Nonlinear Evolution of the Matter Trispectrum with Primordial Parity Violation

TL;DR

The paper addresses how parity-violating primordial physics imprints itself on the nonlinear evolution of the matter trispectrum. It develops a 1-loop EFTofLSS framework to compute the parity-odd trispectrum, proving IR cancellations and deriving UV counterterms, and then applies a concrete primordial parity-violating template to quantify nonlinear evolution and BAO effects. The results show that nonlinear evolution distorts the primordial parity-odd signal and induces BAO damping and a pronounced phase shift, with the EFT providing a reliable description up to k ~ 0.4 h Mpc^{-1} at z ~ 0.5. This work establishes a bridge between early-universe parity-violating models and large-scale structure observations, enabling model-dependent searches for new physics in nonlinear regimes and paving the way for extensions to biased tracers and IR resummation.

Abstract

Parity-odd four-point correlation functions, or trispectra, of cosmic matter density fields provide a unique probe of fundamental symmetries in cosmology. Trispectra of primordial matter density fluctuations produced in the early universe are modified by the subsequent nonlinear structure formation. In this paper, we compute the nonlinear evolution of the parity-odd matter trispectrum to one-loop order, i.e., to third order in density fluctuations, within the framework of effective field theory of the large-scale structure of the universe. By analyzing the different terms in the perturbation series, we demonstrate the structure of infrared divergence cancellations, as required by the equivalence principle. We also derive the forms of the counterterms required to renormalize the ultraviolet divergences. Adopting a specific model for a primordial parity-odd trispectrum, we numerically compute the leading-order effects of nonlinear gravitational evolution and study its impact on baryonic acoustic oscillations within the signal. These calculations are essential for comparing the observed trispectra of nonlinear cosmic density fields with theoretical expectations.

Figures (7)

• Figure 1: Feynman rules for diagrammatic representations of correlation functions. The dashed circle represents the full primordial power spectrum with general PNG, including loops.
• Figure 2: Diagrammatic representations of the matter power spectrum with PNG up to 1-loop order, corresponding to Eqs. \ref{['eq:p11']}--\ref{['eq:p13']}.
• Figure 3: Diagrammatic representations of the trispectrum from Eq. \ref{['eq:trispectrum']} with PNG represented by the dashed circles. Diagram (f) does not contribute to the parity-odd trispectrum since it contains the parity-odd bispectrum.
• Figure 4: Absolute values of the linear and nonlinear parity-odd trispectra evaluated with the primordial template in Eq. \ref{['eq:template']} in the configuration of Eq. \ref{['eq:conf']} at $z=0.5$. Dashed (solid) lines denote negative (positive) values. The linear trispectrum, $T_{m,-}^{lin} \equiv T_{m,-}^{1111}$, defined in Eq. \ref{['eq:Tlin']}, is shown in blue. We also show the SPT trispectrum from Eq. \ref{['eq:trispectrum']} in red and the EFT trispectrum from Eq. \ref{['eq:Teft']} in black. Nonlinear 1-loop corrections are given by $T_{m,-}^{1113,I}$ (Eq. \ref{['eq:T1113I']}, orange), $T_{m,-}^{1113,II}$ (Eq. \ref{['eq:T1113II']}, green), and $T_{m,-}^{1122,I}$ (Eq. \ref{['eq:T1122I']}, purple), summing all permutations in $(a,b,c,d)$ for $T_{m,-}^{abcd}$. The EFT trispectrum remains reliable up to $k_{max} \simeq 0.4 ~ h~\mathrm{Mpc}^{-1}$.
• Figure 5: Impact of nonlinearities on the BAO in the power spectrum. Top: Ratios of wiggle to no-wiggle power spectrum for linear (blue) and SPT 1-loop at redshifts $z=0.5$ (orange), 1 (green) and 2 (purple). Bottom: Ratios of wiggle to no-wiggle power spectra for linear (blue) and SPT 1-loop corrections, with $P_m^{13}$ in orange and $P_m^{22}$ in green.