Nonlinear Evolution of Anisotropic Cosmological Power

TL;DR

The results suggest that primordial power anisotropies will be suppressed by < or = 7% in the quasilinear regime and show that the skewness in the statistically anisotropic theory differs by no more than 1% from that in the isotropic theory.

Abstract

There has been growing interest in the possibility of testing more precisely the assumption of statistical isotropy of primordial density perturbations. If it is to be tested with galaxy surveys at distance scales <~ 10 Mpc, then nonlinear evolution of anisotropic power must be understood. To this end, we calculate the angular dependence of the power spectrum to third order in perturbation theory for a primordial power spectrum with a quadrupole dependence on the wavevector direction. Our results suggest that primordial power anisotropies will be suppressed by <~ 7% in the quasilinear regime. We also show that the skewness in the statistically anisotropic theory differs by no more than 1% from that in the isotropic theory.

Figures (1)

• Figure 1: Coefficients of anisotropic terms in the third-order power spectrum, $c_1(k)-1$, $c_2(k)$, and $c_3(k)$. The definitions are given in Eqs. (\ref{['eq:third-order power spectrum\n 3']})--(\ref{['eq:g_4']}). Solid curves are the result of numerical integration, while dotted curves are the fitting functions (\ref{['eqn:ansatz 1']})--(\ref{['eqn:ansatz 3']}).