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

TL;DR

The study targets detecting parity-violating signatures in the stochastic gravitational-wave background by measuring circular polarization $V$ through cross-correlations of ground-based interferometers. It develops the overlap-function framework with $C_{ab}(f)=\gamma_{I,ab}(f)I(f)+\gamma_{V,ab}(f)V(f)$ and analyzes broadband SNR under realistic detector noise, identifying geometry-driven strategies to maximize either the isotropic intensity $I$ or the circular polarization $V$. The results show that widely separated detector pairs can probe the $V$-mode with reduced sensitivity to the total energy density $\Omega_{\rm GW}$, and that with at least three detectors one can separate $I$ and $V$ by combining cross-correlations and compiled overlaps such as $\Gamma_{V,ab:cd}$. This provides a concrete, implementable path to test parity-violating physics from the early Universe using existing and planned GW detector networks $($e.g., $\gamma_{I,ab}$ and $\gamma_{V,ab}$ over $f$-bands$)$.

Abstract

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 LIGO(Livingston)-LCGT and AIGO-Virgo that are relatively insensitive to Omega_GW (the simple intensity of the background). Using at least three detectors, information of the intensity Omega_GW and the degree of asymmetry V can be separately measured.

Figures (3)

• Figure 1: Geometrical configuration of ground-based detectors $a$ and $b$ for the cross-correlation analysis. Detector planes are tangential to the Earth. Two 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 counter-clockwise manner relative to the great circle joining two sites.
• Figure 2: Overlap functions for the un-polarized $I$ 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 $f_D=100$Hz). The middle one is results for the LCGT-Livingston (CL) pair ($f_D=31$Hz). The normalized SNRs ${\it S}_{I,V}$ (with the adv LIGO noise spectrum) are also presented. The bottom one show the compiled functions $\Gamma_{I,V}$ (eq.(\ref{['co']})) made from both pairs.
• Figure 3: Normalized signal to noise ratios (${\it S}_{I,ab}$ and ${\it S}_{V,ab}$) 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 purpose). We use the noise curve for the advanced LIGO. For each detector pair, ${\it S}_I$ and ${\it S}_V$ 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).