Parity violation in the CMB bispectrum by a rolling pseudoscalar

TL;DR

The paper investigates parity-violating signatures in the CMB bispectrum arising from a rolling pseudoscalar coupled to a U(1) gauge field during inflation, which generates large equilateral tensor non-Gaussianity and chiral gravitational waves. Using a full-sky radiation-transfer formalism and a separable reconstruction of the primordial tensor bispectrum, the authors predict nonzero CMB bispectra in both parity-even and parity-odd spaces, largely uncorrelated with scalar equilateral NG. Fisher-forecast analyses show that incorporating temperature, E-mode, and B-mode bispectra dramatically improves detectability—by up to about 400% with polarization and parity information—and that B-mode data can further tighten constraints for a given tensor-to-scalar ratio r. The results yield projected 1σ uncertainties on the pseudoscalar coupling parameter X for Planck and PRISM, highlighting the crucial role of CMB polarization in probing parity-violating tensor NG across current and future observations.

Abstract

We investigate parity-violating signatures of temperature and polarization bispectra of the cosmic microwave background (CMB) in an inflationary model where a rolling pseudoscalar produces large equilateral tensor non-Gaussianity. By a concrete computation based on full-sky formalism, it is shown that resultant CMB bispectra have nonzero signals in both parity-even $(\ell_1 + \ell_2 + \ell_3 = {\rm even})$ and parity-odd $(\ell_1 + \ell_2 + \ell_3 = {\rm odd})$ spaces, and are almost uncorrelated with usual scalar-mode equilateral bispectra. These characteristic signatures and polarization information help to detect such tensor non-Gaussianity. Use of both temperature and E-mode bispectra potentially improves of $400\%$ the detectability with respect to an analysis with temperature bispectrum alone. Considering B-mode bispectrum, the signal-to-noise ratio may be able to increase by 3 orders of magnitude. We present the $1σ$ uncertainties of a parameter depending on a coupling constant and a rolling condition for the pseudoscalar expected in the ${\it Planck}$ and the proposed PRISM experiments.

Figures (5)

• Figure 1: All possible CMB bispectra, i.e., ${ \left\langle{III}\right\rangle}$, ${ \left\langle{IIE}\right\rangle}$, ${ \left\langle{IEE}\right\rangle}$ and ${ \left\langle{EEE}\right\rangle}$ (top two panels), and ${ \left\langle{IIB}\right\rangle}$, ${ \left\langle{IEB}\right\rangle}$, ${ \left\langle{IBB}\right\rangle}$, ${ \left\langle{EEB}\right\rangle}$, ${ \left\langle{EBB}\right\rangle}$ and ${ \left\langle{BBB}\right\rangle}$ (bottom two panels), induced by the tensor non-Gaussianity with $X = 2.1 \times 10^{5}$ and ${\cal P} = 2.5 \times 10^{-9}$ for $\ell_1 + 2 = \ell_2 + 1 = \ell_3$. Left and right two panels describe the parity-even ($\ell_1 + \ell_2 + \ell_3 = {\rm even}$) and parity-odd ($\ell_1 + \ell_2 + \ell_3 = {\rm odd}$) components, respectively. For comparison, we also plot ${ \left\langle{III}\right\rangle}$ and ${ \left\langle{EEE}\right\rangle}$ from the equilateral non-Gaussianity with $f_{\rm NL} = 150$. Other cosmological parameters are fixed using the Planck results Ade:2013lta. The parity-odd bispectra seem to oscillate rapidly since they hate symmetric signals as $\ell_1 \sim \ell_2 \sim \ell_3$.
• Figure 2: Expected $1\sigma$ errors of $X^3$ (\ref{['eq:X3_fnl']}) obtained by using the parity-even (left panel) and parity-odd (right panel) signals in all types of the temperature and E-mode bispectra (red lines), the E-mode auto-bispectrum alone (green lines) and the temperature auto-bispectrum alone (blue lines). Here we assume the Planck, PRISM, and cosmic-variance-limited ideal experiments.
• Figure 3: Expected $1\sigma$ errors of $X^3$ (\ref{['eq:X31D']}) estimated by using the parity-even (left panel) and parity-odd (right panel) signals in the B-mode auto-bispectrum. As the cosmic variance spectra, we adopt the B-mode power spectra with $r = 0.05$ (red lines) and $5 \times 10^{-4}$ (green lines). Here we assume the Planck, PRISM, and cosmic-variance-limited ideal experiments.
• Figure 4: Expected $1\sigma$ errors of $f_{\rm NL}$ (\ref{['eq:X3_fnl']}) estimated from all information of the temperature and E-mode bispectra (red lines), ${ \left\langle{EEE}\right\rangle}$ (green lines) and ${ \left\langle{III}\right\rangle}$ (blue lines) in the Planck, PRISM and ideal experiments.
• Figure 5: Expected $1\sigma$ errors of $X^2$ estimated from the TB and EB correlations. Here we adopt the cosmic variance spectra and the noise spectra used in figure \ref{['fig:error_BBB']}.