Numeric Spectrum of Relic Gravitational Waves in Accelerating Universe

Abstract

The accelerating expansion of the Universe at the present stage is a process that will change the spectrum of relic gravitational waves. Here we present a numerical calculation for the power spectrum of relic gravitational waves in the accelerating Universe. The results show that although the overall features of the power spectrum is similar to that in the non-accelerating models, the amplitude is smaller by an order of $10^{-1}$. We also find that the spectrum is very sensitive to the index $β$ of the inflationary expansion with the scale factor $a(τ) \propto |τ|^{1+β}$. With increase of $β$, the resulting spectrum is tilted to be flatter with more power on high frequencies, and the sensitivity of the second science run of the LIGO detectors puts a restriction on the parameter $β< -1.8$. The influence of reheating following the inflation has been examined.