Parity-violation signatures in the large-scale distribution of galaxies

Last year, two separate experimental groups, Oliver H. E. Philcox et al. and Hou et al., reported claims of parity-violating signatures in the connected four-point correlation function of the matter over-density field δ(t, x), which is often referred to as the galaxy-four point correlation function. The matter over-density field parametrizes the excess of matter-energy density with respect to the homogeneous background and it’s defined as δ(t, x) ≡ (δρ(t,x)−ρ¯(t))/ ρ¯(t) , where ρ(t, x) is the energy density field and ρ¯(t) is the average density field. The four-point correlation function is the most simple statistic capable of detecting parity violation in the case of a scalar field. The galaxy four-point correlation function basically quantifies the excess of quartets of galaxies compared to a random distribution. If these measurements are confirmed, they would have two fundamental implications. First of all, the detection of a connected correlator beyond the two-point statistic serves as possible evidence of primordial non-Gaussianity. Moreover, since we know that weak forces play no role in the formation of large-scale structures it would be evidence of new physics. The goal of this work is to investigate the possibility to formulate an inflationary model capable of leaving parity-violating imprints on late-times observables. Consequently, we examine the inflationary phase within the framework of parity-violating theories of modified gravity. We need to modify the standard scenario of single-field slow-roll Inflation with standard gravitational interaction since it is parity-conserving. We examine the dynamical Chern-Simons (dCS) theory of modified gravity, which extends the standard inflationary model with the lowest-order parity violating coupling between the inflaton and the graviton. In this context, we demonstrate that dCS leaves a distinctive parity-violating signature in the primordial trispectrum of scalar perturbations. However, the signal is too weak to account for the observed parity violation. Thus, we explore alternative theories where, a priori, an enhancement is feasible due to gravitational waves’ birefringence, i.e. the two chiral polarizations, left and right, of the graviton propagate at different speeds. We present an original analysis of the graviton-mediated trispectrum in the case of the chiral-scalar tensor theories of gravity. The graviton-mediated trispectrum is the leading parity-violating contribution to the Fourier transform of the four-point correlation function. The theories we analyze extend Chern-Simons gravity by including parity-violating operators containing first and second derivatives of the non-minimally coupled inflaton field. We manage to generate a parity-violating signal, but we don’t observe any significant enhancement compared to the previous scenario.