arxiv: 2605.13636 · v1 · submitted 2026-05-13 · 🌀 gr-qc · hep-th

Recognition: unknown

Cosmological horizons in regular bouncing backgrounds

M. Gasperini

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Pith reviewed 2026-05-14 18:03 UTC · model grok-4.3

classification 🌀 gr-qc hep-th

keywords cosmological horizonsbouncing cosmologyregular bounceevent horizonsparticle horizonscausal structurespacetime geometryscale-factor history

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The pith

Cosmological horizons depend on the full spacetime history rather than the local expansion phase alone.

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

The paper shows that the usual link between decelerated expansion and absent event horizons, or accelerated expansion and absent particle horizons, does not always hold. Horizons are non-local quantities fixed by integrating over the entire past and future conformal-time evolution of the scale factor. The work constructs explicit regular bouncing models that join a pre-bounce phase of growing curvature to a final asymptotic decelerated expansion and determines the resulting horizon structure in each case. A reader would care because this changes how causal connectedness is assessed in any cosmology whose complete history includes a bounce.

Core claim

In regular bouncing backgrounds that connect an initial regime of growing curvature through a smooth bounce to a final phase of standard decelerated expansion, both global event horizons and particle horizons are controlled by the complete past-to-future history of the metric; their presence or absence therefore cannot be read off from the asymptotic expansion rate in the final phase alone.

What carries the argument

Non-local horizon definitions obtained by integrating the conformal-time distance from past infinity to future infinity across the full regular scale-factor history.

If this is right

A final decelerated phase can possess a global event horizon when the pre-bounce contraction supplies enough conformal time.
A final accelerated phase can possess a particle horizon when the pre-bounce history limits the total conformal-time range.
Standard horizon statements derived for pure power-law or de-Sitter expansions must be re-examined once the full history through a bounce is included.
The absence of curvature singularities guarantees that the horizon integrals remain finite and well-defined across the transition.

Where Pith is reading between the lines

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

Bouncing models may alter the usual horizon problem by permitting causal contact through the pre-bounce phase.
CMB or gravitational-wave observables sensitive to large-scale causal structure could carry imprints of these full-history horizons.
The same logic applies to any cosmology whose scale factor is defined over an extended past, whether bouncing or cyclic.

Load-bearing premise

The background must admit a regular bounce that joins the two regimes smoothly without singularities that would render the horizon integrals undefined.

What would settle it

An explicit regular bouncing scale factor for which the event-horizon integral converges or diverges independently of the choice of future expansion history after the bounce.

Figures

Figures reproduced from arXiv: 2605.13636 by M. Gasperini.

**Figure 1.** Figure 1: Left: the Hubble parameter H for the bouncing solution (5). Right: the corresponding radius of the Hubble horizon RH (red curve) and of the event horizon RE (blue dashed curve), from Eqs. (5), (6). It may be appropriate to stress, at this point, that to obtain regular bouncing solutions it is not at all crucial to refer to self-dual string cosmology models (as previously done); also, it is not essential t… view at source ↗

**Figure 2.** Figure 2: Left: the Hubble parameter H for a numerical solution of Eqs. (7), (8), obtained with the same initial conditions used in [9]. The background geometry describes a smooth evolution from decelerated contraction to accelerated expansion. Right: the associated behaviour of the Hubble horizon RH (red curve), of the event horizon RE (blue dashed curve) and of the particle horizon RP (black dotted curve). The num… view at source ↗

**Figure 3.** Figure 3: Left: the Hubble parameter H for the bouncing solution (10), with s = 1 and r = 1/2. Right: the associated behaviour of the Hubble horizon RH (red curve), of the event horizon RE (blue dashed curve) and of the particle horizon RP (black dotted curve). where Γ(x) is the Euler gamma function and 2F1 (a, b, c; x) is the Gauss hypergeometric function. The time evolution of the above expressions for RP , RE, co… view at source ↗

**Figure 4.** Figure 4: Left: the Hubble radius RH (red curve) and the local perturbation radius Rλ (black dashed curve) for the bouncing solution (9) with q = 4. Right: the same for the bouncing solution (10) with s = 1 and r = 1/2. and event horizon presented here have no direct consequences at all for the amplification of the quantum metric fluctuations, whose evolution is governed by a different local horizon Rλ(t), defined b… view at source ↗

read the original abstract

It is often stated that a phase of standard, decelerated cosmological expansion is characterised by the absence of global event horizons, while a phase of accelerated expansion is associated with the absence of particle horizons. This is not necessarily true because such horizons, being non-local properties of the spacetime geometry, depend on the full (past and future) history of the given cosmological background. We provide examples of various different scenarios for the case in which the final asymptotic phase of standard expansion and decreasing curvature is connected, through a regular bounce, with an initial (and possibly infinitely extended in time) regime of growing curvature.

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

0 major / 3 minor

Summary. The paper argues that the presence or absence of cosmological event and particle horizons is not determined solely by the local expansion behavior (decelerated vs. accelerated) but depends on the full past and future history of the scale factor. It constructs explicit examples of regular bouncing spacetimes that connect an initial regime of growing curvature (possibly infinitely extended) to a final asymptotic phase of standard decelerated FLRW expansion, showing that horizons in the final phase can deviate from naive expectations based on local dynamics alone.

Significance. If the constructed metrics are regular and the horizon integrals are correctly computed, the result usefully clarifies the non-local character of horizons and provides concrete counterexamples to common textbook statements. This is relevant for bouncing cosmology models, where the full spacetime history must be considered when discussing horizon problems or observational signatures.

minor comments (3)

[§3] §3: The explicit form of the scale factor a(η) across the bounce should include a brief verification that the curvature invariants remain finite at the matching point to confirm regularity.
The horizon integrals (e.g., the particle horizon distance) are evaluated over the full conformal-time range; adding a short numerical table for one example would make the dependence on the past history more transparent.
[References] References: Include citations to standard treatments of horizons in FLRW spacetimes (e.g., Rindler or Misner) to situate the non-local argument.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive evaluation and the recommendation of minor revision. The referee's summary correctly identifies the central claim of the paper: that the presence or absence of event and particle horizons in cosmological spacetimes is determined by the complete past and future evolution of the scale factor rather than by the local expansion rate alone. We appreciate the recognition that the constructed regular bouncing metrics serve as concrete counterexamples to common textbook statements.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper applies the standard non-local definitions of particle and event horizons (integrals over the full conformal-time history of the scale factor) to explicitly constructed regular bouncing metrics that connect a past growing-curvature regime to a future decelerated FLRW-like phase. These metrics are introduced directly as solutions satisfying the regularity assumption, and the horizon properties are computed from them without any parameter fitting, self-definitional reduction, or load-bearing self-citation chains. The central claim that horizons depend on the complete spacetime history follows immediately from the definitions themselves when applied to the new backgrounds, rendering the derivation self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard general-relativistic definition of particle and event horizons together with the assumption that the spacetime admits a regular bounce. No free parameters, new entities, or ad-hoc axioms are introduced in the abstract.

axioms (1)

domain assumption Cosmological spacetimes are described by metrics that admit a regular bounce connecting growing-curvature and standard-expansion phases
Invoked to define the backgrounds in which the horizon properties are examined.

pith-pipeline@v0.9.0 · 5380 in / 1193 out tokens · 91455 ms · 2026-05-14T18:03:05.534953+00:00 · methodology

discussion (0)

Reference graph

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