Imprint of inflation on galaxy shape correlations

TL;DR

This work proposes intrinsic galaxy shape correlations as a new probe of primordial non-Gaussianity with anisotropic squeezed-limit signatures. By deriving all-sky shape–density and shape–shape correlations in the presence of non-Gaussianity, the authors show that a quadrupolar (spin-2) component $A_2$ induces a scale-dependent, tidal-alignment bias in galaxy shapes, complementary to the standard isotropic $f_{ m NL}^{ m loc}$ effects on galaxy counts. They develop a renormalized bias framework to treat divergences and provide forecasts for LSST-like surveys, finding constraints on $A_2$ comparable to current CMB limits but probing different, smaller scales ($k \u2265 1\,h\,{ m Mpc}^{-1}$) and potentially accessing superhorizon information via the quadrupole. The results depend on the poorly known response coefficient $b_{ m NG}^I$, but nonetheless indicate that three-dimensional shape statistics can substantially augment inflationary tests when combined with clustering data.

Abstract

We show that intrinsic (not lensing-induced) correlations between galaxy shapes offer a new probe of primordial non-Gaussianity and inflationary physics which is complementary to galaxy number counts. Specifically, intrinsic alignment correlations are sensitive to an anisotropic squeezed limit bispectrum of the primordial perturbations. Such a feature arises in solid inflation, as well as more broadly in the presence of light higher spin fields during inflation (as pointed out recently by Arkani-Hamed and Maldacena). We present a derivation of the all-sky two-point correlations of intrinsic shapes and number counts in the presence of non-Gaussianity with general angular dependence, and show that a quadrupolar (spin-2) anisotropy leads to the analog in galaxy shapes of the well-known scale-dependent bias induced in number counts by isotropic (spin-0) non-Gaussianity. Moreover, in presence of non-zero anisotropic non-Gaussianity, the quadrupole of galaxy shapes becomes sensitive to far superhorizon modes. These effects come about because long-wavelength modes induce a local anisotropy in the initial power spectrum, with which galaxies will correlate. We forecast that future imaging surveys could provide constraints on the amplitude of anisotropic non-Gaussianity that are comparable to those from the Cosmic Microwave Background (CMB). These are complementary as they probe different physical scales. The constraints, however, depend on the sensitivity of galaxy shapes to the initial conditions which we only roughly estimate from observed tidal alignments.

Figures (7)

• Figure 1: The tidal bias induced by anisotropic non-Gaussianity, Eq. (\ref{['eq:totalbias']}), for $b_1^I = - 0.1\Omega_m D(0)/D(z)$, $b_{\rm NG}^I = - 0.1\Omega_m$ and $A_2=-10$ (see Section \ref{['sec:redgal']}). The increasing thickness of the curves represents different redshifts from $z=0$ to $z=1.5$. At $k>10^{-2}$$h$ Mpc$^{-1}$, the effect of non-Gaussianity is negligible and all curves asymptote to $-b_1^I$. Anisotropic non-Gaussianity changes the tidal bias on large scales and the effect is larger at high redshift at a given scale.
• Figure 2: The angular auto-power spectrum of intrinsic shapes (without accounting for weak gravitational lensing) for our fiducial choice of $b_{\rm NG}^I$ and $A_2=+10$ (left) and for $A_2=-10$ (right). The Gaussian case is shown in solid black for three redshifts, $z=\{0.5,1,1.5\}$ from top to bottom. We show the case with anisotropic non-Gaussianity at the same redshifts (dashed).
• Figure 3: Fractional change in the angular cross-spectrum of galaxy positions and intrinsic shapes at $z=1$ for different levels of non-Gaussianity and our fiducial choice of $b_{\rm NG}^I$. We assume $b_{1}^n=2$ and $b_{\rm NG}^n=(b_{1}^n-1)\delta_c$. The left panel shows results for $A_2=+10$, while the right panel shows $A_2=-10$. In addition, we show results for isotropic non-Gaussianity, $A_2=0$, $A_0=+10$ in both panels.
• Figure 4: The expected fraction of red galaxies observed by LSST as a function of redshift for a limiting magnitude of $i_{\rm lim}=25.3$ (AB). The gray dashed curve shows $dN_{\rm red}/dz$ with an arbitrary normalization.
• Figure 5: Position-shape correlations and shape-shape correlations of red galaxies expected to be observed in LSST between $0.1<z<1.5$. The case of Gaussian initial conditons is shown in solid black, and the case with $A_2=100$ is shown as dashed gray lines. The error bars show the expected uncertainties for a Gaussian fiducial cosmology.