Early universe thermostatistics in curved momentum spaces

TL;DR

This paper explores the thermodynamics of the early universe within doubly special relativity theories formulated on curved momentum spaces, revealing finite microstates and entropy bounds consistent with loop quantum cosmology.

Contribution

It introduces a method to study statistical mechanics in doubly special relativity models on curved momentum spaces, deriving entropy bounds for early universe thermodynamics.

Findings

Finite total microstates in a specific anti-de Sitter momentum space model.

Entropy and energy bounds for early universe radiation.

Results align with nonsingular loop quantum cosmology equations.

Abstract

The theories known as doubly special relativity are introduced in order to take into account an observer-independent length scale and the speed of light in the framework of special relativity. These theories can be generally formulated on the de Sitter and also recently proposed anti-de Sitter momentum spaces. In the context of these theories, we study the statistical mechanics and to do this, we consider the natural measure on the corresponding extended phase space. The invariant measure on the space of distinct microstates is obtained by restriction of the natural measure of the extended phase space to the physical phase space through the disintegration theorem. Having the invariant measure, one can study the statistical mechanics in an arbitrary ensemble for any doubly special relativity theory. We use the constructed setup to study the statistical properties of four doubly special relativity models. Applying the results to the case of early universe thermodynamics, we show that one of these models that is defined by the cosmological coordinatization of anti-de Sitter momentum space, implies a finite total number of microstates. Therefore, without attribution to any ensemble density and quite generally, we obtain entropy and internal energy bounds for the early radiation dominated universe. We find that while these results cannot be supported by the standard Friedmann equations, they indeed are in complete agreement with the nonsingular effective Friedmann equations that arise in the context of loop quantum cosmology.