Energy-momentum tensor of bouncing gravitons

Abstract

In models of the Universe with extra dimensions gravity propagates in the whole space-time. Graviton production by matter on the brane is significant in the early hot Universe. In a model of 3-brane with matter embedded in 5D space-time conditions for gravitons emitted from the brane to the bulk to return back to the brane are found. For a given 5-momentum of graviton falling back to the brane the interval between the times of emission and return to the brane is calculated. A method to calculate contribution to the energy-momentum tensor from multiple graviton bouncings is developed. Explicit expressions for contributions to the energy-momentum tensor of gravitons which have made one, two and three bounces are obtained and their magnitudes are numerically calculated. These expressions are used to solve the evolution equation for dark radiation. A relation connecting reheating temperature and the scale of extra dimension is obtained. For the reheating temperature $T_R\sim 10^{6}GeV$ we estimate the scale of extra dimension $\m$ to be of order $10^{-9} GeV\,\,\, (\m^{-1}\sim 10^{-5} cm )$.

20 pages, 3 figures. Reference added, minor modifications

References in corpus (5)

• The luminosity-redshift relation in brane-worlds: II. Confrontation with experimental data
• Graviton emission from the brane in the bulk in a model with extra dimension
• Cosmological constraints on parameters of one-brane models with extra dimension
• Connection between two forms of extra-dimensional metrics revisited
• Bouncing of gravitons emitted from the brane to the bulk back to the brane