An EFT description of galaxy intrinsic alignments

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. 42A.1 Two-point functions 44 A.2 Three-point functions 47 B Fields in Fourier space 50 B.1 Bias expansion and renormalisation of the one-loop power spectrum 55 B.2 Degeneracy of the bias operators 62 B.3 Bias expansion of the tree-level bispectrum 63 C Bias renormalisation for tensor fields 65 1 Explicitly, we writewhere the Dirac delta function ensures the total momentum conservation, and is a consequence of the statistical translation invariance.

Prospects for detection and application of the alignment of galaxies with the large-scale velocity field

“…8by the nonlinear one. Alternatives are perturbation theory approaches such as those presented in [11,12]. In the long run, these could be more suitable to extend the predictions of this work consistently into the quasi-linear regime for both the alignment and velocity fields.…”

“…For blue galaxies with angular momenta correlations as the relevant statistics [1], there has not yet been a significant observation of alignments [6,8]. To describe intrinsic alignment effects on smaller scales, nonlinear extensions have been developed, including phenomenological ones [9,10], perturbative methods [11,12] or halo modelbased approaches [13,14].…”

Perturbative description of biased tracers using consistency relations of LSS

“…Furthermore, the extension of the formalism to incorporate the redshift space distortions, as well as the expansion of bias tensor fields (see e.g. [65] for a recent treatment) should be of interest and charts some of the future developments. Finally, we note that, in our opinion, presented Monkey formalism for the perturbative construction of the generic bias tracer fields utilizes one of the simplest and yet most explicit applications of the consistency relations of large scale structure so far.…”

Anisotropies of galaxy ellipticity correlations in real and redshift space: angular dependence in linear tidal alignment model

“…Following the success of the LA model, in another companion paper (Taruya & Okumura 2020) we perform a Fisher matrix analysis of the IA statistics and demonstrate that cosmological constraints will be significantly improved compared to the case using galaxy clustering alone. Small-scale behaviors of the IAs beyond linear theory have been actively studied using nonlinear perturbation theory, and higher-order terms need to be taken into account particularly at r < 10 h −1 Mpc (Blazek et al 2015(Blazek et al , 2019Vlah et al 2020). The nonlinearity not only puts an impact on the anisotropies in the IA statistics but also induces non-zero Bmode.…”