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.

arXiv comment17 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

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