Clustering Fossils from the Early Universe

TL;DR

Inflationary models often predict couplings between the inflaton and additional scalar, vector, or tensor fields that imprint distinctive non-Gaussian, anisotropic signatures in the primordial density field. The authors develop a general, model-agnostic formalism that maps these signatures onto off-diagonal density-mode correlations and an associated trispectrum, decomposed into scalar, vector, and tensor components using polarization tensors $\epsilon^p_{ij}$. They derive minimum-variance estimators for the Fourier amplitudes $h_p(\mathbf{K})$ and the corresponding power-spectrum amplitudes $A_h$, and analyze their sensitivity as functions of survey volume, range of wavenumbers, and noise. They also discuss parity-violating probes and practical considerations like redshift-space distortions and biasing, providing a general diagnostic for inflationary physics applicable to galaxy and future 21-cm surveys.

Abstract

Many inflationary theories introduce new scalar, vector, or tensor degrees of freedom that may then affect the generation of primordial density perturbations. Here we show how to search a galaxy (or 21-cm) survey for the imprint of primordial scalar, vector, and tensor fields. These new fields induce local departures to an otherwise statistically isotropic two-point correlation function, or equivalently, nontrivial four-point correlation functions (or trispectra, in Fourier space), that can be decomposed into scalar, vector, and tensor components. We write down the optimal estimators for these various components and show how the sensitivity to these modes depends on the galaxy-survey parameters. New probes of parity-violating early-Universe physics are also presented.

Figures (2)

• Figure 1: left six: The six possible polarizations to an otherwise statistically isotropic two-point correlation function. The first two modes are the usual transverse traceless tensor polarizations (gravitational waves), in which there are quadrupolar distortions in the plane transverse to the direction $\mathbf{\hat{z}}$ of the wave. The next two are scalar and longitudinal-vector distortions, respectively. The scalar mode represents an isotropic modulation while the longitudinal-vector mode stretches and compresses the correlations along $\mathbf{\hat{z}}$. The two transverse-vector modes induce quadrupolar distortions in the $xz$ and $yz$ directions, respectively. right two: The circular polarizations of the tensor mode ($h_{+t}$) and vector mode ($h_{+v}$).
• Figure 2: The smallest scalar, vector, and tensor power-sepctrum amplitudes $A_s$, $A_v$ and $A_t$, respectively, detectable at the 3$\sigma$ level as a function of the maximum wavenumber $k_{\rm max}$ of the survey. Shown are results for survey volumes of $10~[\rm{Gpc}/h]^3$ and $200~[\rm{Gpc}/h]^3$, or minimum wavenumbers $k_{\rm min} \simeq 0.001~[h/\rm{Mpc}]$ and $k_{\rm min} \simeq 0.003~[h/\rm{Mpc}]$, respectively.