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.
