Gravitational Entropy and the Second Law of Thermodynamics

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 $O(3,1)\to O(3)\times R$, where $O(3)$ is the rotational symmetry of the Friedmann-Lemaître-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 $⟨0|{\psi }_{\mu }|0⟩\ne 0$ 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.

4 pages, no figures

References in corpus (3)

• Variable Speed of Light Cosmology, Primordial Fluctuations and Gravitational Waves
• Nonlinear Perturbations in a Variable Speed of Light Cosmology
• Superluminal Gravitational Waves

Cited by in corpus (1)

• Variable Speed of Light Cosmology, Primordial Fluctuations and Gravitational Waves