The matter power spectrum in redshift space using effective field theory
(69 pages)

By including and resumming oneloop corrections to an EFT for the redshiftspace matter power spectrum, it is possible to go beyond standard perturbation theory into the mildly nonlinear regime (with good agreement beow k of 0.4 h/Mpc). A positivity bound on the l=0 mode restricts the EFT's validity to k below 0.75 h/Mpc.

The positivity bound implemented here is the condition that the zeroth multipole moment of the power spectrum should be positive. The zero angular momentum mode of the partial wave expansion often imposes the tightest unitarity constraint on EFTs, however there are other consistency conditions (such as analyticity) which may be broken by the EFT before unitarity. It is correctly pointed out that higher order effects must be included near the cutoff to obtain the correct answer, and so it would be interesting to investigate whether a significantly lower cutoff might be required from other consistency conditions. That is to say, this cutoff of 0.75 h/Mpc is only an upper bound on the true cutoff of the EFT. However, the good agreement with simulation around k=0.4 h/Mpc reassuringly suggests that the oneloop EFT is still valid here.
