Biased tracers in redshift space in the EFTofLSS with exact time dependence
We study the effect of the Einstein - de Sitter (EdS) approximation on the one-loop power spectrum of galaxies in redshift space in the Effective Field Theory of Large-Scale Structure. The dark matter density perturbations and velocity divergence are treated with exact time dependence. Splitting the density perturbation into its different temporal evolutions naturally gives rise to an irreducible basis of biases. While, as in the EdS approximation, at each time this basis spans a seven-dimensional space, this space is a slightly different one, and the difference is captured by a single calculable time- and $\vec k$-dependent function. We then compute the redshift-space galaxy one-loop power spectrum with the EdS approximation ($P^{\text{EdS-approx}}$) and without ($P^{\text{Exact}}$). For the monopole we find $P_{\text{0}}^{\text{Exact}}/P_{\text{0}}^{\text{EdS-approx}}\sim 1.003$ and for the quadrupole $P_{\text{2}}^{\text{Exact}}/P_{\text{2}}^{\text{EdS-approx}}\sim 1.007$ at $z=0.57$, and sharply increasing at lower redshifts. Finally, we show that a substantial fraction of the effect remains even after allowing the bias coefficients to shift within a physically allowed range. This suggests that the EdS approximation can only fit the data to a level of precision that is roughly comparable to the precision of the next generation of cosmological surveys. Furthermore, we find that implementing the exact time dependence formalism is not demanding and is easily applicable to data. Both of these points motivate a direct study of this effect on the cosmological parameters.