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Physical Review D

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High-energy effects on the spectrum of the inflationary gravitational wave background in braneworld cosmology

Takashi Hiramatsu^*

Department of Physics, School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan

^*Electronic address: hiramatsu_at_utap.phys.s.u-tokyo.ac.jp

Phys. Rev. D 73, 084008 – Published 7 April, 2006

DOI: https://doi.org/10.1103/PhysRevD.73.084008

Abstract

We discuss the cosmological evolution of the inflationary gravitational wave background in the Randall-Sundrum single-brane model. In braneworld cosmology, in which the three-dimensional spacelike hypersurface that we live in is embedded in five-dimensional anti–de-Sitter ( ${AdS}_{5}$ ) spacetime, the evolution of gravitational wave (GW) modes is affected by the nonstandard expansion of the universe and the excitation of the Kaluza-Klein modes. These are significant in the high-energy regime of the universe. We numerically evaluate these two effects by solving the evolution equation for GWs propagating through the ${AdS}_{5}$ spacetime. Using a plausible initial condition from inflation, we find that the excitation of Kaluza-Klein modes can be characterized by a simple scaling relation above the critical frequency $f_{crit}$ determined from the length scale of the fifth dimension $ℓ$ . The remarkable point is that this relation generally holds as long as the matter content of the universe is described by the perfect fluid with the equation of state $p = w ρ$ for $0 \leq w \leq 1$ . The resultant scaling relation is translated into the energy spectrum of the inflationary gravitational wave background as $Ω_{GW} \propto f^{(3 w - 1) / (3 w + 2)}$ for $f > f_{crit}$ . This indicates that in the radiation dominant case ( $w = 1 / 3$ ), the two high-energy effects accidentally compensate each other and the spectrum becomes almost the same as the one predicted in the four-dimensional theory, i.e., $Ω_{GW} \propto f^{0}$ .

Article Text

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