On the Holographic Principle in a Radiation Dominated Universe

By Erik P. Verlinde. 2000

221 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9515357cd11895762cd62277be659da300ab3ac6

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Citations in the corpus

FRIEDMANN–ROBERTSON–WALKER BRANE COSMOLOGICAL EQUATIONS FROM THE FIVE-DIMENSIONAL BULk (A)dS BLACK HOLE (2002, methodology): “The definitions for the Hubble, Bekenstein [11] and Bekenstein-Hawking entropies are given as following [ 4 ]:”
Viscous Cosmology for Early- and Late-Time Universe (2017, background): “rovided to assume the universe’s maximum entropy to be identiﬁed with the entropy of a black hole having the same size as the Hubble radius [161–164]. Nevertheless, more precise arguments of Verlinde [160] lead to the replacement of the factor 4 in the denominator with a factor 2, that is SH ∼ HV 2G”
D‐branes in Standard Model building, gravity and cosmology (2003, background): “3) (8)See also [62] for a related view.”
Anti-de Sitter Black Holes, Thermal Phase Transition and Holography in Higher Curvature Gravity (2002, methodology): “metric on the brane takes the standard Robertson-Walker form ds2 d = −dη 2 +r2(η)dΩ2 d−1 , (77) and the radial distance r measures the size of d-dimensional universe from the center of the black hole [48]. When applying the holography in the above context, one considers an d-dimensional brane with a”
The Holographic principle (2002, background): “A number of authors (e.g., Brustein and Veneziano, 2000; Verlinde, 2000; Brustein, Foffa, and Veneziano, 2001; see Cai, Myung, and Ohta, 2001, for additional references) have discussed interesting bounds which are not directly based on the area of surfaces.”
CFT and Entropy on the Brane (2001, background): “We show that the induced geometry of the brane is exactly given by that of a standard radiation dominated FRW-universe.”
Emergent Gravity and the Dark Universe (2016, background): “will be presented elsewhere. 4 The result (2.20) looks identical to the Cardy formula, but does not require the existence of 2d-CFT. Similar expressions for the holographic entropy have been found in [45, 46]. 12 3 Glassy Dynamics and Memory Eects in Emergent Gravity In this section we address an im”
Lectures on string/brane cosmology (2002, methodology): “Here we will follow Verlinde [27] who, in a very elegant way, recovered the Fried- mann equation (see also [88]).”