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 $\varphi (x):=g^{\mu \nu }{l}_{\mu \nu }$. Removal of the degeneracy shows that $\varphi$ acquires a non-zero vev $⟨\varphi {⟩}_0=\mu$ which, together with the free parameters of the potential, defines the cosmological constant. The latter is zero for a certain choice of the parameters.

Comments: 17 pages, V3, matches the published version with minor improvements in Introduction and presentation, discussion in Summary about mass terms explicitly breaking the scale symmetry, typos corrected