 2011

  6. [6]

    Piattella.Lecture Notes in Cosmology

    Oliver F. Piattella.Lecture Notes in Cosmology. UNITEXT for Physics. Cham: Springer, 2018.doi: 10.1007/978-3-319-95570-4. arXiv:1803.00070 [astro-ph.CO]

    work page doi:10.1007/978-3-319-95570-4 2018

  7. [7]

    Liddle and D

    Andrew R. Liddle and D. H. Lyth.Cosmological inflation and large scale structure. 2000.doi:10. 1017/CBO9781139175180

    work page 2000

  8. [8]

    Encyclopædia Inflationaris: Opiparous Edition

    Jerome Martin, Christophe Ringeval, and Vincent Vennin. Encyclopædia Inflationaris: Opiparous Edition. In:Phys. Dark Univ.5-6 2014, pp. 75–235.doi:10 . 1016 / j . dark . 2024 . 101653. arXiv: 1303.3787 [astro-ph.CO]

    work page arXiv 2014

  9. [9]

    Planck 2018 results. X. Constraints on inflation

    Y. Akrami et al. Planck 2018 results. X. Constraints on inflation. In:Astron. Astrophys.641 2020, A10.doi:10.1051/0004-6361/201833887. arXiv:1807.06211 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201833887 2018

  10. [10]

    The Best Inflationary Models After Planck

    Jérôme Martin et al. The Best Inflationary Models After Planck. In:JCAP03 2014, p. 039.doi: 10.1088/1475-7516/2014/03/039. arXiv:1312.3529 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1475-7516/2014/03/039 2014

  11. [11]

    The Atacama Cosmology Telescope: DR6 Power Spectra, Likelihoods and $\Lambda$CDM Parameters

    Thibaut Louis et al. The Atacama Cosmology Telescope: DR6 Power Spectra, Likelihoods andΛCDM Parameters. In: 2025. arXiv:2503.14452 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  12. [12]

    The Atacama Cosmology Telescope: DR6 Constraints on Extended Cosmological Models

    Erminia Calabrese et al. The Atacama Cosmology Telescope: DR6 Constraints on Extended Cosmo- logical Models. In: 2025. arXiv:2503.14454 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  13. [13]

    Atacama Cosmology Telescope, South Pole Tele- scope, and Chaotic Inflation

    Renata Kallosh, Andrei Linde, and Diederik Roest. Atacama Cosmology Telescope, South Pole Tele- scope, and Chaotic Inflation. In:Phys. Rev. Lett.13516 2025, p. 161001.doi:10.1103/d6gn-78hn. arXiv:2503.21030 [hep-th]

    work page doi:10.1103/d6gn-78hn 2025

  14. [14]

    The early universe isACT-ingwarm

    Arjun Berera et al. The early universe isACT-ingwarm. In: 2025. arXiv:2504.02655 [hep-th]

    work page arXiv 2025

  15. [15]

    Supersymmetric hybrid inflation in light of the Atacama CosmologyTelescopedatarelease6,Planck2018,andLB-BK18.In:Phys

    Mansoor Ur Rehman and Qaisar Shafi. Supersymmetric hybrid inflation in light of the Atacama CosmologyTelescopedatarelease6,Planck2018,andLB-BK18.In:Phys. Rev. D11222025,p.023529. doi:10.1103/mwn8-rnsx. arXiv:2504.14831 [astro-ph.CO]

    work page doi:10.1103/mwn8-rnsx

  16. [16]

    Increase of ns in regularized pole inflation & Einstein- Cartan gravity

    Minxi He, Muzi Hong, and Kyohei Mukaida. Increase of ns in regularized pole inflation & Einstein- Cartan gravity. In:JCAP09 2025, p. 080.doi:10.1088/1475-7516/2025/09/080. arXiv:2504.16069 [astro-ph.CO]

    work page doi:10.1088/1475-7516/2025/09/080 2025

  17. [17]

    Refined predictions for Starobinsky inflation and post-inflationary con- straints in light of ACT

    Manuel Drees and Yong Xu. Refined predictions for Starobinsky inflation and post-inflationary con- straints in light of ACT. In:Phys. Lett. B867 2025, p. 139612.doi:10.1016/j.physletb.2025. 139612. arXiv:2504.20757 [astro-ph.CO]

    work page doi:10.1016/j.physletb.2025 2025

  18. [18]

    D. S. Zharov, O. O. Sobol, and S. I. Vilchinskii. Reheating ACTs on Starobinsky and Higgs inflation. In: 2025. arXiv:2505.01129 [astro-ph.CO]

    work page arXiv 2025

  19. [19]

    Reconciling Nonminimally Coupled Higgs Inflation with ACT DR6 Observations through Reheating

    Lang Liu, Zhu Yi, and Yungui Gong. Reconciling Higgs Inflation with ACT Observations through Reheating. In: 2025. arXiv:2505.02407 [astro-ph.CO]. 14

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  20. [20]

    Byrnes, Marina Cortês, and Andrew R

    Christian T. Byrnes, Marina Cortês, and Andrew R. Liddle. The curvaton ACTs again. In: 2025. arXiv: 2505.09682 [astro-ph.CO]

    work page arXiv 2025

  21. [21]

    Andrea Addazi, Yermek Aldabergenov, and Sergei V. Ketov. Curvature corrections to Starobinsky inflation can explain the ACT results. In:Phys. Lett. B869 2025, p. 139883.doi:10 . 1016 / j . physletb.2025.139883. arXiv:2505.10305 [gr-qc]

    work page arXiv 2025

  22. [22]

    The polynomial potential inflation in light of ACT observations

    Zhi-Zhang Peng, Zu-Cheng Chen, and Lang Liu. The polynomial potential inflation in light of ACT observations. In: 2025. arXiv:2505.12816 [astro-ph.CO]

    work page arXiv 2025

  23. [23]

    S. D. Odintsov and V. K. Oikonomou. GW170817 Viable Einstein-Gauss-Bonnet inflation compatible with the atacama cosmology telescope data. In:Phys. Lett. B868 2025, p. 139779.doi:10.1016/j. physletb.2025.139779. arXiv:2506.08193 [gr-qc]

    work page doi:10.1016/j 2025

  24. [24]

    Jumaniyozov, S

    Yigan Zhu et al. Inflationary Models with Gauss-Bonnet Coupling in Light of ACT Observations. In: Eur. Phys. J. C85 2025, p. 1227.doi:10.1140/epjc/s10052- 025- 14969- 2. arXiv:2508.09707 [astro-ph.CO]

    work page doi:10.1140/epjc/s10052- 2025

  25. [25]

    D. S. Zharov, O. O. Sobol, and S. I. Vilchinskii. ACT observations, reheating, and Starobinsky and Higgs inflation. In:Phys. Rev. D1122 2025, p. 023544.doi:10.1103/km3q-rm34

    work page doi:10.1103/km3q-rm34 2025

  26. [26]

    Observational constraints on inflationary models with non-minimally derivative cou- pling by ACT

    Qing Gao et al. Observational constraints on inflationary models with non-minimally derivative cou- pling by ACT. In:JCAP08 2025, p. 083.doi:10.1088/1475-7516/2025/08/083. arXiv:2506.18456 [gr-qc]

    work page doi:10.1088/1475-7516/2025/08/083 2025

  27. [27]

    Smooth hybrid inflation in light of ACT DR6 data

    Nobuchika Okada and Osamu Seto. Smooth hybrid inflation in light of ACT DR6 data. In:Phys. Rev. D1128 2025, p. 083549.doi:10.1103/y9s8-7b5b. arXiv:2506.15965 [hep-ph]

    work page doi:10.1103/y9s8-7b5b 2025

  28. [28]

    What new physics can we extract from inflation using the ACT DR6 and DESI DR2 Observations? In: 2025

    Sayantan Choudhury et al. What new physics can we extract from inflation using the ACT DR6 and DESI DR2 Observations? In: 2025. arXiv:2506.15407 [astro-ph.CO]

    work page arXiv 2025

  29. [29]

    In: 2025

    JohnEllisetal.ConstraintsonAttractorModelsofInflationandReheatingfromPlanck,BICEP/Keck, ACT DR6, and SPT-3G Data. In: 2025. arXiv:2510.18656 [hep-ph]

    work page arXiv 2025

  30. [30]

    Validation of NANOGrav 15-year data and ACT data by modified inflation in entropic cosmology

    Simone D’Onofrio, Sergei Odintsov, and Tanmoy Paul. Validation of NANOGrav 15-year data and ACT data by modified inflation in entropic cosmology. In: 2025. arXiv:2510.20484 [gr-qc]

    work page arXiv 2025

  31. [31]

    A. G. Adame et al. DESI 2024 VI: cosmological constraints from the measurements of baryon acoustic oscillations. In:JCAP02 2025, p. 021.doi:10.1088/1475-7516/2025/02/021. arXiv:2404.03002 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1475-7516/2025/02/021 2024

  32. [32]

    A. G. Adame et al. DESI 2024 III: baryon acoustic oscillations from galaxies and quasars. In:JCAP 04 2025, p. 012.doi:10.1088/1475-7516/2025/04/012. arXiv:2404.03000 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1475-7516/2025/04/012 2024

  33. [33]

    P. A. R. Ade et al. Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season. In:Phys. Rev. Lett.12715 2021, p. 151301.doi:10.1103/PhysRevLett.127.151301. arXiv:2110.00483 [astro-ph.CO]

    work page doi:10.1103/physrevlett.127.151301 2018

  34. [34]

    Shankaranarayanan and Joseph P

    S. Shankaranarayanan and Joseph P. Johnson. Modified theories of gravity: Why, how and what? In: Gen. Rel. Grav.545 2022, p. 44.doi:10.1007/s10714-022-02927-2. arXiv:2204.06533 [gr-qc]

    work page doi:10.1007/s10714-022-02927-2 2022

  35. [35]

    Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution

    S. Nojiri, S. D. Odintsov, and V. K. Oikonomou. Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution. In:Phys. Rept.692 2017, pp. 1–104.doi:10.1016/j.physrep. 2017.06.001. arXiv:1705.11098 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physrep 2017

  36. [36]

    Starobinsky

    Alexei A. Starobinsky. A New Type of Isotropic Cosmological Models Without Singularity. In:Phys. Lett. B91 1980. Ed. by I. M. Khalatnikov and V. P. Mineev, pp. 99–102.doi:10 . 1016 / 0370 - 2693(80)90670-X

    work page 1980

  37. [37]

    Non-minimalRTcoupling and its impact on inflationary evolution inf(R, T)gravity

    Sohan Kumar Jha and Anisur Rahaman. Non-minimalRTcoupling and its impact on inflationary evolution inf(R, T)gravity. In:Nucl. Phys. B1019 2025, p. 117102.doi:10.1016/j.nuclphysb. 2025.117102. arXiv:2504.10876 [gr-qc]

    work page doi:10.1016/j.nuclphysb 2025

  38. [38]

    Belhaj et al

    A. Belhaj et al. On inflationary models inf(R, T)gravity with a kinetic coupling term. In:Int. J. Mod. Phys. A3806n07 2023, p. 2350043.doi:10.1142/S0217751X23500434. arXiv:2303.12561 [hep-th]. 15

    work page doi:10.1142/s0217751x23500434 2023

  39. [39]

    Analysis off(R, T)inflationary models and their response to Planck data

    Sahazada Aziz and Anisur Rahaman. Analysis off(R, T)inflationary models and their response to Planck data. In:Phys. Scripta999 2024, p. 095001.doi:10.1088/1402-4896/ad6650

    work page doi:10.1088/1402-4896/ad6650 2024

  40. [40]

    Inflation inf(R, T)gravity with double-well potential

    Biswajit Deb and Atri Deshamukhya. Inflation inf(R, T)gravity with double-well potential. In:Int. J. Mod. Phys. A3718 2022, p. 2250127.doi:10.1142/S0217751X22501275. arXiv:2201.04378 [gr-qc]

    work page doi:10.1142/s0217751x22501275 2022

  41. [41]

    Exploring new subclass of k-inflation: tachyon in- flation inR+ηTgravity model

    Abolhassan Mohammadi and Fardin Kheirandish. Exploring new subclass of k-inflation: tachyon in- flation inR+ηTgravity model. In: 2023. arXiv:2301.12793 [gr-qc]

    work page arXiv 2023

  42. [42]

    V. K. Oikonomou. Exponential Inflation withF(R)Gravity. In:Phys. Rev. D976 2018, p. 064001. doi:10.1103/PhysRevD.97.064001. arXiv:1801.03426 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.97.064001 2018

  43. [43]

    Cosmological inflation in $F(R,\mathcal{G})$ gravity

    Mariafelicia De Laurentis, Mariacristina Paolella, and Salvatore Capozziello. Cosmological inflation in F(R, G)gravity. In:Phys. Rev. D918 2015, p. 083531.doi:10.1103/PhysRevD.91.083531. arXiv: 1503.04659 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.91.083531 2015

  44. [44]

    Inflation and cosmological evolution with F(R, G)gravity theory

    Dalia Saha, Jyoti Prasad Saha, and Abhik Kumar Sanyal. Inflation and cosmological evolution with F(R, G)gravity theory. In:Int. J. Geom. Meth. Mod. Phys.2012 2023, p. 2350213.doi:10.1142/ S0219887823502134. arXiv:2308.11770 [gr-qc]

    work page arXiv 2012

  45. [45]

    Built-in inflation inf(G)gravity

    M Sharif and H Ismat Fatima. Built-in inflation inf(G)gravity. In:International Journal of Modern Physics D2501 2016, p. 1650011

    work page 2016

  46. [46]

    Slow-roll Hilltop Inflation inf(ϕ, T)gravity

    Biswajit Deb and Atri Deshamukhya. Slow-roll Hilltop Inflation inf(ϕ, T)gravity. In: 2024. arXiv: 2408.01863 [gr-qc]

    work page arXiv 2024

  47. [47]

    Embedding warm natural inflation inf(ϕ)Tgravity

    Sabina Yeasmin and Atri Deshamukhya. Embedding warm natural inflation inf(ϕ)Tgravity. In:Int. J. Mod. Phys. A4003 2025, p. 2450158.doi:10 . 1142 / S0217751X24501586. arXiv:2408 . 00595 [gr-qc]

    work page 2025

  48. [48]

    Tiberiu Harko et al.f(R, T)gravity. In:Phys. Rev. D84 2011, p. 024020.doi:10.1103/PhysRevD. 84.024020. arXiv:1104.2669 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd 2011

  49. [49]

    Energy conditions in non-minimally coupledf(R, T)gravity

    Pradyumn Kumar Sahoo, Sanjay Mandal, and Simran Arora. Energy conditions in non-minimally coupledf(R, T)gravity. In:Astron. Nachr.3421-2 2021. Ed. by C. A. Zen Vasconcellos et al., pp. 89– 95.doi:10.1002/asna.202113886. arXiv:2201.00502 [gr-qc]

    work page doi:10.1002/asna.202113886 2021

  50. [50]

    F. G. Alvarenga et al. Testing some f(R,T) gravity models from energy conditions. In:J. Mod. Phys. 4 2013, pp. 130–139.doi:10.4236/jmp.2013.41019. arXiv:1205.4678 [gr-qc]

    work page doi:10.4236/jmp.2013.41019 2013

  51. [51]

    Myrzakulov et al

    N. Myrzakulov et al. Dark energy and cosmic evolution: A study inf(R, T)gravity. In:JHEAp47 2025, p. 100374.doi:10.1016/j.jheap.2025.100374. arXiv:2501.08362 [gr-qc]

    work page doi:10.1016/j.jheap.2025.100374 2025

  52. [52]

    Constraining Logarithmicf(R, T)Model Using Dark Energy Density ParameterΩΛ and Hubble parameterH0

    Biswajit Deb and Atri Deshamukhya. Constraining Logarithmicf(R, T)Model Using Dark Energy Density ParameterΩΛ and Hubble parameterH0. In:East Eur. J. Phys.20243 2024, pp. 21–26.doi: 10.26565/2312-4334-2024-3-02. arXiv:2207.10610 [gr-qc]

    work page doi:10.26565/2312-4334-2024-3-02 2024

  53. [53]

    Dark Matter Fromf(R, T)Gravity

    Raziyeh Zaregonbadi, Mehrdad Farhoudi, and Nematollah Riazi. Dark Matter Fromf(R, T)Gravity. In:Phys. Rev. D94 2016, p. 084052.doi:10 . 1103 / PhysRevD . 94 . 084052. arXiv:1608 . 00469 [gr-qc]

    work page 2016

  54. [54]

    Strong lensing effect and quasinormal modes of oscillations of black holes in f(R, T)gravity theory

    Gayatri Mohan et al. Strong lensing effect and quasinormal modes of oscillations of black holes in f(R, T)gravity theory. In:Phys. Dark Univ.49 2025, p. 102007.doi:10.1016/j.dark.2025.102007. arXiv:2503.08402 [gr-qc]

    work page doi:10.1016/j.dark.2025.102007 2025

  55. [55]

    Dynamical Wormhole Solutions inf(R, T)Gravity

    Yaghoub Heydarzade and Maryam Ranjbar. Dynamical Wormhole Solutions inf(R, T)Gravity. In: Gen. Rel. Grav.577 2025, p. 113.doi:10.1007/s10714-025-03452-8. arXiv:2504.17910 [gr-qc]

    work page doi:10.1007/s10714-025-03452-8 2025

  56. [56]

    Slow-roll inflation inf(R, T)gravity with a RT mixing term

    Che-Yu Chen, Yakefu Reyimuaji, and Xinyi Zhang. Slow-roll inflation inf(R, T)gravity with a RT mixing term. In:Phys. Dark Univ.38 2022, p. 101130.doi:10.1016/j.dark.2022.101130. arXiv: 2203.15035 [gr-qc]

    work page doi:10.1016/j.dark.2022.101130 2022

  57. [57]

    Warm inflation inf(R, T)gravity

    Sabina Yeasmin, Biswajit Deb, and Atri Deshamukhya. Warm inflation inf(R, T)gravity. In:Chin. J. Phys.85 2023, pp. 359–374.doi:10.1016/j.cjph.2023.07.004. arXiv:2211.05059 [gr-qc]. 16

    work page doi:10.1016/j.cjph.2023.07.004 2023

  58. [58]

    Koussour et al

    M. Koussour et al. Observational constraints on the equation of state of viscous fluid in f(R,T) gravity. In:Phys. Dark Univ.46 2024, p. 101577.doi:10.1016/j.dark.2024.101577. arXiv:2407.18023 [astro-ph.CO]

    work page doi:10.1016/j.dark.2024.101577 2024

  59. [59]

    FLRW Cosmological Models with Dynamic Cosmological Term in Modified Gravity

    Rishi Kumar Tiwari, Aroonkumar Beesham, and Bhupendra Kumar Shukla. FLRW Cosmological Models with Dynamic Cosmological Term in Modified Gravity. In:Universe79 2021, p. 319.doi: 10.3390/universe7090319

    work page doi:10.3390/universe7090319 2021

  60. [61]

    Barun Kumar Pal, Supratik Pal, and B. Basu. A semi-analytical approach to perturbations in mutated hilltop inflation. In:Int. J. Mod. Phys. D21 2012, p. 1250017.doi:10.1142/S0218271812500174. arXiv:1010.5924 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1142/s0218271812500174 2012

  61. [62]

    Mutated hilltop inflation revisited

    Barun Kumar Pal. Mutated hilltop inflation revisited. In:Eur. Phys. J. C785 2018, p. 358.doi: 10.1140/epjc/s10052-018-5856-3. arXiv:1711.00833 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1140/epjc/s10052-018-5856-3 2018

  62. [63]

    Realising Mutated Hilltop Inflation in Supergravity

    Tony Pinhero and Supratik Pal. Realising Mutated Hilltop Inflation in Supergravity. In:Phys. Lett. B796 2019, pp. 220–224.doi:10.1016/j.physletb.2019.07.042. arXiv:1905.04737 [hep-th]

    work page doi:10.1016/j.physletb.2019.07.042 2019

  63. [64]

    Gangopadhyay, Hussain Ahmed Khan, and Yogesh

    Mayukh R. Gangopadhyay, Hussain Ahmed Khan, and Yogesh. A case study of small field inflationary dynamics in the Einstein–Gauss–Bonnet framework in the light of GW170817. In:Phys. Dark Univ. 40 2023, p. 101177.doi:10.1016/j.dark.2023.101177. arXiv:2205.15261 [astro-ph.CO]

    work page doi:10.1016/j.dark.2023.101177 2023

  64. [65]

    Allys et al

    E. Allys et al. Probing Cosmic Inflation with the LiteBIRD Cosmic Microwave Background Polar- ization Survey. In:PTEP20234 2023, 042F01.doi:10 . 1093 / ptep / ptac150. arXiv:2202 . 02773 [astro-ph.IM]

    work page 2023

  65. [66]

    CMB-S4 Science Book, First Edition

    Kevork N. Abazajian et al.CMB-S4 Science Book, First Edition. Oct. 2016.doi:10.2172/1352047. arXiv:1610.02743 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.2172/1352047 2016

  66. [67]

    G. R. Dvali and S. H. Henry Tye. Brane inflation. In:Phys. Lett. B450 1999, pp. 72–82.doi:10. 1016/S0370-2693(99)00132-X. arXiv:hep-ph/9812483

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  67. [68]

    Towards Inflation in String Theory

    Shamit Kachru et al. Towards inflation in string theory. In:JCAP10 2003, p. 013.doi:10.1088/1475- 7516/2003/10/013. arXiv:hep-th/0308055

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1475- 2003

  68. [69]

    On hilltop and brane inflation after Planck

    Renata Kallosh and Andrei Linde. On hilltop and brane inflation after Planck. In:JCAP09 2019, p. 030.doi:10.1088/1475-7516/2019/09/030. arXiv:1906.02156 [hep-th]

    work page doi:10.1088/1475-7516/2019/09/030 2019

  69. [70]

    Woods and David S

    Roger D. Woods and David S. Saxon. Diffuse Surface Optical Model for Nucleon-Nuclei Scattering. In:Phys. Rev.95 1954, pp. 577–578.doi:10.1103/PhysRev.95.577

    work page doi:10.1103/physrev.95.577 1954

  70. [71]

    V. K. Oikonomou and N. Th. Chatzarakis. Canonical scalar field inflation with a Woods–Saxon po- tential. In:Annals Phys.411 2019, p. 167999.doi:10.1016/j.aop.2019.167999. arXiv:1908.09218 [gr-qc]

    work page doi:10.1016/j.aop.2019.167999 2019

  71. [72]

    S. A. Venikoudis and F. P. Fronimos. Reheating era in Gauss-Bonnet theories of gravity compatible with the GW170817 event. In:Nucl. Phys. B984 2022, p. 115945.doi:10.1016/j.nuclphysb.2022. 115945. arXiv:2208.08333 [gr-qc]

    work page doi:10.1016/j.nuclphysb.2022 2022

  72. [73]

    Woods–Saxon inflation driven by GB term

    Younes Younesizadeh et al. Woods–Saxon inflation driven by GB term. In:Int. J. Mod. Phys. D 3407n08 2025, p. 2550030.doi:10.1142/S0218271825500300

    work page doi:10.1142/s0218271825500300 2025

  73. [74]

    Scalar field dominated cosmol- ogy with Woods-Saxon like potential

    Sreerag Radhakrishnan, Sarath Nelleri, and Navaneeth Poonthottathil. Scalar field dominated cosmol- ogy with Woods-Saxon like potential. In:JCAP05 2025, p. 009.doi:10.1088/1475-7516/2025/05/

    work page doi:10.1088/1475-7516/2025/05/ 2025

  74. [75]

    arXiv:2405.06750 [astro-ph.CO]. 17

    work page arXiv