Cosmological Entropy Bounds

Abstract

I review some basic facts about entropy bounds in general and about cosmological entropy bounds. Then I review the Causal Entropy Bound, the conditions for its validity and its application to the study of cosmological singularities. This article is based on joint work with Gabriele Veneziano and subsequent related research. I. TO GABRIELEOn the occasion of your 65th birthday may you continue to find joy in science and life as you have always had, and continue to help us understand our universe with your creative passion and vast knowledge. It is a pleasure and an honor to contribute to this volume and present one of the subjects among your many interests. Thank you for explaining to me why entropy bounds are interesting and for your collaboration on this and other subjects. II. INTRODUCTION A. What are entropy bounds?The second law of thermodynamics states that the entropy of a closed system tends to grow towards its largest possible value. But what is this maximal value? Entropy bounds aim to answer this question.Bekenstein [1] has suggested that for a system of energy E whose size R is larger than its gravitational radius R > R g ≡ 2G N E, entropy is bounded by S ≤ ER/h = R g R l −2 P .Here l P is the Planck length. This is known as the Bekenstein entropy bound (BEB).Entropy bounds are closely related to black hole (BH) thermodynamics and their interplay with their "normal" environment. They are also probably associated with instabilities to forming BH's, however, this has not been proved in an explicit calculation. The original argument of Bekenstein was based on the Geroch process: a thought experiment in which a small thermodynamic system is moved from infinity into a BH. The small system is lowered slowly until it is just outside the BH horizon, and then falls in. By requiring that the generalized second law (GSL) will not be violated one gets inequality (1).A long debate about the relationship between entropy bounds and the GSL has been going on. On one side Unruh, Wald and others [2,3] have argued that the GSL holds automatically, so that entropy bounds cannot be inferred from situations where the law seems to be violated. They argue that the microphysics will eventually take care of any apparent violation. Consequently, they argued that the BEB does not have to be postulated as a separate requirement in addition to the GSL. Responding to their arguments Bekenstein 2[4] has argued that it is not always obvious in a particular example how the system avoids violating the bound and analyzed in detail several of the purported counterexamples of this type and demonstrated in each case the specific mechanism enforcing the bound.Holography [5] (see below) suggests that the maximal entropy of any system is bounded by S HOL ≤ Al −2 P , where A is the area of the space-like surface enclosing a certain region of space. For systems of limited gravity R > R g , and since A = R 2 , the BEB implies the holography bound. Physics up to scales of about 1 TeV is very well described in terms of quantum field theory,...

A Note on the Swampland Distance Conjecture

“…The same bound is obtained if one uses instead the Hubble entropy bound for the entropy in a region of linear size R . Using , we find that the maximum temperature is Then, the condition leads again to Equation .…”

A refined trans-Planckian censorship conjecture

“…The similar bound could also be obtained if the radiation entropy is bounded by the Hubble entropy [65,66],…”

Model of interacting holographic dark energy at the Ricci scale

“…[7][8][9][10]. The rationale behind the latter is that it corresponds to the size of the maximal perturbation leading to the formation of a black hole [11]. The radius of the future event horizon have been profusely used but it suffers from a severe circularity problem.…”