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Holographic bounce

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Pith's one-line read Holographic infrared and ultraviolet cutoffs can produce bouncing solutions, including nonsingular ones, and can be designed to reproduce F(R) gravity bounce.

arxiv 1908.00389 v2 pith:IQQA4QJG submitted 2019-08-01 gr-qc astro-ph.COhep-th

Shin'ichi Nojiri , Sergei D. Odintsov , Emmanuel N. Saridakis This is my paper · ORCID
classification gr-qcastro-ph.COhep-th
keywords bouncecutoffsholographichorizonsapplicationbouncingconsidercorrection
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Holographic dark energy is an old idea for the late universe: it says the vacuum energy density is set by the largest distance, or horizon, in the theory. This paper tries the same idea at early times. If the universe's energy is proportional to one over the square of a horizon length, then as the horizon shrinks during a contracting phase the energy density grows. The authors solve the Friedmann equation with the particle horizon and the future event horizon as the relevant length. For a specially chosen value of the constant c, the solution is a scale factor that shrinks and then grows again, which looks like a bounce.

The simple solutions touch zero scale factor, so they are singular. The authors then add an ultraviolet correction to the horizon, as is common in high-energy models. The corrected equations have a bounce where the scale factor stays positive, and the minimum size is controlled by the ultraviolet scale. They plot examples.

In the last part, the authors construct more general extended infrared cutoffs. By choosing the cutoff function appropriately, the first Friedmann equation becomes exactly the equation of F(R) gravity, in particular R-squared gravity. Since R-squared gravity is already known to have bounce solutions, the holographic framework can be made to reproduce those bounces. The paper does not analyze perturbations or compare with observations, and it does not explicitly compute the null energy condition, so the model is a construction rather than a tested scenario.

Extended reading notes

Core claim

The central claim is that applying the holographic principle at early times, with the particle or future event horizon as the infrared cutoff, produces a bouncing scale factor, and that adding an ultraviolet correction yields nonsingular bounces whose minimum scale factor is controlled by the ultraviolet cutoff. The paper states in the abstract: 'adding a simple correction to the horizons due to the Ultraviolet cutoff we analytically obtain improved nonsingular bouncing solutions, in which the value of the minimum scale factor is controlled by the UV correction.'

Load-bearing premise

The load-bearing premise is the holographic relation in Eq (5), H^2 = c^2/L_IR^2, where L_IR is taken to be a horizon integral from Eq (3) and the same holographic fluid is assumed to be the only energy content of the early universe. If the horizon integrals diverge at the turnaround, or if the cutoff relation is only heuristic, the bounce solution does not follow. The paper never checks that a(t) proportional to (t-t0)^2 keeps the particle or future event horizon finite across the bounce, and the null energy condition violation is asserted without computation.

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Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The model rests on the holographic density relation (1), the Friedmann equation (4), and the chosen horizon definitions. The bounce behavior is obtained by fixing c = 2, selecting branches, and for the generalized cutoffs by designing L_IR to match the known F(R) gravity equations. No new particles, forces, or geometric objects are introduced.

free parameters (7)
  • c = 2 (chosen to make the exponent in Eq (7) even)
    The holographic density parameter c is set to 2 to obtain a(t) proportional to (t-t0)^2.
  • Lambda_UV = 20, 30, 50 in Figure 1
    The ultraviolet cutoff is a free scale chosen to illustrate the nonsingular bounce; its value controls the minimum scale factor.
  • alpha = constrained by Eq (20), with lambda = 1/(36 alpha)
    The R^2 coefficient alpha in the F(R)-reproducing cutoff is a free model parameter tied to the bounce rate lambda.
  • beta = free
    Parameter in the extended cutoffs (21) and (26) controlling the power-law behavior a(t) ~ t^(2 beta).
  • B = free / integration constant
    Parameter in the cutoff (21) and in the solution (24).
  • A = free / integration constant
    Parameter in the cutoff (26) and in the solution (24).
  • H0 = H0^2 = 1/(216 alpha) from Eq (20)
    The cosmological-constant scale in the F(R) model is set by alpha to allow the bounce.
assumptions (6)
  • domain assumption Holographic energy density satisfies rho = 3 c^2/(kappa^2 L_IR^2).
    Equation (1) is assumed from the holographic dark energy literature; it is the starting point for the whole construction.
  • domain assumption The Friedmann equation H^2 = kappa^2 rho/3 holds with only the holographic fluid as the energy content.
    Equation (4) neglects matter and radiation in the early universe.
  • domain assumption The infrared cutoff is a particle or future event horizon, with ultraviolet modification L_IR -> sqrt(L^2 + 1/Lambda_UV^2).
    Equations (3) and (8) are taken from prior literature without derivation.
  • ad hoc to paper Extended infrared cutoffs may be arbitrary functions of Lp, Lf, a, H, and their derivatives.
    Equation (13) posits a very broad class of cutoffs; the specific examples (14), (21), and (26) are chosen to reproduce desired equations.
  • domain assumption Bounce conditions require H < 0 before, H = 0 at, and H > 0 after the bounce, with H_dot > 0 throughout.
    These are standard bounce criteria and are used to select parameters in Figure 1.
  • domain assumption The known F(R) bounce solution a(t) = a_B exp(lambda t^2/2) is imposed as the solution to test.
    Equation (18) is assumed in Section III, and parameters are adjusted to satisfy Eq (19).

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Pith. "Pith review of Holographic bounce." pith.science (2026). https://pith.science/paper/IQQA4QJG

@misc{pith2026190800389,
  author       = {Pith},
  title        = {Pith review of: Holographic bounce},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IQQA4QJG}},
  note         = {Machine review of arXiv:1908.00389}
}
abstract

We investigate the bounce realization arising from the application of the holographic principle in the early universe, inspired by its well-studied late-time application. We first consider as Infrared cutoffs the particle and future event horizons, and we show that the decrease of the horizons at early times naturally increases holographic energy density at bouncing scales, while we additionally obtain the necessary null energy condition violation. Furthermore, adding a simple correction to the horizons due to the Ultraviolet cutoff we analytically obtain improved nonsingular bouncing solutions, in which the value of the minimum scale factor is controlled by the UV correction. Finally, we construct generalized scenarios, arisen from the use of extended Infrared cutoffs, and as specific examples we consider cutoffs that can reproduce $F(R)$ gravity, and the bounce realization within it.

Figures

Figures reproduced from arXiv: 1908.00389 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

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Forward citations

Cited by 3 Pith papers

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