Can a Brans-Dicke scalar account for dark matter in extended inflation models?

McDonald, John (1993) Can a Brans-Dicke scalar account for dark matter in extended inflation models? Physical Review D, 48 (6). pp. 2462-2476. ISSN 0556-2821

Abstract

We discuss the possibility that the dark matter in the Universe could be due to the oscillation of the Brans-Dicke scalar in extended inflation models. The constraints following from the requirement that the energy density perturbations due to quantum scalar field fluctuations are within observational limits, and from the requirement that the energy density in the oscillating Brans-Dicke scalar field, induced by the expansion of bubbles at the first-order phase transition, is smaller than the critical density at present, are discussed for the case of a coupling of the Brans-Dicke scalar to the Ricci scalar of the form phi(n+2)/M(n). Solutions of the equations of motion are given in the slow-rolling approximation for a general value of n, and the cases of n = 0 (minimal extended inflation) and n = 2 are discussed in detail. It is shown that the dominant source of energy density fluctuations produced during inflation is the isocurvature fluctuations of the Brans-Dicke scalar. The requirement that the fluctuations in the microwave background due to the isocurvature fluctuations are not too large implies that the reheat temperature at the end of inflation is less than 3 x 10(13) GeV. For the case where gravity is neglected during the expansion of bubbles at the first-order transition and where the isocurvature fluctuations account for the density perturbations observed by COBE, it is shown that only for a very small range of reheat temperatures at the end of inflation is the model consistent with the requirements that the range of non-Newtonian corrections to the gravitational potential is less that 1 cm and that there are no inhomogeneities in the cosmic microwave background radiation due to large bubbles. If we do not require that the isocurvature fluctuations account for the density perturbations observed by COBE, then the range of reheat temperatures can be larger. In general, the range of non-Newtonian corrections to the gravitational potential is not expected to be much smaller than the present upper limits from Cavendish-type experiments. The possible effects of gravitational suppression of the growth of large bubbles is also considered. It is shown that although gravity can suppress the growth of large bubbles, allowing for a wider range of reheat temperatures and shorter range non-Newtonian forces, gravity will have no effect on bubble percolation at the end of the first-order phase transition. The possible advantages of an oscillating Brans-Dicke scalar with respect to structure formation are considered, in particular, the possibility that the Brans-Dicke scalar could account for both cold and hot dark matter in a combined CDM + HDM scenario for structure formation, with the hot component arising from excitation of the Brans-Dicke scalar field by the expansion of bubbles during the first-order phase transition.