Propagating q-field and q-ball solution

TL;DR

This paper explores the dynamic properties of the $q$-field, demonstrating the existence of propagating $q$-waves and soliton-like $q$-balls, which could influence early universe vacuum energy regulation.

Contribution

It introduces the concept of propagating $q$-waves and $q$-balls, extending the understanding of $q$-field behavior beyond static solutions.

Findings

Existence of propagating $q$-waves in the vacuum

Identification of a soliton-like $q$-ball solution

Implications for early universe vacuum energy dynamics

Abstract

One possible solution of the cosmological constant problem involves a so-called $q$-field, which self-adjusts so as to give a vanishing gravitating vacuum energy density (cosmological constant) in equilibrium. We show that this $q$-field can manifest itself in other ways. Specifically, we establish a propagating mode ($q$-wave) in the nontrivial vacuum and find a particular soliton-type solution in flat spacetime, which we call a $q$-ball by analogy with the well-known $Q$-ball solution. Both $q$-waves and $q$-balls are expected to play a role for the equilibration of the $q$-field in the very early universe.