Perturbation theory for the redshift-space matter power spectra after reconstruction

Abstract

We derive the one-loop perturbative formula of the redshift-space matter power spectrum after density field reconstruction in the Zeldovich approximation. We find that the reconstruction reduces the amplitudes of nonlinear one-loop perturbative terms significantly by partially erasing the nonlinear mode-coupling between density and velocity fields. In comparison with N-body simulations, we find that both the monopole and quadrupole spectra of reconstructed matter density fields agree with the one-loop perturbation theory up to higher wavenumber than those before reconstruction. We also evaluate the impact on cosmic growth rate assuming the survey volume and the number density like the Baryon Oscillation Spectroscopic Survey and find that the total error, including statistical and systematic ones due to one-loop approximation, decreases by half.

Covariance of the redshift-space matter power spectrum after reconstruction

“…This comes from that the values of the tree-level trispectra shift from positive to negative by replacing the perturbative kernels with the reconstructed one. This is related to our previous finding that the amplitudes of the one-loop terms of the power spectrum given by the same perturbative kernels decrease after the reconstruction [58].…”

“…The tree-level covariance after reconstruction can be obtained by replacing Z n with the kernel of postreconstructed (postrec) spectra Z ðrecÞ n derived by [58]. The first-order kernel is not changed by the reconstruction…”

“…For the theoretical model, we adopt the one-loop perturbative formulas derived in our previous work [58]. In order to correct the effects from small-scale physics on large-scale modes, we include the lowest-order counterterms given by α l ðl ¼ 0; 2Þ multiplied with k 2 times the linear power spectrum P linear l as suggested from the effective field theory [e.g., 79],…”

“…In the theoretical covariance, P l is again estimated from simulations with the survey volume V ¼ ð500 h −1 MpcÞ 3 and the number density n ∼ 1½ðh −1 MpcÞ −3 including a volume-size correction [Eq. ( 15)], which fully takes into account the mode coupling between different bins of k. Note that in our previous paper [58] we assumed the Gaussian covariance with different volumes and number density for simplicity to estimate the impact of the growth rate measurement. We estimate the posterior distribution using a nested sampling algorithm MULTINEST [80], implemented in MONTE PYTHON [81].…”

“…The authors of Ref. [58] extended their formula to redshiftspace clustering and demonstrated that the growth rate measurement from the redshift-space distortion is significantly improved.…”