McDonald, John
(1991)
*Dark matter from an oscillating Brans-Dicke scalar in the extended inflation model.*
Physical Review D, 44 (8).
pp. 2325-2334.
ISSN 0556-2821

## Abstract

We consider the possibility that the discrepancy between the dynamical estimate of the density of matter in the Universe OMEGA almost-equal-to 0.2 and the prediction of inflation OMEGA = 1 can be accounted for by oscillation of the Brans-Dicke scalar of the simplest extended inflation model. It is shown that such an explanation requires an extremely small self-coupling for the Brans-Dicke scalar (lambda <10(-60)) as well as an apparent fine-tuning of the initial amplitude of the Brans-Dicke scalar at the end of inflation, which may however be understood by the anthropic principle. The requirement that the anisotropies of the cosmic microwave background radiation induced by quantum fluctuations of the Brans-Dicke field during inflation are acceptably small constrains the coupling of the Brans-Dicke scalar to the Ricci scalar to be not much greater than approximately 0.01, which is close to the lower limit allowed in the simplest extended inflation model. It is also shown that if one imposes the constraint that the spatial fluctuations of the Brans-Dicke scalar induced by bubble growth during the first-order phase transition do not give too large a contribution to the energy density at present, then the frequency of the oscillations has an upper bound, which is typically approximately 10(6) GHz. This significantly reduces the range of frequencies allowed, which would otherwise have an upper bound approximately 10(12) GHz coming from the stability of the Brans-Dicke oscillations, while leaving a range of frequencies above the approximately 1 GHz observational limit coming from terrestrial experiments designed to observe deviations from Newtonian gravity. Thus the constraints from spatially varying fluctuations of the Brans-Dicke scalar do not rule out the model.