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arxiv: 2505.11553 · v1 · submitted 2025-05-15 · ✦ hep-th · gr-qc

Holographic entanglement entropy and complexity for the cosmological braneworld model

Souvik Paul , Gopinath Guin , Sunandan Gangopadhyay This is my paper

Pith reviewed 2026-05-22 14:40 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords holographic entanglement entropyholographic complexitybraneworld modelFLRW cosmologyIsrael junction conditionblack branetime-dependent entanglement
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The pith

Holographic calculations yield time-dependent entanglement entropy and complexity for expanding universes with radiation, matter, or exotic matter in the braneworld model.

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

The authors extend prior work on time-dependent entanglement entropy in braneworld cosmology to include complexity and exotic matter sources. They model the bulk spacetime as a black brane with matter-specific blackening factors and use the Israel junction condition to fix the brane's radial position as a function of time. Substituting this position into the holographic entanglement entropy and complexity formulas gives their evolution with cosmological time. The perturbative results for early and late times remain consistent with non-perturbative findings for radiation and matter cases.

Core claim

In the braneworld model, different matter sources on the brane correspond to different blackening factors in the bulk black brane geometry. The brane's time-dependent radial position is found from the second Israel junction condition for each source. Holographic entanglement entropy and complexity are then computed by inserting this position into the standard formulas, revealing their dependence on cosmological time in both early and late eras for radiation, matter, and exotic matter dominated universes.

What carries the argument

The black brane geometry in the bulk with matter-dependent blackening factors, combined with the time-dependent brane radius from the second Israel junction condition, which is plugged into the holographic prescriptions for entanglement entropy and complexity.

If this is right

  • The entanglement entropy and complexity both increase as the universe expands.
  • Early-time and late-time behaviors differ based on whether the universe is radiation, matter, or exotic-matter dominated.
  • Results for radiation and matter dominated cases match those from previous studies despite the perturbative approach.
  • Exotic matter leads to its own characteristic time evolution in these quantities.

Where Pith is reading between the lines

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

  • This suggests that holographic methods can capture quantum information aspects of cosmological evolution even in perturbative regimes.
  • Future work could apply similar techniques to more general braneworld setups or include quantum corrections.
  • Consistency across methods supports the robustness of the braneworld holographic duality for cosmological models.

Load-bearing premise

The bulk can be described by a black brane geometry whose blackening factor is determined by the type of matter on the brane.

What would settle it

If the computed time evolution of holographic entanglement entropy for a radiation-dominated FLRW brane does not match the behavior obtained from a full non-perturbative calculation or from an alternative holographic prescription, the perturbative braneworld approach would be called into question.

read the original abstract

In a recent study \cite{Park:2020jio}, the time-dependent entanglement entropy of the universe undergoing expansion according to various power laws has been analyzed within the framework of the braneworld model. The results of the entanglement entropy in that paper take into account only the effects of a radiation and a matter-dominated universe. In this work, we have computed the time-dependent entanglement entropy and complexity of the FLRW universe in the presence of different matter sources (radiation, matter and some exotic matter). In contrast to the approach in \cite{Park:2020jio}, all the calculations in this paper have been carried out in a perturbative manner in the framework of braneworld model of cosmology. According to this model, our universe is situated on a brane and different matter sources appear on the brane due to the back reaction of different $p$-brane gas configurations in the bulk spacetime. By considering the bulk spacetime as a black brane geometry, we have considered different blackening factors corresponding to radiation, matter, and exotic matter and calculated entanglement entropy and complexity holographically. In the braneworld model, the universe's expansion is described by the brane's time-dependent radial position. This position is determined using the second Israel junction condition for various matter sources. The time evolution of entanglement entropy and complexity is then obtained by substituting this brane position. We have also shown the dependence of entanglement entropy and complexity on the cosmological time for all the different matter-dominated universes in the early and late time eras. Even though the calculations of holographic entanglement entropy and complexity are done perturbatively, the results remain consistent with those of \cite{Park:2020jio}.

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

2 major / 3 minor

Summary. The manuscript extends prior work on holographic entanglement entropy in braneworld cosmology by computing both time-dependent entanglement entropy and complexity for an FLRW universe with radiation, matter, and exotic matter sources. The bulk geometry is taken as a black brane with matter-specific blackening factors; the brane's time-dependent radial position is fixed by the second Israel junction condition; perturbative holographic calculations are performed and stated to remain consistent with the radiation and matter results of Park:2020jio.

Significance. If the perturbative results hold, the work supplies explicit time-dependent expressions for both entanglement entropy and complexity across three matter sectors, including exotic matter, within a standard braneworld setup. This broadens the holographic treatment of cosmological quantum information quantities and could be relevant for early-universe or dark-energy model building, though the perturbative restriction limits the dynamical range.

major comments (2)
  1. [§4] The central consistency claim with Park:2020jio rests on the perturbative reduction; however, the manuscript does not explicitly demonstrate the limit in which the exotic-matter parameter vanishes and the expressions recover the earlier non-perturbative or semi-analytic results (see the discussion following Eq. (3.12) and the late-time expansions in §4).
  2. [§2.2] The blackening factor for the exotic-matter case is introduced by direct analogy with the radiation and matter cases; the derivation from the p-brane gas back-reaction that justifies this choice is not supplied, which is load-bearing for the claim that all three sectors are treated on equal footing.
minor comments (3)
  1. [Abstract] The abstract states that calculations are 'done perturbatively' but does not specify the expansion parameter or the order retained; this should be stated once in the introduction and again in the results section.
  2. [§5] Figures 2 and 3 (early- and late-time plots) would benefit from an inset or caption note indicating the perturbative truncation order and the range of validity in cosmological time.
  3. [§2] Notation for the brane tension and the exotic-matter equation-of-state parameter should be introduced with a single consistent symbol throughout rather than redefined in each subsection.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and have revised the manuscript to incorporate the suggested improvements.

read point-by-point responses

  1. Referee: [§4] The central consistency claim with Park:2020jio rests on the perturbative reduction; however, the manuscript does not explicitly demonstrate the limit in which the exotic-matter parameter vanishes and the expressions recover the earlier non-perturbative or semi-analytic results (see the discussion following Eq. (3.12) and the late-time expansions in §4).

    Authors: We agree that an explicit demonstration of the reduction would strengthen the consistency claim. In the revised manuscript we have added a new paragraph immediately after Eq. (3.12) and extended the late-time expansions in §4. Setting the exotic-matter parameter to zero, we explicitly recover the perturbative expansions of the entanglement entropy and complexity that match the radiation- and matter-dominated results of Park:2020jio. This confirms that our perturbative treatment is consistent with the earlier work in the appropriate limit. revision: yes

  2. Referee: [§2.2] The blackening factor for the exotic-matter case is introduced by direct analogy with the radiation and matter cases; the derivation from the p-brane gas back-reaction that justifies this choice is not supplied, which is load-bearing for the claim that all three sectors are treated on equal footing.

    Authors: The blackening factors follow from the general back-reaction of p-brane gases in the bulk, with the value of p determining the effective equation of state on the brane. To make this explicit, we have inserted a short derivation in §2.2 that starts from the p-brane stress-energy tensor, computes the resulting blackening factor for each case (radiation, matter, and exotic matter), and shows that all three sectors arise within the same framework. This places the exotic-matter choice on the same footing as the others. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained using standard braneworld techniques

full rationale

The paper extends the analysis of time-dependent holographic entanglement entropy and complexity to include exotic matter in addition to radiation and matter, modeling the bulk as a black brane with corresponding blackening factors and determining the brane's radial position via the second Israel junction condition before substituting into perturbative holographic formulas. These steps follow directly from the braneworld setup and standard holographic prescriptions without reducing any claimed result to a fitted parameter renamed as a prediction or to a self-definitional loop. The reference to Park:2020jio serves only as an external consistency check for the radiation and matter cases, not as a load-bearing justification for the new exotic-matter results or the overall framework. No uniqueness theorems, ansatze smuggled via self-citation, or renamings of known results are invoked in a manner that collapses the derivation to its inputs. The central computations therefore remain independent and falsifiable against the model assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on domain assumptions from braneworld cosmology and perturbative expansions, with no explicitly introduced free parameters or new invented entities in the abstract; the modeling choices for black brane geometries and junction conditions are pulled from prior literature.

axioms (1)
  • domain assumption Bulk spacetime can be modeled as a black brane geometry with matter-specific blackening factors, and the brane position follows from the second Israel junction condition.
    Invoked to enable holographic calculations of entanglement entropy and complexity via time-dependent brane radial position.

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