Non-linear Power Spectrum including Massive Neutrinos: the Time-RG Flow Approach

TL;DR

The paper addresses predicting the non-linear matter power spectrum $P_m(k,z)$ in a $\Lambda$CDM universe with massive neutrinos, where linear theory underestimates suppression and non-linearities modify the signal at $k \gtrsim 0.05\,h\,\mathrm{Mpc}^{-1}$. It extends the Time Renormalization Group (TRG) flow, summing perturbative corrections to all orders for the CDM+baryon fluid while treating neutrino effects via a $k$-dependent effective density parameter $\Omega_{cb}^{eff}({\bf k},\eta)$ and a doublet $\varphi_a$ evolving with a matrix $\Theta({\bf k},\eta)$ and perturbative vertices $\gamma_{abc}$. Initial conditions come from linear theory with a CAMB-derived $P^L_{11}(k,0)$, and non-linear corrections are obtained by integrating the coupled PS and bispectrum equations with a trispectrum truncation. Compared to linear theory and one-loop PT, and against N-body simulations with neutrinos, the Time-RG approach better reproduces the neutrino-induced suppression and BAO features up to $k \sim 0.3\,h\mathrm{Mpc}^{-1}$ at $z \lesssim 1$, demonstrating a practical analytic tool for precision cosmology and future surveys.

Abstract

Future large scale structure observations are expected to be sensitive to small neutrino masses, of the order of 0.05 eV or more. However, forecasts are based on the assumption that by the time at which these datasets will be available, the non-linear spectrum in presence of neutrino mass will be predicted with an accuracy at least equal to the neutrino mass effect itself, i.e. about 3%. Motivated by these considerations, we present the computation of the non-linear power spectrum of LambdaCDM models in the presence of massive neutrinos using the Renormalization Group time-flow approach, which amounts to a resummation of perturbative corrections to the matter power spectrum to all orders. We compare our results with those obtained with other methods, i.e. linear theory, one-loop perturbation theory and N-body simulations and show that the time-RG method improves the one-loop method in fitting the N-body data, especially in determining the suppression of the matter power spectrum when neutrino are massive with respect to the linear power spectrum.

Figures (3)

• Figure 1: Matter power spectra at $a=0.3$ ($z=2.33$) normalized to the linear one for $M_\nu=0$. The red, solid lines are the result of the TRG method described in the text, while the green, dash-dotted ones are the linear approximation. The curves from top to bottom correspond to $M_\nu =0,\,0.3,$ and $0.6$ eV, respectively.
• Figure 2: Power spectra divided by the linear one for the same value of $M_\nu$ as computed in one-loop perturbation theory (black, dotted), and by the TRG method (red, solid). Blue diamonds are the results of N-body simulation of Ref. Brandbyge:2008js, when neutrinos are treated like particles.
• Figure 3: Suppression on the total PS induced by non-zero neutrino masses at different epochs, as computed in linear approximation (green, dash-dotted line), one-loop perturbation theory (black, dotted), and by the TRG method (red, solid). Blue diamonds are the results of N-body simulation of Ref. Brandbyge:2008js.The upper (lower) group of lines corresponds to $M_\nu = 0.3$ ($0.6$) eV, respectively.