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arxiv: 1907.10295 · v1 · pith:H6RO4BB2new · submitted 2019-07-24 · 🌀 gr-qc · astro-ph.CO

Einstein or Jordan: seeking answers from the reheating constraints

Debottam Nandi (IIT Madras , India) , Pankaj Saha (IIT Madras This is my paper

Pith reviewed 2026-05-24 17:05 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.CO
keywords Einstein frameJordan framereheating constraintsinflationary energy scalethermal historyconformal framesobservational signatures
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The pith

Reheating constraints can distinguish Einstein and Jordan frames despite nearly identical ns and r values.

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

The paper investigates whether the Einstein and Jordan frames, which are conformally related and yield almost the same scalar spectral index and tensor-to-scalar ratio, can be separated by studying the reheating phase after inflation. Background evolution differs substantially between the frames, producing different inflationary energy scales. These scale differences drive distinct values for the reheating e-folding number and therefore different reheating temperatures. The resulting contrast in thermal history may leave detectable traces in future observations and could help select the correct gravitational frame for the universe.

Core claim

The difference in the inflationary energy scales in these frames contributes to a significant difference in the reheating e-folding number and hence different reheating temperature, leading to a contrasting thermal history in the two frames that may have a potential observational signature.

What carries the argument

The reheating e-folding number, which links the end of inflation to the onset of radiation domination and depends directly on the inflationary energy scale in each frame.

Load-bearing premise

The difference in background evolution between the frames produces a reheating temperature shift large enough to survive later cosmic evolution and remain detectable by future observations independent of other model uncertainties.

What would settle it

A future measurement of the reheating temperature or the duration of the reheating epoch that matches the prediction of one frame but lies outside the range allowed by the other frame.

Figures

Figures reproduced from arXiv: 1907.10295 by Debottam Nandi (IIT Madras, India), Pankaj Saha (IIT Madras.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
read the original abstract

Distinguishing conformally coupled frames from the tree-level perturbative observables (scalar spectral index $n_{\rm s}$ and tensor-to-scalar ratio $r$) is challenging in cosmology as they are nearly identical. However, since the background evolution in these two frames differs significantly, we can look for potential signatures in the reheating constraints to discriminate these frames. In this work, we study the reheating phase in these frames and find that the difference in the inflationary energy scales in these frames contributes to a significant difference in the reheating e-folding number and hence, different reheating temperature. This difference will eventually lead to a contrasting thermal history in the two frames, which may have a potential observational signature in future observations. This study will open up an avenue for distinguishing various conformally connected otherwise indistinguishable frames and may finally lead us to the correct theory of gravity for our Universe.

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 / 1 minor

Summary. The paper claims that while the scalar spectral index ns and tensor-to-scalar ratio r are nearly identical in conformally related Einstein and Jordan frames (making them hard to distinguish from tree-level perturbative observables), the differing background evolution produces a significant difference in the reheating e-folding number and thus reheating temperature; this leads to contrasting thermal histories that may yield observable signatures in future data and could help identify the correct gravitational theory.

Significance. If the frame-induced shift in reheating temperature is robustly larger than the spread induced by standard reheating modeling freedoms (w_reh, Gamma, g_*), the result would supply a concrete, falsifiable route to break the degeneracy between conformally related frames that are indistinguishable at the level of ns and r, thereby adding a new observable handle on the choice of frame in scalar-tensor or f(R) inflation.

major comments (1)
  1. [Abstract] Abstract, paragraph 2: the central claim that the difference in inflationary energy scales produces a 'significant difference' in N_reh and T_reh (leading to an observable signature) is load-bearing, yet the text supplies no explicit numerical comparison of the frame-induced Delta T_reh against the variation obtained by scanning plausible ranges of w_reh (e.g., -1/3 to 1) or post-reheating entropy injection; without this, it remains unclear whether the effect survives modeling uncertainty.
minor comments (1)
  1. The abstract would be clearer if it named the specific conformal frames or inflationary potentials under study rather than referring generically to 'these frames'.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful and constructive report. The single major comment is addressed point-by-point below. We agree that an explicit numerical comparison is required to support the central claim and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract, paragraph 2: the central claim that the difference in inflationary energy scales produces a 'significant difference' in N_reh and T_reh (leading to an observable signature) is load-bearing, yet the text supplies no explicit numerical comparison of the frame-induced Delta T_reh against the variation obtained by scanning plausible ranges of w_reh (e.g., -1/3 to 1) or post-reheating entropy injection; without this, it remains unclear whether the effect survives modeling uncertainty.

    Authors: We agree that the abstract claim requires an explicit benchmark against reheating-parameter uncertainties to be robust. In the revised manuscript we will (i) add a short quantitative comparison (new table or paragraph) that reports the frame-induced ΔT_reh for the models considered and contrasts it with the spread obtained by scanning w_reh ∈ [-1/3,1] and plausible g_* and entropy-injection variations; (ii) update the abstract to reference this comparison. The core result that the frames produce different background evolution and therefore different N_reh remains unchanged, but the revision will make the significance statement evidence-based. revision: yes

Circularity Check

0 steps flagged

No circularity: frame differences follow from standard conformal transformations and background equations.

full rationale

The provided abstract and context describe a comparison of reheating e-folds and temperature between Einstein and Jordan frames arising from their differing inflationary energy scales under conformal rescaling. This is a direct consequence of the metric and field transformations (standard in the literature), not a quantity fitted from the paper's own data or defined in terms of the target observable. No equations, self-citations, or fitted inputs are shown that reduce the central claim to a tautology or self-referential fit. The derivation remains independent of the paper's results and rests on external, falsifiable background cosmology.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Assessment limited to abstract; the central claim rests on standard assumptions of single-field inflation and perturbative reheating whose validity is not re-derived here.

axioms (1)
  • domain assumption Standard single-field slow-roll inflation and perturbative reheating dynamics hold in both frames
    Invoked to translate energy-scale difference into e-folding and temperature difference (abstract paragraph 2)

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discussion (0)

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Reference graph

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