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We calculate the non-linear matter power spectrum using the 3rd-order perturbation theory without ignoring the pressure gradient term. We consider a semi-realistic system consisting of two matter components with and without pressure, and both are expanded into the 3rd order in perturbations in a self-consistent manner, for the first time. While the pressured component may be identified with baryons or neutrinos, in this paper we mainly explore the physics of the non-linear pressure effect using a toy model in which the Jeans length does not depend on time, i.e., the sound speed decreases as 1/a^{1/2}, where a is the scale factor. The linear analysis shows that the power spectrum below the so-called filtering scale is suppressed relative to the power spectrum of the cold dark matter. Our non-linear calculation shows that the actual filtering scale for a given sound speed is smaller than the linear filtering scale by a factor depending on the redshift and the Jeans length. A ~40% change is common, and our results suggest that, when applied to baryons, the temperature of the Inter-galactic Medium inferred from the filtering scale observed in the flux power spectrum of Lyman-alpha forests would be underestimated by a factor of two, if one used the linear filtering scale to interpret the data. The filtering mass, which is proportional to the filtering scale cubed, can also be significantly smaller than the linear theory prediction especially at low redshift, where the actual filtering mass can be smaller than the linear prediction by a factor of three. Finally, when applied to neutrinos, we find that neutrino perturbations deviate significantly from linear perturbations even below the free-streaming scales, and thus neutrinos cannot be treated as linear perturbations.
We compare and contrast two different metric based formulations of non- linear cosmological perturbation theory: the MW2009 approach in [K. A. Malik and D. Wands, Phys. Rept. 475 (2009), 1.] following Bardeen and the recent approach of the paper KN20
The galaxy number density is a key quantity to compare theoretical predictions to the observational data from current and future Large Scale Structure surveys. The precision demanded by these Stage IV surveys requires the use of second order cosmolog
The large-scale matter distribution in the late-time Universe exhibits gravity-induced non-Gaussianity, and the bispectrum, three-point cumulant is expected to contain significant cosmological information. In particular, the measurement of the bispec
We propose a new approach to the spectral theory of perturbed linear operators , in the case of a simple isolated eigenvalue. We obtain two kind of results: radius bounds which ensure perturbation theory applies for perturbations up to an explicit si
We explore structure formation in the dark ages ($zsim 30-6$) using two well-known methods for initializing cosmological $N$-body simulations. Overall, both the Zeldovich approximation (za) and second order Lagrangian perturbation theory (lpt) are kn