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arxiv: 2604.09843 · v1 · submitted 2026-04-10 · ✦ hep-ph · astro-ph.CO· gr-qc· hep-th

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Induced Multi-phase Inflation with Reheating: Leptogenesis and Dark Matter Production in Metric versus Palatini

Nilay Bostan , Rafid H. Dejrah , Anish Ghoshal , Zygmunt Lalak
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Pith reviewed 2026-05-10 17:14 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COgr-qchep-th
keywords multi-phase inflationmetric gravityPalatini gravitynon-thermal dark matterleptogenesisreheatingspectral indextensor-to-scalar ratio
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The pith

Multi-phase inflation in metric and Palatini gravity produces spectral indices consistent with data while yielding sharply different tensor-to-scalar ratios and viable non-thermal dark matter plus leptogenesis.

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

This paper examines non-minimally coupled scalar-induced multi-phase inflation in metric and Palatini gravity, including linear, Brans-Dicke-like and Higgs-like sectors. It establishes that the scalar spectral index falls in the range 0.93 to 0.98, compatible with Planck and Planck plus ACT observations. Reheating proceeds through perturbative inflaton decays to Higgs bosons and fermionic dark matter via portal and Yukawa couplings, with radiative stability constraining those couplings and producing a reheating temperature window from a few MeV to 10^15 GeV. The work shows that non-thermal dark matter production is viable over keV to PeV masses with small couplings, and estimates the inflaton-right-handed neutrino Yukawa needed for non-thermal leptogenesis in a Type-I seesaw. A sympathetic reader cares because the analysis directly connects the inflationary epoch to the generation of dark matter and the baryon asymmetry while exposing observable differences between two gravitational formulations.

Core claim

The paper claims that scalar-induced multi-phase inflation with non-minimal coupling yields ns approximately 0.93 to 0.98 in both metric and Palatini cases. Metric realizations permit tensor-to-scalar ratios up to 0.03, whereas Palatini realizations give r less than or equal to 10 to the minus 5, with sub-Planckian field excursions. Reheating occurs via inflaton decays into Higgs and fermionic dark matter through the portal coupling lambda12 and Yukawa y chi, with radiative stability requiring couplings between 10 to the minus 7 and 10 to the minus 3. This produces reheating temperatures from 4 MeV to 10^15 GeV, allows non-thermal dark matter production for masses from keV to PeV with y chi,

What carries the argument

Non-minimally coupled scalar field driving multi-phase inflation, with reheating and particle production controlled by the portal coupling lambda12 and the Yukawa coupling y chi under radiative stability constraints.

If this is right

  • Both metric and Palatini formulations produce scalar spectral indices between 0.93 and 0.98 that match Planck and combined Planck plus ACT data.
  • Metric models allow tensor-to-scalar ratios up to 0.03 while Palatini models are restricted to values below 10 to the minus 5.
  • Non-thermal dark matter production from inflaton decays is viable for masses between keV and PeV when the Yukawa coupling is below 10 to the minus 6.
  • Successful non-thermal leptogenesis requires the inflaton-right-handed neutrino Yukawa coupling to lie in a range set by the lightest right-handed neutrino mass between 10^9 and 10^14 GeV and the maximum temperature after reheating.
  • Palatini scenarios impose narrower parameter space because they demand smaller couplings and lower maximum temperatures.

Where Pith is reading between the lines

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

  • Palatini realizations would predict an absence of detectable primordial gravitational waves at the level r approximately 0.01, directing future experiments toward other observables such as specific dark matter properties or non-Gaussianities.
  • The tight radiative stability bounds suggest that protecting the inflationary plateau may require additional symmetries or dynamical mechanisms not explored in the paper.
  • The framework could be extended by including the effects of the produced dark matter or right-handed neutrinos on the subsequent thermal history, potentially tightening the leptogenesis window further.

Load-bearing premise

Radiative stability of the inflationary plateau requires the portal and Yukawa couplings to remain small enough that reheating proceeds only through perturbative inflaton decays.

What would settle it

A future measurement of the tensor-to-scalar ratio r greater than 0.03 would rule out the Palatini realizations and strain the metric realizations described.

Figures

Figures reproduced from arXiv: 2604.09843 by Anish Ghoshal, Nilay Bostan, Rafid H. Dejrah, Zygmunt Lalak.

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read the original abstract

We study non-minimally coupled scalar-induced multi-phase inflation in metric and Palatini gravity, considering linear, Brans-Dicke-like, and Higgs-like sectors. The scalar spectral index lies in the range \( n_s \simeq 0.93 \ \text{--} \ 0.98 \), consistent with \textit{Planck} and combined \textit{Planck}+ACT data. The tensor-to-scalar ratio can reach \( r \sim 0.03 \) in metric, whereas Palatini models generically predict \( r \lesssim 10^{-5} \). In the Palatini case, field excursions remain sub-Planckian, and the perturbative unitarity cutoff is raised. Reheating proceeds via perturbative inflaton decays into Higgs bosons and fermionic dark matter (DM) through the portal coupling \( \lambda_{12} \) and Yukawa coupling \( y_\chi \). Radiative stability of the inflationary plateau constrains the couplings to \( y_\chi, \lambda_{12} \sim 10^{-7} \ \text{--} \ 10^{-3} \), implying \( 4\,\mathrm{MeV} \lesssim T_{\rm rh} \lesssim 10^{15}\,\mathrm{GeV} \). Palatini realizations require smaller couplings and thus a narrower reheating window. Non-thermal DM production $\chi$ from inflaton decays is viable for DM mass \( m_\chi \sim \mathrm{keV} \ \text{--} \ \mathrm{PeV} \) with \( y_\chi \lesssim 10^{-6} \) over large parameter regions. We estimate the inflaton-right-handed neutrino (RHN) Yukawa coupling \( y_N \) required for successful baryogenesis via non-thermal leptogenesis within a Type-I seesaw framework, for the lightest RHN mass \( M_{N_1} \sim 10^{9} \ \text{--} \ 10^{14}\,\mathrm{GeV} \), provided \( M_{N_1} > T_{\rm max} \), where \( T_{\rm max} \) follows from radiatively consistent reheating. In Palatini scenarios, the lower maximal temperature and tighter stability bounds further restrict the leptogenesis parameter space.

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

1 major / 2 minor

Summary. The paper studies non-minimally coupled scalar-induced multi-phase inflation in metric and Palatini gravity across linear, Brans-Dicke-like, and Higgs-like sectors. It reports ns in the range 0.93–0.98 (consistent with Planck and Planck+ACT), r up to ~0.03 in metric gravity versus r ≲ 10^{-5} in Palatini, sub-Planckian field excursions in Palatini, and reheating via perturbative inflaton decays to Higgs and fermionic DM through λ12 and yχ. Radiative stability is invoked to bound yχ, λ12 ~ 10^{-7}–10^{-3}, yielding 4 MeV ≲ Trh ≲ 10^{15} GeV, with viability claims for non-thermal DM (mχ ~ keV–PeV, yχ ≲ 10^{-6}) and non-thermal leptogenesis via yN for MN1 ~ 10^9–10^{14} GeV.

Significance. If the stability bounds and reheating derivations hold, the work provides a comparative analysis of metric versus Palatini realizations that links inflation to post-inflationary DM and baryogenesis, with potentially observable differences in r and field excursions. The explicit parameter windows for DM and leptogenesis under stability constraints could guide model building, though the absence of detailed loop calculations limits immediate falsifiability.

major comments (1)
  1. [Reheating and stability analysis] Reheating and stability analysis (abstract and associated reheating discussion): the claim that radiative stability constrains yχ, λ12 ∼ 10^{-7}–10^{-3} and thereby fixes 4 MeV ≲ Trh ≲ 10^{15} GeV is load-bearing for the DM viability (mχ ∼ keV–PeV) and leptogenesis (MN1 > Tmax) ranges, yet no explicit one-loop effective potential, renormalization-scale choice, or truncation-order check is supplied to confirm that slow-roll parameters remain controlled across this coupling interval.
minor comments (2)
  1. [Abstract] The abstract states consistency with Planck and Planck+ACT data for ns but does not quote the specific central values or error bars used for comparison.
  2. [Reheating discussion] Notation for the portal coupling λ12 and Yukawa yχ is introduced without an explicit Lagrangian term or interaction vertex diagram in the provided text.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive feedback. We appreciate the positive assessment of the comparative analysis between metric and Palatini realizations and the potential implications for dark matter and leptogenesis. We address the single major comment below.

read point-by-point responses

  1. Referee: [Reheating and stability analysis] Reheating and stability analysis (abstract and associated reheating discussion): the claim that radiative stability constrains yχ, λ12 ∼ 10^{-7}–10^{-3} and thereby fixes 4 MeV ≲ Trh ≲ 10^{15} GeV is load-bearing for the DM viability (mχ ∼ keV–PeV) and leptogenesis (MN1 > Tmax) ranges, yet no explicit one-loop effective potential, renormalization-scale choice, or truncation-order check is supplied to confirm that slow-roll parameters remain controlled across this coupling interval.

    Authors: We agree that an explicit derivation of the radiative stability bounds would strengthen the presentation and make the constraints on y_χ and λ_{12} more transparent. The quoted range follows from requiring that one-loop corrections (via the Coleman-Weinberg potential) do not lift the inflationary plateau enough to violate slow-roll conditions, using the standard renormalization prescription in non-minimally coupled models where the scale is chosen at the background field value during inflation. To address the concern directly, in the revised manuscript we will add a dedicated subsection (or appendix) that: (i) writes the explicit one-loop effective potential for the relevant sectors, (ii) specifies the renormalization-scale choice and its justification, and (iii) provides a truncation-order estimate by power-counting higher-loop contributions and verifying that they remain sub-dominant for the quoted coupling window. This addition will confirm that the slow-roll parameters stay controlled and will support the subsequent DM and leptogenesis viability ranges. We believe these clarifications will also improve the falsifiability of the stability claims. revision: yes

Circularity Check

0 steps flagged

No significant circularity; stability constraint is independent of viability claims

full rationale

The derivation begins with the inflationary potential in metric and Palatini gravity, yielding ns in 0.93-0.98 and r values as direct outputs of the slow-roll parameters. Radiative stability is imposed as an external consistency requirement on the portal and Yukawa couplings (yχ, λ12 ∼ 10^{-7}–10^{-3}), which then determines the allowed Trh window via standard perturbative decay rate formulas. DM and leptogenesis viability are subsequently checked inside that window (mχ ∼ keV–PeV, yχ ≲ 10^{-6}, yN estimates for M_N1 > T_max). This is a one-way restriction of parameter space rather than any reduction of the claimed predictions to the inputs by construction. No self-definitional loop, fitted quantity renamed as prediction, or load-bearing self-citation appears in the chain; the stability condition is falsifiable independently of the final DM/leptogenesis statements.

Axiom & Free-Parameter Ledger

3 free parameters · 3 axioms · 0 invented entities

Central results rest on several fitted couplings constrained by stability, plus standard assumptions about reheating and seesaw mechanisms; no new entities postulated.

free parameters (3)
  • portal coupling λ12
    Constrained to 10^{-7}–10^{-3} by radiative stability and reheating requirements
  • Yukawa coupling yχ
    Constrained to 10^{-7}–10^{-3} by radiative stability and viable DM production
  • inflaton-RHN Yukawa yN
    Estimated to achieve successful leptogenesis for given M_N1 range
axioms (3)
  • domain assumption Reheating proceeds via perturbative inflaton decays to Higgs and fermionic DM
    Used to calculate Trh and DM abundance from λ12 and yχ
  • domain assumption Type-I seesaw framework for leptogenesis with lightest RHN mass M_N1
    Invoked to estimate yN required for baryogenesis
  • domain assumption Inflationary plateau remains radiatively stable for the chosen couplings
    Directly sets the allowed range for yχ and λ12

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Forward citations

Cited by 1 Pith paper

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

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