Modified Brans-Dicke Theory

Concerning the decrease in the cosmological term Λ from a large magnitude in a very early universe to a small value at the present epoch, we explore the Brans-Dicke theory modified with a variable Λ term which is a function of the scalar field. The fundamental equations are derived for the gravitational and scalar fields from the variational principle of the action. In the framework of the Robertson-Walker metric, we obtain the expression for the expansion rate of the universe like the Friedmann equation. Then we turn to summarize the observational constraints on the intrinsic parameters contained in this theory. We confirm that the evolution of the universe deviates significantly from the standard model in the early stage. Calculations of Big Bang nucleosynthesis (BBN) are performed with the use of the nuclear reaction network. Comparing the resultant amounts of the light elements,4He, D, and 7Li, with the observed primordial abundances and using also the magnitude-redshift relation of Type Ia supernovae (SNe Ia), we derive reasonable ranges of the parameters.