The zero-helicity waves in a Brans-Dicke cosmology

Abstract

The authors study the gravitational instability of a cosmological model in the presence of a scalar field using the Brans-Dicke theory to describe the gravitational interaction. Using an isotropic distribution function to describe the matter of the universe and assuming a 'de Donder type' gauge condition, they solve the wave equation for the perturbed gravitational field. As in the case of general relativity, the gravitational field is completely classified by its spin and helicity. By using the two-timescales method they solve the perturbed equation for zero helicity waves for the case p=0 and show the time behaviour of the density contrast. Their result shows that the density perturbation grows slightly faster than previously shown by general relativity. This effect is associated with the presence of the scalar field. However, this growth is not explosive.

Regular Bouncing Solutions, Energy Conditions, and the Brans—Dicke Theory

“…[18], and some features connected with the Gurevich et al solutions have been displayed in Ref. [19]. For the bouncing regular solutions analysed here, it is natural to implement the Bunch-Davies vacuum state as the initial condition.…”

“…A bounce can be obtained if we choose the lower sign in Eqs. (19) (20) for − 3 2 < ω < 0. Moreover, for − 3 2 < ω ≤ 4 3 the bounce is regular with no curvature singularity, but for − 4 3 < ω < 0 there is a singularity at η = η + , even if the scale factor diverges at this point.…”

“…However, in this case, the scalar field (the inverse of the gravitational coupling) varies with time, and its variation depends essentially on the sign in the exponent in Eqs. (19) (20). For the upper sign, we find…”

“…Bounce solutions can be obtained from the Gurevich et al solutions in the radiative case if the lower sign is chosen in Eqs. (19) (20) for − 3 2 < ω < 0. However, there is a singularity at η = η + for − 4 3 < ω < 0 at η = η + , even if the scale factor diverges at this point.…”