On possible composite structure of scalar fields in expanding universe

Abstract

AbstractScalar 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 $$l_{\mu \nu }(x)$$ l μ ν ( x ) in a 4-dim. background $$g_{\mu \nu }(x)$$ g μ ν ( x ) with spontaneously broken Weyl and scale symmetries. It is shown that the potential of $$l_{\mu \nu }$$ l μ ν , represented by a scalar quartic polynomial, has the degenerate extremal described by the composite Nambu–Goldstone scalar boson $$\phi (x):=g^{\mu \nu }l_{\mu \nu }$$ ϕ ( x ) : = g μ ν l μ ν . Removal of the degeneracy shows that $$\phi $$ ϕ acquires a non-zero vev $$\langle \phi \rangle _{0}=\mu $$ ⟨ ϕ ⟩ 0 = μ which, together with the free parameters of the potential, defines the cosmological constant. The latter is zero for a certain choice of the parameters.