  We investigate the accuracy of Eulerian perturbation theory for describing
the matter and galaxy power spectra in real and redshift space in light of
future observational probes for precision cosmology. Comparing the analytical
results with a large suite of N-body simulations (160 independent boxes of 13.8
(Gpc/h)^3 volume each, which are publicly available), we find that re-summing
terms in the standard perturbative approach predicts the real-space matter
power spectrum with an accuracy of < 2% for k < 0.20 h/Mpc at redshifts z <
1.5. This is obtained following the widespread technique of writing the
resummed propagator in terms of 1-loop contributions. We show that the accuracy
of this scheme increases by considering higher-order terms in the resummed
propagator. By combining resummed perturbation theories with several models for
the mappings from real to redshift space discussed in the literature, the
multipoles of the dark-matter power spectrum can be described with sub-percent
deviations from N-body results for k < 0.15h/Mpc at z < 1. As a consequence,
the logarithmic growth rate, f, can be recovered with sub-percent accuracy on
these scales. Extending the models to massive dark-matter haloes in redshift
space, our results describe the monopole term from N-body data within 2%
accuracy for scales k < 0.15 h/Mpc at z < 0.5; here f can be recovered within <
5% when the halo bias is known. We conclude that these techniques are suitable
to extract cosmological information from future galaxy surveys.
