Spontaneous Symmetry Breaking and the Cosmological Constant

TL;DR

This paper explores how spontaneous symmetry breaking in a cosmological model involving antisymmetric fields can lead to a small or neutralized cosmological constant, using a Ginzburg-Landau analogy to identify possible solutions.

Contribution

It introduces a novel approach linking instantons and symmetry breaking to the cosmological constant problem through a Ginzburg-Landau framework.

Findings

Identifies three solutions based on the relative magnitude of cosmological constants.

Shows that symmetry restoration via instantons can neutralize the cosmological constant.

Proposes a scenario consistent with a small, non-zero cosmological constant.

Abstract

An approach that allows studying the relationship between the neutralization of the cosmological constant and instantons for cosmology coupled to antisymmetric fields is proposed. Using suitable variables, the Lagrangian leading to the FRW equations can be written analogously to a Ginzburg-Landau theory and we show how spontaneous symmetry breaking appears. The approach leads to three possible solutions, if we denote $\Lambda_1$ and $\Lambda_2$ as the cosmological constants that come from gravity ($\Lambda_1$) and antisymmetric fields ($\Lambda_2$), then the solutions, a) $ |\Lambda_2|>|\Lambda_1|$ is consistent with a very small but non-zero $\Lambda_1$, b) $|\Lambda_2|<|\Lambda_1|$, then $\Lambda_1$ is observationally ruled out and, c) $|\Lambda_2|=|\Lambda_1|$ is a solution with finite action and instantons restoring the symmetry $\varphi \to -\varphi$. The third solution is also consistent with neutralization of the cosmological constant in four dimensions.