Non-linear power spectra in the synchronous gauge

Understand

We study the non-linear corrections to the matter and velocity power spectra in the synchronous gauge (SG).

• We consider the perturbations up to third order in a zero-pressure fluid in flat cosmological background, which is relevant for the non-linear growth of cosmic structure.
• As a result, we point out that the SG is an inappropriate coordinate choice when handling the non-linear growth of the large-scale structure.
• Although the equations in the SG happen to coincide with those in the comoving gauge (CG) to linear order, they differ from second order.