Parity-Violating Trispectrum from Chern-Simons Gravity

TL;DR

This paper demonstrates how dynamical Chern-Simons gravity induces a detectable parity-violating signal in the primordial scalar trispectrum, which can be observed in large-scale structure and CMB data, providing a new probe of gravitational parity violation.

Contribution

It introduces a novel mechanism where dCS gravity imprints a parity-odd scalar trispectrum, linking gravitational parity violation to observable cosmological signatures.

Findings

Parity-odd trispectrum amplitude comparable to parity-even

Constraints on dCS parameters from large-scale structure surveys

Potential for large enhancement in non-standard inflation models

Abstract

We show that dynamical Chern-Simons (dCS) gravity imprints a parity-violating signal in primordial scalar perturbations. Specifically, we find that, after dCS amplifies one graviton helicity due to a tachyonic instability, the graviton-mediated correlation between two pairs of scalars develops a parity-odd component. This correlation, the primordial scalar trispectrum, is then transferred to the corresponding curvature correlator and thus is imprinted in both LSS and the CMB. We find that the parity-odd piece has roughly the same amplitude as its parity-even counterpart, scaled linearly by the degree of gravitational circular polarization $\Pi_{\rm circ} \sim \sqrt{\varepsilon}[H^2/(M_{\rm Pl} f)] \leq 1$, with $\varepsilon$ the slow-roll parameter, $H$ the inflationary Hubble scale, $f$ the dCS decay constant, and the upper bound saturated for purely circularly-polarized gravitons. We also find that, in the collapsed limit, the ratio of the two trispectra contains direct information about the graviton's spin. In models beyond standard inflationary dCS, e.g. those with multiple scalar fields or superluminal scalar sound speed, there can be a large enhancement factor $F \gtrsim 10^6$ to the trispectrum. We find that an LSS survey that contains $N_{\rm modes}$ linear modes would place an $n\sigma$ constraint on $\Pi_{\rm circ}r$ of $\sim 0.04\ (n/3)(10^6/F)(10^6/N_{\rm modes})^{1/2}$ from the parity-odd galaxy trispectrum, for tensor-to-scalar ratio $r$. We also forecast for several spectroscopic and 21-cm surveys. This constraint implies that, for high-scale single-field inflation parameters, LSS can probe very large dCS decay constants $f \lesssim 4\times 10^9\ {\rm GeV}(3/n)(F/10^6)\left(N_{\rm modes}/10^6\right)^{1/2}$. Our result is the first example of a massless particle yielding a parity-odd scalar trispectrum through spin-exchange.