Constraints upon the spectral indices of relic gravitational waves by LIGO S5

With LIGO having achieved its design sensitivity and the LIGO S5 strain data being available, constraints on the relic gravitational waves (RGWs) becomes realistic. The analytical spectrum of RGWs generated during inflation depends sensitively on the initial condition, which is generically described by the index $\beta$, the running index ${\alpha }_t$, and the tensor-to-scalar ratio $r$. By the LIGO S5 data of the cross-correlated two detectors, we obtain constraints on the parameters $(\beta ,{\alpha }_t,r)$. As a main result, we have computed the theoretical signal-to noise ratio (SNR) of RGWs for various values of $(\beta ,{\alpha }_t,r)$, using the cross-correlation for the given pair of LIGO detectors. The constraints by the indirect bound on the energy density of RGWs by BBN and CMB have been obtained, which turn out to be still more stringent than LIGO S5.