Physical Significance of the Difference between the Brans-Dicke Theory and General Relativity

TL;DR

This paper examines the physical meaning of the scalar field in Brans-Dicke theory, comparing its asymptotic behavior to general relativity for different matter distributions and coupling parameters.

Contribution

It analyzes the asymptotic behavior of the scalar field in Brans-Dicke theory for various conditions, clarifying its physical significance and differences from general relativity.

Findings

Scalar field behaves as <φ> + O(1/ω) with local matter

Cosmological scalar field asymptotically approaches O(ρ/ω)

Scalar field converges to zero as ρ/ω → 0

Abstract

The asymptotic behavior of the scalar field and its physical meaning are discussed for T=0 and T\neq 0 for the large enough coupling parameter \omega. The special character of the Brans-Dicke theory is also discussed for local and cosmological problems in comparison with general relativity and the selection rules are introduced respectivley. The scalar field by locally-distributed matter should exhibit the asymptotic behavior \phi = <\phi> +O(1/\omega) because of the presence of cosmological matter. The scalar field of a proper cosmological solution should have the asymptotic form \phi =O(\rho /\omega) and should converge to zero in the continuous limit \rho /\omega \to 0.