Obtaining a scalar fifth force via a symmetry-breaking coupling between the scalar field and matter

Abstract

A matter-coupled scalar field model is presented in obtaining a scalar fifth force when the constraint of the current cosmological constant is satisfied. The interaction potential energy density between the scalar field and matter has a symmetry-breaking form with two potential wells. The cosmological constant is proven to be a value of the scalar-field's self-interaction potential energy density at the minimum of an effective matter-density-dependent potential energy density. The effective potential is a sum of the interaction potential and the self-interaction potential of the scalar field. The scalar field can stably sit at the minimum and then the time-dependent cosmological `constant' behaves like a constant. The observed cosmic acceleration can be accounted for the scalar field. The scalar field is also extrapolated to account for inflation at the inflationary era of the Universe. In this era matter fluid is relativistic and then the interaction potential wells vanish. The unconfined quintessence therefore dominates the evolution of the Universe. It is concluded that `Planck 2018 results' favour the closed space of the Universe. The reasons are not only the measured value of the current Hubble constant, but also the observed feature of a concave potential in the framework of single-field inflationary models. By invoking a pseudo-potential in the inflationary era, the concave feature can be attributed to the pseudo-potential although the self-interaction potential is a convex function. The pseudo-potential is defined by a sum of the self-interaction potential and the energy density scale of the curvature of the Universe. It is that the positive curvature leads to the concave feature of the pseudo-potential.