An EFT description of galaxy intrinsic alignments

TL;DR

This work develops a general perturbative EFT framework to describe galaxy intrinsic alignments as 3D tensor fields, anchored in the equivalence principle. It extends standard bias theory to trace-free rank-2 tensors, using a generation-based Pi^{[n]} operator basis and irreducible spherical tensor decomposition to compute auto- and cross-correlations of shapes, sizes, and counts up to one-loop order and tree-level bispectra. The authors provide explicit expressions for one-loop power spectra, tree-level bispectra, selection effects, higher-derivative and stochastic contributions, and discuss renormalization and IR resummation, laying groundwork for robust IA modeling in weak lensing surveys. The framework enables accounting for IA contamination and extracting cosmological information from intrinsic alignments, with clear paths for projection to the sky and inclusion of projection and RD effects in companion work.

Abstract

We present a general perturbative effective field theory (EFT) description of galaxy shape correlations, which are commonly known as intrinsic alignments. This rigorous approach extends current analytical modelling strategies in that it only relies on the equivalence principle. We present our results in terms of three-dimensional statistics for two- and three-point functions of both galaxy shapes and number counts. In case of the two-point function, we recover the well-known linear alignment result at leading order, but also present the full next-to-leading order expressions. In case of the three-point function we present leading order results for all the auto- and cross-correlations of galaxy shapes and densities. We use a spherical tensor basis to decompose the tensor perturbations in different helicity modes, which allows us to make use of isotropy and parity properties in the correlators. Combined with the results on projection presented in a forthcoming companion paper, our framework is directly applicable to accounting for intrinsic alignment contamination in weak lensing surveys, and to extracting cosmological information from intrinsic alignments.

Figures (4)

• Figure 1: $I_{nm}(k)$ and $J_n(k)$ contributions that are present in the power spectra of size and shape fields at one-loop order, at $z=0$. Dashed lines represent negative contributions while the solid ones are positive. Left panel shows $I_{nm}$ mode coupling terms, obtained from correlating two second order fields. Right panel shows $J_n$, propagator like, terms that are obtained from correlating the linear and third order fields.
• Figure 2: The size and shape auto- and cross- power spectra. In each of the four panels, the upper plot shows the power spectra themselves, while the lower plot shows the ratio to the linear theory or leading low-$k$ dependence (in case of $q=1$ and $2$). In all configurations we use characteristic bias values $b_1=1$, $b_{R_*}= - 3/2$ (and $R_* = 1 {\rm Mpc}/h$), as well as $b_{n} = b_1/4$ for all of the other one-loop bias contributions. In all cases, we neglect the stochastic bias contributions. In the upper-left panel, we show the size-size contribution $P^{(0)}_{00}$. Dashed lines are linear theory predictions containing only $b_1$ bias parameter, solid lines are nonlinear predictions but again using only $b_1$ bias parameter, while the dot-dashed lines show the full one-loop bias result. In the upper-right panel, we show size-shape power spectrum $P^{(0)}_{02}$, containing only helicity zero component. Dashed, solid, and dot-dashed lines again correspond to contributions as in the previous panel. Lower-left panel shows the helicity zero component of the shape-shape power spectrum $P^{(0)}_{22}$, where again, three different lines are the same as in the previous panels. Lastly, the lower-right panel shows helicity one and two components of the shape-shape power spectrum $P^{(1)}_{22}$ and $P^{(2)}_{22}$. Here the leading order contributions start at one-loop with the characteristic mode coupling $\sim k^2$ dependence at large scales. Note that the amplitude of the helicity one contribution, which is the only one contributing to the $C_{BB}$ angular spectrum, is approximately two orders of magnitude suppressed relative to the helicity two case (which contributes to the $C_{EE}$).
• Figure 3: Relative contributions of the one-loop bias contributions compared to the dark matter one-loop power spectra for $P^{(0)}_{00}$, $P^{(0)}_{02}$, $P^{(0)}_{22}$. We again used $b_1=1$, $b_{R_*}= - 3/2$ and for the rest of the biases we use the values $|b_n| = b_1/4$. The sign of bias values $b_n$ are adjusted so that the grey area represents the band of potential bias one-loop contributions where $|b_n|<b_1/4$. In all cases we neglect the stochastic bias contributions. Effectively this provides an estimate of the validity regime of linear alignment model, provided our bias coefficient choice is realistic.
• Figure 4: Linearly dependent mode coupling terms $I_{14}$, $I_{66}$, $I_{67}$ and $I_{66}$ shown at $z=0$. Dashed lines represent negative contributions while the solid ones are positive.