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arxiv: 2605.09571 · v1 · submitted 2026-05-10 · 🌌 astro-ph.CO · hep-ph· hep-th

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Einstein-Cartan pseudoscalaron inflation, reheating and nonthermal leptogenesis

Carlo Di Benedetto , Alessandro Di Marco , Emanuele Orazi , Gianfranco Pradisi
Authors on Pith no claims yet

Pith reviewed 2026-05-12 04:41 UTC · model grok-4.3

classification 🌌 astro-ph.CO hep-phhep-th
keywords Einstein-Cartan gravitypseudoscalaron inflationnonthermal leptogenesisbaryon asymmetryMajorana neutrinosBarbero-Immirzi parameterreheatingseesaw mechanism
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The pith

Nonthermal leptogenesis emerges necessarily from universal inflaton couplings in Einstein-Cartan pseudoscalaron inflation to explain the baryon asymmetry.

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

The paper studies the post-inflationary phase of an inflationary model derived from Einstein-Cartan-Holst gravity, extended by a type-I seesaw with three heavy right-handed Majorana neutrinos. It establishes that the inflaton's universal coupling to these fermions forces nonthermal leptogenesis as the mechanism that produces the observed baryon asymmetry after reheating. The predictions remain compatible with CMB, BAO, BBN, and neutrino oscillation data for a broad range of the Barbero-Immirzi parameter gamma that shapes both inflation and reheating. A sympathetic reader would care because the setup ties a gravitational modification during the early universe directly to the origin of matter without introducing extra tuning parameters.

Core claim

In the Einstein-Cartan pseudoscalaron inflation scenario coupled to a type-I seesaw extension of the Standard Model with three heavy Majorana neutrinos, nonthermal leptogenesis arises as a necessary and self-consistent process for generating the baryon asymmetry, driven by the universal coupling of the inflaton to the additional fermions. For gamma approximately -1/100 and a lightest Majorana-neutrino mass of order 10^13 GeV, the model gives a scalar spectral index n_s approximately 0.970, tensor-to-scalar ratio r approximately 0.004, and baryon-to-entropy ratio n_B/s approximately 8.7 times 10^-11, all consistent with constraints for N_e less than or equal to 60.

What carries the argument

The universal coupling of the pseudoscalaron inflaton to the three heavy Majorana fermions, which automatically generates the lepton asymmetry during reheating without extra suppression factors.

If this is right

  • The model yields a scalar spectral index near 0.970 and tensor-to-scalar ratio near 0.004 that fit current CMB data.
  • It produces the observed baryon-to-entropy ratio of 8.7 times 10^-11 through nonthermal leptogenesis.
  • The results remain compatible with neutrino oscillation experiments and Big Bang Nucleosynthesis bounds.
  • The outcomes hold for a wide range of the Barbero-Immirzi parameter gamma.
  • Reheating dynamics support the necessary particle production for the asymmetry.

Where Pith is reading between the lines

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

  • Similar universal couplings could be examined in other modified-gravity inflationary models to generate baryon asymmetry without extra fields.
  • Future precision CMB measurements of the tensor-to-scalar ratio may further narrow the allowed interval for gamma.
  • The predicted particle spectra from reheating could be tested through collider signatures or high-energy astrophysical processes.

Load-bearing premise

The inflaton couples universally to the three heavy Majorana neutrinos in a manner that produces the required lepton asymmetry without additional tuning or suppression factors.

What would settle it

A measurement of the baryon-to-entropy ratio significantly different from 8.7 times 10^-11, or a scalar spectral index and tensor-to-scalar ratio pair incompatible with n_s approximately 0.970 and r approximately 0.004 at gamma approximately -1/100, for N_e less than or equal to 60.

Figures

Figures reproduced from arXiv: 2605.09571 by Alessandro Di Marco, Carlo Di Benedetto, Emanuele Orazi, Gianfranco Pradisi.

Figure 1
Figure 1. Figure 1: Inflationary potential V (ϕ), normalized to the reference inflationary scale M4 inf, as a function of the rescaled scalar field ϕ/Mp, shown here for the case p = 2 and Barbero–Immirzi parameter γ = −1/100. In this scenario, the reference inflationary scale is assumed to be of order Minf ∼ 1016 GeV. The shaded vertical bands qualitatively highlight the three main regions (or regimes) of the model: the vacuu… view at source ↗
Figure 2
Figure 2. Figure 2: Predictions of the Einstein-Cartan-Holst pseudoscalaron inflationary model (p = 2) in the (ns, r) plane compared with the 68% and 95% marginalized confidence regions derived from recent cosmological observations [132]. The blue region correspond to CMB-only constraints (Planck + ACT + SPT + BK18), while the red region include the additional BAO information from DESI. B. The physics around the vacuum The co… view at source ↗
Figure 3
Figure 3. Figure 3: Representative evolution of the reheating and nonthermal leptogenesis functions ¯fi(x) supposing kϕ→N1N1 ∼ 10−15 , ε1 ∼ −10−5 , M¯N1 ∼ 10−3 and two reference (normalized) values of the RHN decay rate into massless Standard Model particles, i.e. kN1→RR ∼ 10−6 , corresponding to an effective or reference light neutrino mass m˜ 1 ∼ 10−3 eV < mmax ν (left plot) and kN1→RR ∼ 10−8 corresponding to a very small e… view at source ↗
read the original abstract

We study the postinflationary dynamics of an Einstein-Cartan-Holst gravity-motivated inflationary scenario, known as Einstein-Cartan pseudoscalaron inflation, coupled to a type-I seesaw extension of the Standard Model with three heavy right-handed Majorana neutrinos. In particular, we show that nonthermal leptogenesis emerges as a necessary and self-consistent mechanism for generating the observed baryon asymmetry of the Universe, mainly because of the universal coupling of the inflaton to the additional heavy Majorana fermions. The resulting framework provides theoretical predictions that are fully compatible with the latest cosmological constraints from the Cosmic Microwave Background, Baryon Acoustic Oscillations, and Big Bang Nucleosynthesis, as well as with neutrino oscillation experiments, for a wide range of the fundamental Barbero-Immirzi model parameter $\gamma$, which controls the inflationary and postinflationary phases. In particular, for $\gamma \sim -1/100$ and a lightest Majorana-neutrino mass of order $10^{13}$ GeV, we find a scalar spectral index $n_s \sim 0.970$, a tensor-to-scalar ratio $r \sim 0.004$, for a number of e-folds before the end of inflation $N_e \lesssim 60$, and a baryon-to-entropy ratio $n_B/s \sim 8.7 \times 10^{-11}$.

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

3 major / 3 minor

Summary. The manuscript examines post-inflationary dynamics in an Einstein-Cartan-Holst gravity model of pseudoscalaron inflation coupled to a type-I seesaw extension of the Standard Model containing three heavy right-handed Majorana neutrinos. It claims that nonthermal leptogenesis arises necessarily and self-consistently from the universal coupling of the inflaton to these neutrinos, thereby generating the observed baryon asymmetry, while the framework yields predictions for the scalar spectral index, tensor-to-scalar ratio, and baryon-to-entropy ratio that are compatible with CMB, BAO, BBN, and neutrino oscillation data for a wide range of the Barbero-Immirzi parameter γ (exemplified by γ ∼ −1/100 and lightest Majorana mass ∼ 10^13 GeV giving ns ∼ 0.970, r ∼ 0.004, and nB/s ∼ 8.7 × 10^{-11}).

Significance. If the central claim that the observed asymmetry follows automatically from the universal coupling without additional tuning of CP phases or mass splittings holds, the work would furnish a unified description linking modified-gravity inflation to reheating and baryogenesis, with the Barbero-Immirzi parameter controlling both inflationary observables and post-inflationary lepton asymmetry. The explicit numerical compatibility with current data for a range of γ would constitute a concrete, falsifiable prediction.

major comments (3)
  1. [Abstract and leptogenesis calculation] Abstract and the leptogenesis section: the assertion that nonthermal leptogenesis 'emerges as a necessary and self-consistent mechanism' due to the universal inflaton coupling to the three heavy Majorana neutrinos is not supported by an explicit computation showing that the CP asymmetry ε_i (proportional to Im[(Y†Y)ij²] times the loop function of mass ratios) yields |ε| sufficient for nB/s ∼ 8.7 × 10^{-11} when the Yukawa matrix Y is fixed solely by fitting neutrino oscillation data and the seesaw formula; the presented values instead appear selected post hoc for the quoted γ and mass.
  2. [Abstract and results section] Abstract and results on cosmological parameters: the quoted values ns ∼ 0.970, r ∼ 0.004, and nB/s ∼ 8.7 × 10^{-11} for γ ∼ −1/100 and lightest Majorana mass of order 10^13 GeV are presented as compatible with data, yet no derivation, error propagation, or robustness check against variations in the inflationary potential or decay rates is supplied; by the paper's own equations these quantities are outputs of the chosen inputs rather than independent predictions.
  3. [Results and discussion] The claim of compatibility 'for a wide range of the fundamental Barbero-Immirzi model parameter γ' is not accompanied by scans or sensitivity analysis showing how ns, r, and nB/s vary with γ while remaining within observational bounds; the single numerical example undermines the breadth of the statement.
minor comments (3)
  1. [Introduction] The definition and role of the Barbero-Immirzi parameter γ should be stated explicitly at first use in the introduction, with a brief reminder of its appearance in the Holst term.
  2. [Figures] Figure captions for the inflationary potential and reheating dynamics could include the explicit functional form of the potential in terms of γ to aid readability.
  3. [Model setup] A reference to the original Einstein-Cartan pseudoscalaron inflation paper should be added when the model is introduced.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments, which help us improve the clarity and rigor of our presentation. We address each major comment in turn below.

read point-by-point responses

  1. Referee: [Abstract and leptogenesis calculation] Abstract and the leptogenesis section: the assertion that nonthermal leptogenesis 'emerges as a necessary and self-consistent mechanism' due to the universal inflaton coupling to the three heavy Majorana neutrinos is not supported by an explicit computation showing that the CP asymmetry ε_i (proportional to Im[(Y†Y)ij²] times the loop function of mass ratios) yields |ε| sufficient for nB/s ∼ 8.7 × 10^{-11} when the Yukawa matrix Y is fixed solely by fitting neutrino oscillation data and the seesaw formula; the presented values instead appear selected post hoc for the quoted γ and mass.

    Authors: We thank the referee for this observation. The Einstein-Cartan-Holst framework imposes a universal coupling of the pseudoscalaron to all Standard Model fermions and the three right-handed Majorana neutrinos, rendering their production during reheating unavoidable and thereby making nonthermal leptogenesis a necessary consequence rather than an optional add-on. The Yukawa matrix Y is constrained by neutrino oscillation data through the type-I seesaw relation but retains freedom in the CP-violating phases and the mass hierarchy. Using a representative hierarchical spectrum with lightest Majorana mass ∼10^{13} GeV and phases consistent with oscillation fits, the standard CP-asymmetry formula yields |ε_1| ∼ 10^{-6}–10^{-5}, which, after dilution and sphaleron conversion, produces the quoted n_B/s. The numerical values follow directly from the model equations for the chosen γ. In the revised manuscript we will insert an explicit sample calculation of ε_i for a Y matrix fitted to oscillation data, confirming that no extra tuning beyond standard seesaw parameters is introduced. revision: partial

  2. Referee: [Abstract and results section] Abstract and results on cosmological parameters: the quoted values ns ∼ 0.970, r ∼ 0.004, and nB/s ∼ 8.7 × 10^{-11} for γ ∼ −1/100 and lightest Majorana mass of order 10^13 GeV are presented as compatible with data, yet no derivation, error propagation, or robustness check against variations in the inflationary potential or decay rates is supplied; by the paper's own equations these quantities are outputs of the chosen inputs rather than independent predictions.

    Authors: We agree that additional derivation details will strengthen the presentation. The values of n_s and r are obtained from the slow-roll parameters of the γ-dependent Einstein-Cartan pseudoscalaron potential, while n_B/s follows from the inflaton decay width into the Majorana neutrinos, the resulting lepton asymmetry, and its conversion via sphalerons. We will expand the results section with the relevant analytic expressions for the potential, the number of e-folds N_e ≲ 60, the decay rates, and a brief robustness discussion showing that the quoted observables remain stable under small variations in the decay widths and potential parameters. revision: yes

  3. Referee: [Results and discussion] The claim of compatibility 'for a wide range of the fundamental Barbero-Immirzi model parameter γ' is not accompanied by scans or sensitivity analysis showing how ns, r, and nB/s vary with γ while remaining within observational bounds; the single numerical example undermines the breadth of the statement.

    Authors: We accept that a single example does not fully substantiate the breadth of the claim. The Barbero-Immirzi parameter γ enters both the inflationary potential and the post-inflationary couplings such that a continuous interval of values (roughly |γ| ≲ 0.1) produces n_s ∈ [0.96, 0.98] and r < 0.01 while the leptogenesis yield can be kept within observational bounds by modest adjustment of the Majorana mass scale. The revised manuscript will include a sensitivity table or plot demonstrating the variation of n_s, r, and n_B/s over a representative range of γ, confirming compatibility for multiple values. revision: yes

Circularity Check

1 steps flagged

Parameter values for gamma and Majorana mass are selected to reproduce observed nB/s, ns and r; compatibility presented as model prediction

specific steps
  1. fitted input called prediction [Abstract]
    "for γ ∼ -1/100 and a lightest Majorana-neutrino mass of order 10^{13} GeV, we find a scalar spectral index n_s ∼ 0.970, a tensor-to-scalar ratio r ∼ 0.004, for a number of e-folds before the end of inflation N_e ≲ 60, and a baryon-to-entropy ratio n_B/s ∼ 8.7 × 10^{-11}."

    The quoted observables are computed after choosing gamma and the Majorana mass specifically so that the nonthermal leptogenesis calculation yields the observed nB/s while the inflationary sector yields ns and r inside Planck bounds. These are therefore outputs of the chosen inputs rather than independent predictions forced by the Einstein-Cartan structure or the universal coupling alone.

full rationale

The paper selects specific values of the free Barbero-Immirzi parameter gamma and the lightest Majorana mass to obtain ns, r and nB/s that match observations, then reports these as findings of the model. While the universal inflaton coupling to the three Majorana neutrinos is a genuine model feature that enables nonthermal leptogenesis without additional fields, the numerical agreement for the asymmetry still requires choosing the mass scale and implicitly suitable Yukawa phases or splittings to produce the observed nB/s. This is standard parameter fitting rather than a derivation that forces the observed values from first principles alone. No self-citation load-bearing or self-definitional reduction is evident from the provided text; the central mechanism (universal decay) is independent of the fit. Overall circularity is mild because the framework remains falsifiable via the predicted range of gamma and the requirement that the same Yukawas satisfy both neutrino data and the asymmetry.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The central claim rests on the Einstein-Cartan-Holst action, the type-I seesaw mechanism, and the assumption of universal inflaton coupling to heavy neutrinos. Two free parameters (gamma and lightest Majorana mass) are adjusted to match cosmological data.

free parameters (2)
  • Barbero-Immirzi parameter gamma = -1/100
    Controls both inflationary observables and post-inflationary leptogenesis; specific value -1/100 chosen to match ns, r and nB/s
  • lightest Majorana neutrino mass = 10^13 GeV
    Set to ~10^13 GeV to produce the observed baryon asymmetry via nonthermal leptogenesis
axioms (2)
  • domain assumption Universal coupling of the inflaton to the three heavy Majorana neutrinos
    Invoked to make nonthermal leptogenesis automatic and self-consistent
  • standard math Type-I seesaw extension of the Standard Model
    Standard mechanism for generating light neutrino masses and enabling leptogenesis
invented entities (1)
  • Einstein-Cartan pseudoscalaron no independent evidence
    purpose: Inflaton field arising from the Holst term in Einstein-Cartan gravity
    Postulated within the modified-gravity framework; no independent experimental evidence provided

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Reference graph

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