On possible composite structure of scalar fields in expanding universe

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.