Third-Order Density Perturbation and One-Loop Power Spectrum in Dark-Energy-Dominated Universe

TL;DR

This paper analyzes third-order density perturbations and one-loop power spectrum corrections in dark-energy cosmologies, showing minimal dependence on dark energy parameters for certain scales and epochs.

Contribution

It provides analytical solutions and fitting formulas for the third-order perturbations and one-loop power spectrum in models with a general time-varying dark energy equation of state.

Findings

Power spectrum matches EdS approximation within 1% for relevant scales at z=0.

Dark-energy effects on BAO are small in the quasi-nonlinear regime.

Cosmological dependence on the power spectrum is minimal in the studied model.

Abstract

We investigate the third-order density perturbation and the one-loop correction to the linear power spectrum in the dark-energy cosmological model. Our main interest is to understand the dark-energy effect on baryon acoustic oscillations in a quasi-nonlinear regime ($k \approx 0.1h$/Mpc). Analytical solutions and simple fitting formulae are presented for the dark-energy model with the general time-varying equation of state $w(a)$. It turns out that the power spectrum coincides with the approximate result based on the EdS (Einstein de-Sitter) model within 1% for $k<0.4h/$Mpc at $z=0$ in the WMAP (Wilkinson Microwave Anisotropy Probe) 5yr best-fitting cosmological model, which suggests that the cosmological dependence is very small.