Effective search templates for a primordial stochastic gravitational wave background

We calculate the signal-to-noise ratio (SNR) of the stochastic gravitational-wave background in an extreme case that its spectrum has a sharp falloff with its amplitude close to the detection threshold. Such a spectral feature is a characteristic imprint of the change in the number of relativistic degrees of freedom on the stochastic background generated during inflation in the early Universe. We find that, although SNR is maximal with the correct template which is proportional to the assumed real spectrum, its sensitivity to the shape of template is fairly weak indicating that a simple power-law template is sufficient to detect the signature.

Figure 1

The overlap reduction function $\gamma (f)$ for the Hanford and Livingston, LIGO detector pair.

Figure 2

The value (top) and ratio (bottom) of SNRs for ${\Omega }_{\mathrm{filter}}={\Omega }_{\mathrm{gw}}$ (solid line in top panel) and ${\Omega }_{\mathrm{filter}}\propto f^0$ (dotted line in top panel) for LIGO II. We set $d=0.7$.

Figure 3

The value (top) and ratio (bottom) of SNRs for ${\Omega }_{\mathrm{filter}}={\Omega }_{\mathrm{gw}}$ (solid line in top panel) and ${\Omega }_{\mathrm{filter}}\propto f^0$ (dotted line in top panel) for FP-DECIGO. We set $d=0.7$.

Figure 4

The value (top) and ratio (bottom) of SNRs for ${\Omega }_{\mathrm{filter}}={\Omega }_{\mathrm{gw}}$ (solid line in top panel) and ${\Omega }_{\mathrm{filter}}\propto f^0$ (dotted line in top panel) for LISA. We set $d=0.7$.