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On the Holographic Principle in a Radiation Dominated Universe

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arxiv hep-th/0008140 v2 pith:NM7WHSST submitted 2000-08-17 hep-th

Erik Verlinde This is my paper · ORCID
classification hep-th
keywords boundenergyentropyholographichubbleradiationuniversecardy
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abstract

The holographic principle is studied in the context of a $n+1$ dimensional radiation dominated closed Friedman-Robertson-Walker (FRW) universe. The radiation is represented by a conformal field theory with a large central charge. Following recent ideas on holography, it is argued that the entropy density in the early universe is bounded by a multiple of the Hubble constant. The entropy of the CFT is expressed in terms of the energy and the Casimir energy via a universal Cardy formula that is valid for all dimensions. A new purely holographic bound is postulated which restricts the sub-extensive entropy associated with the Casimir energy. Unlike the Hubble bound, the new bound remains valid throughout the cosmological evolution. When the new bound is saturated the Friedman equation exactly coincides with the universal Cardy formula, and the temperature is uniquely fixed in terms of the Hubble parameter and its time-derivative.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Finite-cutoff Holographic Thermodynamics

    hep-th 2025-07 conditional novelty 6.0 of 10

    Finite-cutoff holography yields a thermodynamic duality between T^2-deformed CFTs and Schwarzschild-AdS black holes with a Dirichlet wall, including a teardrop coexistence curve with up to three states at one temperature.

  2. Cardy Entropy of Charged and Rotating Asymptotically AdS and Lifshitz Solutions with a Generalized Chern-Simons term

    hep-th 2025-06 conditional novelty 6.0 of 10

    A generalized Cardy-like formula using the soliton mass as vacuum energy reproduces the entropy of charged rotating AdS and Lifshitz black holes in three dimensions.

  3. The Cardy Formula from Goldstone Bosons

    hep-th 2019-07 unverdicted novelty 6.0 of 10

    Derives the Cardy formula for 2D CFTs from the Schwarzian action of pseudo Goldstone bosons under anomalous conformal symmetry breaking, without modular invariance.

  4. Entropy bounds, Geroch process, and the sign of deformation parameter

    hep-th 2026-07 conditional novelty 5.0 of 10

    Negative GUP deformation relaxes the Bekenstein entropy bound and positive deformation tightens it, derived via the Geroch process in both 3+1 and 2+1 dimensions.

  5. Holographic pressure and volume for black holes

    hep-th 2026-02 unverdicted novelty 5.0 of 10

    Introduces a holographic pressure and volume for static spherically symmetric black holes via quasi-local thermodynamics, showing large black holes become extensive in the large-system limit while small ones do not.

  6. Hamilton-Jacobi Approach to Inflationary Scenarios through Extended Entropies: An Observational Perspective

    astro-ph.CO 2026-05 unverdicted novelty 4.0 of 10

    Hamilton-Jacobi analysis of slow-roll inflation with non-Bekenstein-Hawking entropies yields fitted entropy parameters (δ≈1.1-1.2, α∼10^{-14}, K∼10^{-17}) consistent with ns and r data.

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