A Cosmology of the Brane World

Abstract

We develop a possible cosmology for a Universe with n additional spatial dimensions of variable scale, and an associated scalar field, the radion, which is distinct from the field responsible for inflation, the inflaton. Based on a particular ansatz for the effective potential for the inflaton and radion (which may emerge in string theory), we show that the early expansion of the Universe may proceed in three stages. First, the radion becomes trapped at a value much smaller than the size of the extra dimensions today. Second, the Universe expands exponentially, but with a Planck mass smaller than its present value. Because the Planck mass during inflation is small, density fluctuations in agreement with observations can arise naturally. Third, when inflation ends, the Universe reheats, and the radion becomes free to expand once more. During the third phase the Universe is ``radiation-dominated'' and tends toward a fixed-point evolutionary model in which the radion grows but the temperature remains unchanged. Ultimately, the radion becomes trapped once again at its present value, and a short period of exponential expansion, which we identify with the electroweak phase transition, ensues. Once this epoch is over, the Universe reheats to a temperature of order the electroweak scale, and the mature Universe evolves as in standard cosmological models. We show that the present day energy density in radions can be smaller than the closure density if the second inflationary epoch lasts about 8 e-foldings or more; the present-day radion mass turns out to be small (less than or of the order of an eV, depending on parameters). We argue that although our model envisages considerable time evolution in the Planck mass, substantial spatial fluctuations in Newton's constant are not produced.