Conformal analogs of the Jordan-Brans-Dicke theory. I.

Abstract

Recent cosmological observations of large-scale structures (red shift of type Ia supernovae) confirm that the universe is currently expanding at an accelerating rate and its dominant component is dark energy. This has stimulated the development of the theory of gravity and led to many alternative variants, including tensor-scalar ones. This paper deals with the role of conformal transformations in the Jordan-BransDicke theory. Variants of intrinsic, conformally coupled, and Einstein representations are examined. In the Einstein representation an exact analytic solution for the standard cosmological model is obtained. Itis expressed in terms of the relative energy contributions of ordinary matter m Ω , the scalar field CK Ω , and a term Λ Ω related to the cosmological constant Λ . Information on the evolution of the universe for the case with a minimally coupled scalar field is given in the form of graphs.

Representation of the evolution of the Universe in the JBD theory considering vacuum phenomena

“…Here we consider the de Sitter cosmological model in the proper presentation of the JBD theory with P = 0, ε = 0, ϕ(y) = αH 2 . The equations for the standard cosmological model, corresponding to the modified action of the JBD theory [4]…”

“…By taking into account known considerations [4] on the existence of the relationship between Λ and the Hubble parameter H, in the first section of the paper we assume that ϕ(y) = αH 2 . This assumption can also be argued on the base of the time-dependence of H given in [5], where it has been shown that in the limit t → ∞ one has H 2 = Λ/3.…”