Circularly polarized gravitational waves from parity-violating scalar-tensor theory

TL;DR

This work analyzes a ghost-free parity-violating scalar-tensor theory built from seven Qi-Xiu Lagrangians (PVST) to study gravitational waves in the early Universe. At linear order, parity violation modifies tensor propagation for certain L_n, producing chiral primordial GWs with nonzero circular polarization, while the background and scalar sector remain GR-like. At second order, two Lagrangians (L_3 and L_4) contribute exclusively to the SIGW source, enabling parity-violating signatures in SIGWs even when linear GWs are GR-like. The authors compute SIGWs during radiation domination for monochromatic and lognormal curvature spectra, finding PV-induced deviations in Ω_GW and a sizable degree of circular polarization around the peak, with Π reaching up to about 0.5 in some cases. These results provide concrete, testable predictions for parity violation in the GW sector and motivate joint observations by future space-based detectors (e.g., LISA-Taiji) to constrain PVST gravity.

Abstract

We study both primordial GWs and scalar-induced gravitational waves (SIGWs) in a class of the parity-violating scalar-tensor (PVST) theory, of which the Lagrangian is the linear combination of seven ghost-free parity-violating scalar-tensor monomials dubbed the ``Qi-Xiu'' Lagrangians. At linear order, we obtain the quadratic action for tensor perturbations and show that parity-violating terms associated with $\mathcal{L}_{1,2,5,6,7}$ render the tensor propagation polarization dependent, leading to chiral primordial spectra and a nonvanishing degree of circular polarization. At second order, we derive the EOM for SIGWs and identify the explicit parity-violating source terms. In particular, $\mathcal{L}_3$ and $\mathcal{L}_4$ enter exclusively through the source term for SIGWs, allowing parity violation to arise even when the linear GWs propagation remains effectively GR-like. During the radiation-dominated era, we compute the fractional energy density of SIGWs for both monochromatic and lognormal curvature power spectra. We find that, around the peak frequency, SIGWs in PVST gravity exhibit characteristic deviations from those in GR, resulting in a nonzero degree of circular polarization.

Figures (6)

• Figure 1: The fractional energy density $\Omega_{\mathrm{GW}}$ of SIGWs in GR and the PVST theory with a monochromatic curvature spectrum.
• Figure 2: The degree of circular polarization of SIGWs with a monochromatic curvature spectrum.
• Figure 3: The fractional energy density $\Omega_{\mathrm{GW}}$ of SIGWs in GR and the PVST theory with a lognormal spectrum. The left panel corresponds to $\sigma=0.2$, while the right panel corresponds to $\sigma=0.3$.
• Figure 4: The degree of circular polarization of SIGWs with a lognormal spectrum. Left: $\sigma=0.2$; Right: $\sigma=0.3$.
• Figure 5: The fractional energy density $\Omega_{\mathrm{GW}}$ of SIGWs in GR and the PVST theory with a lognormal spectrum. Left: $\sigma=0.2$; Right: $\sigma=0.3$.