Gravitational Entropy and the Second Law of Thermodynamics

TL;DR

This paper proposes that spontaneous Lorentz symmetry breaking near the big bang reduces gravitational entropy, establishing an arrow of time consistent with the second law of thermodynamics through a phase transition.

Contribution

It introduces a model linking gravitational entropy, symmetry breaking, and phase transitions to explain the arrow of time in cosmology.

Findings

Spontaneous Lorentz symmetry breaking occurs at a critical temperature.

The ordered phase has vanishingly small entropy, while the disordered phase has large entropy.

A phase transition explains the increase in entropy as the universe expands.

Abstract

The spontaneous violation of Lorentz and diffeomorphism invariance in a phase near the big bang lowers the entropy, allowing for an arrow of time and the second law of thermodynamics. The spontaneous symmetry breaking leads to $O(3,1)\rightarrow O(3)\times R$, where $O(3)$ is the rotational symmetry of the Friedmann-Lema\^{i}tre-Robertson-Walker spacetime. The Weyl curvature tensor $C_{\mu\nu\rho\sigma}$ vanishes in the FLRW spacetime satisfying the Penrose zero Weyl curvature conjecture. The requirement of a measure of gravitational entropy is discussed. The vacuum expectation value $\langle 0\vert\psi_\mu\vert 0\rangle\neq 0$ for a vector field $\psi_\mu$ acts as an order parameter and at the critical temperature $T_c$ a phase transition occurs breaking the Lorentz symmetry spontaneously. During the ordered $O(3)$ symmetry phase the entropy is vanishingly small and for $T < T_c$ as the universe expands the anti-restored $O(3,1)$ Lorentz symmetry leads to a disordered phase and a large increase in entropy creating the arrow of time.