Evolving Maximally Symmetric Spacetime Bubbles from Spontaneous Z_2-Violation at Electroweak Symmetry Breaking Scale

TL;DR

This paper explores how spontaneous Z_2 symmetry breaking at the electroweak scale can lead to the formation of maximally symmetric spacetime bubbles, with implications for cosmology and universe topology.

Contribution

It explicitly formulates Einstein-Gordon equations with spontaneous Z_2 symmetry breaking and finds exact solutions describing anti-de Sitter bubbles in a cosmological context.

Findings

Exact solutions for Z_2-symmetry breaking Einstein-Gordon equations.

Identification of anti-de Sitter and Milne universes as fixed points.

Implications for Higgs-anti-de Sitter bubbles in cosmology.

Abstract

The Einstein-Gordon equations for Friedmann-Robertson-Walker (FRW) geometries in feedback reaction with the quartically self-interacting physical field, arisen from the "inner parity" spontaneous breaking, are explicitly formulated. The Hamiltonian density non-positive extrema would classically forbid both spatially closed and flat homogeneous and isotropic worlds if these were to allow the physical field to (repeatedly) go through and to (finally) settle down in a ground state. In this respect, the fixed point exact solutions of the spontaneous Z_2-symmetry breaking Einstein-Gordon equations (mandatory) describe (k=-1)-FRW manifolds which actually are either Milne or anti-de Sitter Universes. Setting the Z_2-invariance breaking scale at the one of the electroweak symmetry, we speculate on the cosmological implications of the Higgs-anti-de Sitter bubbles and derive a set of particular closed-form solutions to the S_2-cobordism with a spatially flat FRW Universe.