Probing polarization states of primordial gravitational waves with CMB anisotropies

TL;DR

The paper investigates how parity-violating gravitational interactions during inflation, implemented via a gravitational Chern-Simons term, can produce a circularly polarized primordial GWB. This circular polarization induces nonzero TB and EB CMB cross-spectra, while leaving TT, EE, BB, and TE spectra unchanged; the polarization degree $\varepsilon$ parameterizes the left-right asymmetry of tensor modes. The authors derive the TB/EB signatures, account for primary and secondary anisotropies (notably reionization), and derive current constraints from WMAP3 data, finding no strong evidence for $\varepsilon$, as well as future prospects indicating that cosmic-variance-limited experiments could constrain $|\varepsilon|$ down to approximately $0.35\left(\frac{r}{0.05}\right)^{-0.61}$, tying parity-violating inflation to observable CMB polarization. The work highlights TB/EB as unique probes of cosmological parity violation and emphasizes the potential synergy with future GW detectors to test beyond-standard inflationary scenarios.

Abstract

We discuss the polarization signature of primordial gravitational waves imprinted in cosmic microwave background (CMB) anisotropies. The high-energy physics motivated by superstring theory or M-theory generically yield parity violating terms, which may produce a circularly polarized gravitational wave background (GWB) during inflation. In contrast to the standard prediction of inflation with un-polarized GWB, circularly polarized GWB generates non-vanishing TB and EB-mode power spectra of CMB anisotropies. We evaluate the TB and EB-mode power spectra taking into account the secondary effects and investigate the dependence of cosmological parameters. We then discuss current constraints on the circularly polarized GWB from large angular scales (l < 16) of the three year WMAP data. Prospects for future CMB experiments are also investigated based on a Monte Carlo analysis of parameter estimation, showing that the circular polarization degree, varepsilon, which is the asymmetry of the tensor power spectra between right- and left-handed modes normalized by the total amplitude, can be measured down to |varepsilon| 0.35(r/0.05)^{-0.6}.

Figures (9)

• Figure 1: The temperature and polarization cross spectra, $C_{\ell}^{{\rm TB}(t)}$ and $C_{\ell}^{{\rm EB}(t)}$, from circularly polarized gravitational waves. Here, setting the reionization optical depth, $\tau_{\rm ri}=0$, the absolute values of the cross power spectra are plotted for fiducial model with $\varepsilon=+1$. In these plots, the negative correlation is indicated by the short-dashed lines. As a reference, TT ( dotted) and BB-mode ( long-dashed) power spectra are also plotted. The vertical line labeled by $\ell_R (\sim 100)$, roughly corresponds to the angular size of the horizon radius at recombination epoch.
• Figure 2: Dependence of circular polarization degree, $\varepsilon$, on the TB- ( left) and EB-mode ( right) power spectra for the fiducial model except for the reionization optical depth, $\tau_{\rm ri}=0$.
• Figure 3: Dependence of the tensor-to-scalar ratio, $r$, on the TB- ( left) and EB-mode ( right) power spectra for the fiducial model with $\varepsilon=-1.0$. In these plots, the reionization optical depth is set to $\tau_{\rm ri}=0$, keeping the slow-roll consistency relation $n_{\rm T}=-r/8$.
• Figure 4: Dependence of the reionization optical depth, $\tau_{\rm{ri}}$ on the TB- ( left) and EB-mode ( right) power spectra for the fiducial model with $\varepsilon=-1.0$. A large enhancement of the amplitude arises due to the re-scattering of the CMB photons during reionization.
• Figure 5: CMB power spectra for the fiducial cosmology with $\varepsilon=+0.1$, including both scalar and tensor mode. For comparison, three year WMAP data of TT, TE and EE-mode power spectra are plotted. At large-angular scale, the amplitude of the TB-mode ( magenta, solid) exceeds the BB-mode power spectrum ( green, dot-short dashed) and becomes comparable to the EE-mode power spectrum( blue, long-dashed).