On possible composite structure of scalar fields in expanding universe

TL;DR

This paper explores the hypothesis that scalar fields in an expanding universe are composite objects, demonstrating how a tensor field model can produce a scalar Nambu-Goldstone boson whose vacuum expectation value influences the cosmological constant.

Contribution

It introduces a model of a massless tensor field with broken symmetries that results in a composite scalar field affecting cosmological constant dynamics.

Findings

The potential has a degenerate extremum described by a composite scalar.

The scalar acquires a non-zero vacuum expectation value.

The cosmological constant depends on model parameters and can be zero.

Abstract

Scalar fields in curved backgrounds are assumed to be composite objects. As an example realizing such a possibility we consider a model of the massless tensor field $l_{\mu\nu}(x)$ in a 4-dim. background $g_{\mu\nu}(x)$ with spontaneously broken Weyl and scale symmetries. It is shown that the potential of $l_{\mu\nu}$, represented by a scalar quartic polynomial, has the degenerate extremal described by the composite Nambu-Goldstone scalar boson $\phi(x):=g^{\mu\nu}l_{\mu\nu}$. Removal of the degeneracy shows that $\phi$ acquires a non-zero vev $\langle\phi\rangle_{0}=\mu$ which, together with the free parameters of the potential, defines the cosmological constant. The latter is zero for a certain choice of the parameters.