arxiv: 2604.09356 · v1 · submitted 2026-04-10 · ✦ hep-ph · astro-ph.CO· hep-th

Recognition: unknown

CMB signatures of gravity-mediated dark radiation in mathbf{Delta N_{rm eff}}

Anish Ghoshal , Sk Jeesun , Kazunori Kohri

Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:13 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COhep-th

keywords dark radiationN_effgravity-mediated productionreheating temperatureCMB constraintsdark Higgsdark photon

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The pith

Gravity-mediated scatterings inevitably produce light dark radiation particles during reheating, yielding Planck-derived bounds on reheating temperature and equation of state for dark Higgs and dark photon cases.

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

The paper studies how light BSM particles with negligible non-gravitational interactions are still produced in the early universe solely through gravity-mediated processes in an EFT framework. These particles can persist as dark radiation and contribute to the effective neutrino number N_eff observed in CMB data. The analysis focuses on spin-dependent production for scalar dark Higgs and vector dark photon dark radiation, deriving constraints on reheating temperature T_RH and background equation of state w_Φ from Planck 2018 measurements. Comparisons are made to Dirac right-handed neutrinos and axion-like particles, and the work extends to a generic spin-2 mediator to identify currently excluded parameter space and future probeability with experiments like LiteBIRD or CMB-S4.

Core claim

Gravity-mediated production of dark radiation in EFT setups with negligible non-gravitational couplings produces observable contributions to N_eff, allowing Planck 2018 data to constrain reheating temperature T_RH and equation of state w_Φ during reheating for dark Higgs and dark photon scenarios, with analogous results for other particles and a spin-2 mediator.

What carries the argument

Gravity-mediated scatterings in an effective field theory where production of light BSM particles depends on their spin and occurs without non-gravitational couplings, directly affecting Delta N_eff at CMB epoch.

If this is right

Planck 2018 data imposes upper limits on T_RH for dark Higgs dark radiation consistent with observed N_eff.
Similar upper limits on T_RH apply to dark photon dark radiation, with dependence on w_Φ.
The same framework produces bounds on production of right-handed neutrinos and ALPs through gravity.
For a generic spin-2 mediator with effective scale Lambda, Planck data already excludes parts of parameter space, while future CMB experiments can probe more.

Where Pith is reading between the lines

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

Reheating parameters might be independently testable if N_eff precision improves enough to separate spin-dependent production rates.
Models with modified post-reheating expansion histories could alter the mapping from production to observed N_eff.
If gravity-mediated effects dominate, they set a minimum floor for dark radiation abundance independent of other interaction strengths.

Load-bearing premise

All non-gravitational couplings of the BSM particle are negligible, so that production occurs solely through gravity-mediated scatterings.

What would settle it

A future measurement of N_eff that deviates from the value predicted for a given reheating temperature and equation of state in these gravity-only production models would rule out the claimed constraints.

read the original abstract

Measurement of $N_{\rm eff}$ in the CMB (Cosmic Microwave Background) observations, like Planck 2018 and BBN (Big Bang Nucleosynthesis) has already set stringent constraints on the interaction strength of light particles beyond the Standard Model (BSM). Despite such negligible couplings of such BSM particles to the visible sector, they are inevitably produced in the early universe through gravity-mediated processes. If a sizable density of light particles survives around CMB formation, they may act as dark radiation (DR) contributing to $N_{\rm eff}$ at CMB epoch. In this work, we study the production of such light BSM particles through the gravity-mediated scatterings in an effective field theory (EFT) setup assuming that all non-gravitational couplings of the BSM particle are negligible. Since the production is sensitive to the spin of the produced particle, we perform a concrete analysis for two representative cases: scalar dark Higgs DR and vector dark photons DR.Using the Planck 2018 observations, we find constraints on the reheating temperature ($T_{\rm RH}$) and background equation of state ($w_\Phi$) during reheating in such scenarios featuring dark Higgs and dark photon. A comparative discussion involving gravity-mediated production of Dirac right-handed neutrinos ($\nu_R$) and light axion-like particles (ALP) is also presented. Finally, for completeness, we also analyze the scenario where the production occurs through a generic spin-2 mediator characterized by an effective scale $\Lambda$ delineating the parameter space that is currently ruled out from Planck-2018 and can be probed by the future CMB experiments like LiteBird, Simon Observatory, CMB-S4, CMB-HD.

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

This paper applies standard gravity-mediated production to scalar and vector dark radiation and extracts new numerical bounds on reheating temperature and equation of state from Planck 2018.

read the letter

The main thing to know is that the authors compute the minimal ΔN_eff from gravity-only scatterings of light scalars (dark Higgs) and vectors (dark photons) during reheating, then turn the Planck limit into constraints on T_RH and w_Φ. They also run the same exercise for right-handed neutrinos and ALPs and sketch the case of a spin-2 mediator with cutoff Λ. The resulting bounds are new for the two spins they highlight. The calculation follows the usual EFT route: spin-dependent 2-to-2 rates, Boltzmann integration over a constant-w_Φ epoch, conversion to comoving density, and comparison to the observed N_eff. That part is executed cleanly and the spin dependence shows up as expected, with vectors producing more radiation than scalars. The comparative plots and the future-experiment projections are straightforward additions that help place the numbers in context. The work is competent and the central claim holds without internal contradictions or obvious calculation gaps. The soft spots are the usual ones for this class of paper. Everything rests on the assumption that non-gravitational couplings are exactly zero; any small coupling would dominate and erase the bounds. The constant-w_Φ reheating model is a common simplification but not the most general. These are modeling choices rather than errors, and the paper is transparent about them. The citation pattern looks standard and the Planck data are used directly. This is a paper for people who work on dark radiation, reheating dynamics, or weak-coupling BSM scenarios. A reader who needs concrete numbers for gravity-set floors on ΔN_eff will get usable results. It is solid enough to deserve a serious referee even though the advance is incremental rather than foundational.

Referee Report

2 major / 3 minor

Summary. The manuscript examines gravity-mediated production of light BSM particles as dark radiation in an EFT with all non-gravitational couplings set to zero. For scalar dark Higgs and vector dark photon cases, spin-dependent 2-to-2 scattering rates are computed, the Boltzmann equation is integrated over a reheating epoch with constant w_Φ, and the resulting comoving density is converted to ΔN_eff at CMB decoupling. Planck 2018 data are then used to constrain T_RH and w_Φ; extensions to right-handed neutrinos, ALPs, and a generic spin-2 mediator with cutoff Λ are also presented, together with forecasts for future CMB experiments.

Significance. If the EFT assumptions and production integrals hold, the work supplies concrete, falsifiable bounds on reheating parameters that arise even in the complete absence of direct couplings. The spin-dependent treatment and comparative discussion across mediators add value, while the projections for LiteBIRD, CMB-S4, and CMB-HD make the results forward-looking. The approach complements other cosmological probes of early-universe dynamics.

major comments (2)

[§3] §3 (production rates): the vector dark-photon rate includes a polarization sum that appears to be taken in the massless limit; please confirm that the same massless approximation remains valid throughout the reheating integration when w_Φ is varied, and state the resulting uncertainty on the final ΔN_eff.
[§4] §4 (ΔN_eff conversion): the mapping from comoving DR density to ΔN_eff at decoupling assumes instantaneous transition to radiation domination after reheating; an explicit check of how a prolonged w_Φ ≠ 1/3 epoch affects the entropy dilution factor would strengthen the central claim.

minor comments (3)

[§2] Notation for the background field Φ and its equation of state w_Φ is introduced without a dedicated paragraph; a short definition of the reheating epoch boundaries would improve readability.
[Figures 3–5] Figure captions for the T_RH–w_Φ exclusion plots should explicitly state the Planck 2018 ΔN_eff bound adopted (e.g., the 95 % CL value) and whether it is one-sided or two-sided.
[§6] The discussion of the spin-2 mediator (final section) introduces an effective scale Λ but does not compare its numerical reach with the pure-gravity case; a brief sentence on the relative strength would be helpful.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment and constructive comments. We address each major point below and have revised the manuscript accordingly.

read point-by-point responses

Referee: [§3] §3 (production rates): the vector dark-photon rate includes a polarization sum that appears to be taken in the massless limit; please confirm that the same massless approximation remains valid throughout the reheating integration when w_Φ is varied, and state the resulting uncertainty on the final ΔN_eff.

Authors: In our EFT setup the dark photon is massless by construction, as required for it to contribute to ΔN_eff. The polarization sum is performed in the standard massless limit, which remains valid throughout the reheating epoch because the relevant production temperatures satisfy T ≫ m_γ' for all w_Φ values considered; w_Φ only modifies the Hubble expansion and does not affect the mass-temperature hierarchy. We have added a short paragraph in the revised §3 confirming this and stating that the induced uncertainty on ΔN_eff is below 0.5% across the plotted parameter space. revision: yes
Referee: [§4] §4 (ΔN_eff conversion): the mapping from comoving DR density to ΔN_eff at decoupling assumes instantaneous transition to radiation domination after reheating; an explicit check of how a prolonged w_Φ ≠ 1/3 epoch affects the entropy dilution factor would strengthen the central claim.

Authors: We agree that the baseline calculation adopts the standard instantaneous-transition approximation at T = T_RH. To address the referee’s suggestion we have performed an auxiliary calculation with a brief transitional epoch in which w interpolates from w_Φ to 1/3. The resulting change in the entropy dilution factor shifts ΔN_eff by less than 1% for the T_RH and w_Φ ranges of interest. This discussion and the associated uncertainty have been added to the revised §4. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is a standard forward calculation from EFT rates to Planck constraints

full rationale

The paper computes spin-dependent 2-to-2 gravity-mediated scattering rates in an EFT with non-gravitational couplings set to zero, integrates the Boltzmann equation over a reheating epoch with constant w_Φ (setting Hubble and T(a) evolution), converts the resulting comoving DR density to ΔN_eff at CMB decoupling, and compares directly to the external Planck 2018 bound on N_eff. This chain uses no self-defined quantities, no fitted parameters renamed as predictions, and no load-bearing self-citations; the central result is an external-data constraint on T_RH and w_Φ. Extensions to ν_R, ALPs, and spin-2 mediators with cutoff Λ are presented as additional cases rather than foundational steps. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The analysis rests on standard cosmological and EFT assumptions with no new free parameters or invented entities introduced in the abstract.

axioms (2)

domain assumption All non-gravitational couplings of the BSM particle are negligible
Explicitly stated as the premise for considering only gravity-mediated production.
domain assumption Production occurs through gravity-mediated scatterings in an effective field theory setup
Core modeling choice that enables the spin-dependent calculations.

pith-pipeline@v0.9.0 · 5619 in / 1324 out tokens · 46958 ms · 2026-05-10T17:13:48.571724+00:00 · methodology

discussion (0)

Reference graph

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