Cardy-Verlinde formula in FRW Universe with inhomogeneous generalized fluid and dynamical entropy bounds near the future singularity

Diego S\'aez-G\'omez; Iver Brevik; Sergei D. Odintsov; Shin'ichi Nojiri

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Cardy-Verlinde formula in FRW Universe with inhomogeneous generalized fluid and dynamical entropy bounds near the future singularity

Iver Brevik, Shin'ichi Nojiri, Sergei D. Odintsov, Diego Sáez-Gómez

High Energy Physics - Theory · Submitted 9 Feb 2010

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim It is demonstrated that except from some special cases of Type II and Type IV singularities the dynamical entropy bound is violated near the singularity even if quantum effects are taken into account.

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arXiv ID1002.1942 (version 2)

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CitationDiego S\'aez-G\'omez, Iver Brevik, Sergei D. Odintsov, Shin'ichi Nojiri. "Cardy-Verlinde formula in FRW Universe with inhomogeneous generalized fluid and dynamical entropy bounds near the future singularity." arXiv:1002.1942 (2010). https://pith.science/paper/HE5WNFRY

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.91 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.36 · compares with prior results 0.84 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We derive a Cardy-Verlinde-like formula which relates the entropy of the closed FRW universe to its energy, and Casimir energy, for a multicomponent coupled fluid. The generalized fluid obeys an inhomogeneous equation of state. A viscous dark fluid is included, and we include also modified gravity using its fluid representation. It is demonstrated how such an expression reduces to the standard Cardy-Verlinde formula corresponding to the 2d CFT entropy only in some special cases. The dynamical entropy bound for a closed FRW universe with dark components is obtained. The universality of the dynamical entropy bound near a future singularity (of all four types), as well as near the Big Bang singularity, is investigated. It is demonstrated that except from some special cases of Type II and Type IV singularities the dynamical entropy bound is violated near the singularity even if quantum effects are taken into account. The dynamical entropy bound seems to be universal for the case of a regular universe, including the asymptotic de Sitter one.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We derive a Cardy-Verlinde-like formula which relates the entropy of the closed FRW universe to its energy, and Casimir energy, for a multicomponent coupled fluid.	contribution 0.85	0.96	0.20	asserted 1.00
s1	The generalized fluid obeys an inhomogeneous equation of state.	method 0.55	0.42	0.03	asserted 1.00
s2	A viscous dark fluid is included, and we include also modified gravity using its fluid representation.	contribution 0.57	0.88	0.03	asserted 0.98
s3	It is demonstrated how such an expression reduces to the standard Cardy-Verlinde formula corresponding to the 2d CFT entropy only in some special cases.	result 0.77	0.91	0.12	asserted 1.00
s4	The dynamical entropy bound for a closed FRW universe with dark components is obtained.	result 0.68	0.94	0.10	asserted 0.99
s5	The universality of the dynamical entropy bound near a future singularity (of all four types), as well as near the Big Bang singularity, is investigated.	contribution 0.98	0.88	0.11	unclear 0.59
s6	It is demonstrated that except from some special cases of Type II and Type IV singularities the dynamical entropy bound is violated near the singularity even if quantum effects are taken into account.	result 1.00	0.91	0.41	asserted 1.00
s7	The dynamical entropy bound seems to be universal for the case of a regular universe, including the asymptotic de Sitter one.	result 0.95	0.85	0.16	hedged possibility 0.95

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Original abstract

We derive a Cardy-Verlinde-like formula which relates the entropy of the closed FRW universe to its energy, and Casimir energy, for a multicomponent coupled fluid. The generalized fluid obeys an inhomogeneous equation of state. A viscous dark fluid is included, and we include also modified gravity using its fluid representation. It is demonstrated how such an expression reduces to the standard Cardy-Verlinde formula corresponding to the 2d CFT entropy only in some special cases. The dynamical entropy bound for a closed FRW universe with dark components is obtained. The universality of the dynamical entropy bound near a future singularity (of all four types), as well as near the Big Bang singularity, is investigated. It is demonstrated that except from some special cases of Type II and Type IV singularities the dynamical entropy bound is violated near the singularity even if quantum effects are taken into account. The dynamical entropy bound seems to be universal for the case of a regular universe, including the asymptotic de Sitter one.

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9 arXiv papers cite this in 10 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 3 sentences without a confident label

Cites it as background 7 papers

Dark energy universe with a viscous fluid was studied in Refs. [ref] .

The effect of thermal radiation on singularities in the dark universe · Introduction · 0.87
For more details, the reader may consult Refs. [ref] , and additionally the related Ref. [ref] .

Viscous Cosmology for Early- and Late-Time Universe · Viscous cosmology and the Cardy-Verlinde formula · 0.95
[This Chapter is based on: [ref] ]In the above chapters, several alternatives to explain the dark energy epoch have been analised, and even the inflationary phase by means mainly of modifications of gravity, which can be modelled as effective fluids.

On Friedmann-Lema\^{\i}tre-Robertson-Walker cosmologies in non-standard gravity · Discussion · 0.81

What it cites · 31 sentences without a confident label

Builds on 2 papers

This section is devoted to consideration of the Cardy-Verlinde formula for more general scenarios than those considered in previous works (see [ref] - [ref] ).

On the Holographic Principle in a Radiation Dominated Universe · Generalization of Cardy-Verlinde formula in FRW Universe for various types of fluids · 0.83
This section is devoted to consideration of the Cardy-Verlinde formula for more general scenarios than those considered in previous works (see [ref] - [ref] ).

A Note on the Cardy-Verlinde Formula · Generalization of Cardy-Verlinde formula in FRW Universe for various types of fluids · 0.83

Compares with 1 paper

This is the same result as obtained in Ref. [ref] where numerical analysis showed that the singularity is moderated by the conformal anomaly, so that the violation of the bound that naturally occurs in the classical case can be avoided/postponed when quantum effects are included.

Properties of singularities in (phantom) dark energy universe · Big Rip Singularity · 0.80

Cites as support 1 paper

Even if quantum effects are included, as was pointed in Ref. [ref] , for this type of singularity the energy density diverges more rapidly than in the classical case, so that the bound is also violated in the presence of quantum effects.

Properties of singularities in (phantom) dark energy universe · Type III singularity · 0.96

Cites as background 14 papers

In Ref. [ref] , Verlinde proposed a new universal bound on cosmology based on a restriction of the Casimir energy $E_C$; cf. his entropy formula ([ref]).

On the Holographic Principle in a Radiation Dominated Universe · On the cosmological bounds near future singularities · 0.93
Actually, the study of Ref. [ref] shows that there are four different types of future finite-time singularities where the Type I singularity corresponds to the Big Rip, the sudden singularity is of Type II, etc.

Properties of singularities in (phantom) dark energy universe · Introduction · 0.86
(see Refs. [ref] ) * Type III: For $t→t_s$, $a→a_s$ and $ρ→∞$, $|p|→∞$. * Type IV: For $t→t_s$, $a→a_s$ and $ρ→ρ_s$, $p →p_s$ but higher derivatives of Hubble parameter diverge.

The future evolution and finite-time singularities in $F(R)$-gravity unifying the inflation and cosmic acceleration · On the cosmological bounds near future singularities · 0.90

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