Clustering Fossils from the Early Universe

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.

Figure 1

Left six: The six possible types of distortions to an otherwise statistically isotropic two-point correlation function for a single Fourier mode, aimed in the $\widehat{\mathbf{z}}$ direction, of the distortion pattern. The distortions to the sphere show the distortions of the two-point correlation function as one moves along the direction $\widehat{\mathbf{z}}$ of the Fourier mode. 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 $\widehat{\mathbf{z}}$ 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 $\widehat{\mathbf{z}}$. 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-spectrum amplitudes $A_s$, $A_v$, and $A_t$, respectively, detectable at the $3\sigma$ level as a function of the maximum wave number $k_{\max }$ of the survey. Shown are results for survey volumes of 10 $[\mathrm{Gpc}/h{]}^3$ and 200 $[\mathrm{Gpc}/h{]}^3$, or minimum wave numbers $k_{\min }\simeq 0.001$ [$h/\mathrm{Mpc}$] and $k_{\min }\simeq 0.003$ [$h/\mathrm{Mpc}$], respectively.