Cosmological nonlinear density and velocity power spectra including nonlinear vector and tensor modes

TL;DR

This paper derives the complete leading order non-linear density and velocity power spectra, including vector and tensor modes, and demonstrates that Newtonian theory remains accurate for matter fluctuations in cosmology.

Contribution

It provides the first comprehensive calculation of non-linear power spectra including vector and tensor modes, confirming their negligible impact compared to Newtonian contributions.

Findings

Vector and tensor contributions are comparable to relativistic scalar perturbations.

Relativistic effects from Einstein's gravity are five orders of magnitude smaller than Newtonian effects.

Newtonian perturbation theory remains reliable for matter fluctuation calculations.

Abstract

We present the leading order non-linear density and velocity power spectra in the complete form; previous studies have omitted the vector- and tensor-type perturbations simultaneously excited by the scalar-type perturbation in nonlinear order. These additional contributions are comparable to the scalar-type purely relativistic perturbations, and thus negligible in the current paradigm of concordance cosmology: i.e., concerning density and velocity perturbations of the pressureless matter in perturbation regime well inside of matter-dominated epoch, we show that pure Einstein's gravity contributions appearing from the third order are entirely negligible (five orders of magnitude smaller than the Newtonian contributions) in all scales. We thus prove that Newtonian perturbation theory is quite reliable in calculating the amplitude of matter fluctuations even in the precision era of cosmology. Therefore, besides the ones imprinted as the initial condition generated in the earlier phase, the other relativistic effect relevant for interpreting observational data must be the projection effect that occurs when mapping galaxies on to the observed coordinate.