Measuring a Parity-Violation Signature in the Early Universe via Ground-Based Laser Interferometers

We show that pairs of widely separated interferometers are advantageous for measuring the Stokes parameter $V$ of a stochastic background of gravitational waves. This parameter characterizes asymmetry of amplitudes of right- and left-handed waves, and generation of the asymmetry is closely related to parity violation in the early universe. The advantageous pairs include the kilometer-size interferometers LIGO (Livingston)-LCGT and AIGO-Virgo, which are relatively insensitive to ${\Omega }_{\mathrm{GW}}$ (the simple intensity of the background). Using at least three detectors, information of the intensity ${\Omega }_{\mathrm{GW}}$ and the degree of asymmetry $V$ can be separately measured.

Figure 1

Geometrical configuration of ground-based detectors $a$ and $b$ for the cross-correlation analysis. Detector planes are tangential to the Earth. The detectors $a$ and $b$ are separated by the angle $\beta$ measured from the center of the Earth. The angles ${\sigma }_1$ and ${\sigma }_2$ describe the orientation of bisectors of interferometers in a counterclockwise manner relative to the great circle joining two sites.

Figure 2

Overlap functions for the unpolarized $I$ mode (dashed curves), and the circularly polarized $V$ mode (solid curves). The upper panel shows the results for the Hanford-Livingston (HL) pair (the characteristic frequency $f_D=100\mathrm{Hz}$). The middle one is results for the LCGT-Livingston (CL) pair ($f_D=31\mathrm{Hz}$). The normalized SNRs $S_{I,V}$ (with the adv LIGO noise spectrum) are also presented. The bottom one show the compiled functions ${\Gamma }_{I,V}$ [Eq. (10)] made from both pairs.

Figure 3

Normalized signal-to-noise ratios ($S_{I,ab}$ and $S_{V,ab}$) with optimal configurations for the $I$ mode (short dashed curve: type I, long dashed curve: type II) and for the $V$ mode (solid curve: type III with setting $\Pi =1$ for illustrative purposes). We use the noise curve for the advanced LIGO. For each detector pair, $S_I$ and $S_V$ are given with a triangle and a circle, respectively, at its separation $\beta$. There are four other pairs not shown here: CH with $(S_I,S_V)=(0.04,0.08)$, LV with (0.08, 0.04), HV with (0.07, 0.06), and CV with (0.09, 0.04).