Brans Dicke scalar-tensor gravity and unimodular FRW cosmology with Coleman-Weinberg potential

Abstract

As alternative gravity theories with respect to the general relativity, the Brans-Dicke (BD) scalar tensor model is well known for which the BD parameter is controller the best fit observational data and so its cosmological model is studied in the literature well. On the other side, the Coleman Weinberg (CW) self-interaction scalar field potential coming from radiation corrections of Feynman diagrams is used to describe the best fit cosmic inflation phase and reheating phase. This has a logarithmic term with respect to the Higgs potential and it is applicable even for massless bosons. From particle physics point of view, this is used usually to describe the Higgs mechanism and creation of massive Goldstone bosons. As a basic model to describe the cosmic inflation the cosmological constant is used to describe the de Sitter space where the cosmological constant play as dark energy density. Since, the cosmological constant is a hierarchy problem and it is added in the Einstein equation without to describe that where that is come originally? at a first time the Albert Einstein himself proposed a uni-modular frame for which the cosmological constant generate from a integral constant. This idea is very well because it resolve `fine tuning` problem of the cosmological constant parameter. Hence we use this idea for the BD theory in presence of the CW potential and obtained suitable solutions of the field equations for a flat Robertson-Walker space time by regarding the slow roll parameters of cosmic inflation and then we find the best fit correspondence between the theoretical predictions of the parameters of the solutions and the Planck2018, DESI2024, and ACT2025 observational data.