An inflationary universe in Brans-Dicke theory: a hopeful sign of theoretical estimation of the gravitational constant

Abstract

A revised model of the inflationary universe under the framework of Brans-Dicke theory is proposed. It is shown that the scale factor of the universe during the inflation varies as R approximately tw+1/2 and not exponentially, but still it gives rise to enough inflation to solve the cosmological puzzles. It is found that the quantum gravity effects come into play in the same scale as that of grand unified theories (i.e. at T approximately 1014 GeV) rather than at T approximately 1019 GeV, hence providing a natural solution to the 'milder version' of the flatness problem inherent in the conventional inflationary scenarios. This scenario also provides a simple way to estimate theoretically the present value of the gravitational constant. The estimated value agrees well with the actual value despite many approximations and the ignorance of quantum gravity; the difference is only by a factor of the order of 10-2.

Primordial and late-time inflation in Brans–Dicke cosmology

“…This is rapid enough to solve the problems in standard cosmology and at the same time slow enough to make the transition to normal state possible after the inflationary phase. This has come to be known as extended inflation [13,14]. Extended inflation constrains ω to be less than 25.…”

Brans–Dicke Theory and Primordial Black Holes in Early Matter-Dominated Era

“…In BD theory the gravitational constant is set by the inverse of a time-dependent scalar field which couples to gravity with a coupling parameter ω. GTR can be recovered from BD theory in the limit ω → ∞ [3]. BD theory also admits simple expanding solutions [4] for scalar field φ(t) and scale factor a(t) which are compatible with solar system observations [5]. BD theory is also sucessful in explaining many cosmological phenomena such as inflation [6], early and late time behaviour of the Universe [7], cosmic acceleration and structure formation [8], cosmic acceleration and coincidence problem [9,10] etc.…”

Generalized Mattig’s relation in Brans–Dicke–Rastall gravity

“…Moreover, this theory is equivalence to some other alternatives of GR in particular f (R) gravities that provide us a good tool to gain better insights about these theories [14]. Other important property of BD theory is that it produces simple expanding solutions [15] for scalar field φ(t) and scale factor a(t) which are more compatible with solar system experiments [16][17][18]. There are also many works on interesting physical aspects of the BD theory [19].…”