Massive Neutrinos and the Non-linear Matter Power Spectrum (1109.4416v3)

Abstract: We perform an extensive suite of N-body simulations of the matter power spectrum, incorporating massive neutrinos in the range M = 0.15-0.6 eV, probing the non-linear regime at scales k < 10 hMpc-1 at z < 3. We extend the widely used HALOFIT approximation to account for the effect of massive neutrinos on the power spectrum. In the strongly non-linear regime HALOFIT systematically over-predicts the suppression due to the free-streaming of the neutrinos. The maximal discrepancy occurs at k ~ 1 hMpc-1, and is at the level of 10% of the total suppression. Most published constraints on neutrino masses based on HALOFIT are not affected, as they rely on data probing the matter power spectrum in the linear or mildly non-linear regime. However, predictions for future galaxy, Lyman-alpha forest and weak lensing surveys extending to more non-linear scales will benefit from the improved approximation to the non-linear matter power spectrum we provide. Our approximation reproduces the induced neutrino suppression over the targeted scales and redshifts significantly better. We test its robustness with regard to changing cosmological parameters and a variety of modelling effects.

• The paper demonstrates that N-body simulations reveal a scale-dependent suppression of the matter power spectrum by massive neutrinos, with a distinct spoon-shaped feature in the nonlinear regime.
• The paper shows that traditional models like HALOFIT overestimate neutrino-induced suppression by up to 10%, leading to the proposal of an improved fitting formula.
• The paper’s findings enhance cosmological predictions by refining non-linear clustering models and guiding future surveys to better constrain neutrino masses.

Overview of "Massive Neutrinos and the Non-linear Matter Power Spectrum"

This paper, authored by Simeon Bird, Matteo Viel, and Martin G. Haehnelt, presents a comprehensive paper on the impact of massive neutrinos on the non-linear matter power spectrum in the universe. Utilizing extensive N-body simulations, the paper explores neutrino masses in the range of $M_\nu = 0.15 - 0.6$ eV over scales $k < 10$ Mpc and at redshifts $z < 3$. The authors extend traditional linear and mild non-linear approximations to account for the nuanced effects induced by massive neutrinos, particularly in the non-linear regime.

Key Findings and Methodology

• Simulation Details: The paper employs N-body simulations, including both particle-based and Fourier-space representations of neutrinos. The simulations are performed using a new version of the Tree-SPH code, with a focus on accurately capturing the neutrino-induced suppression of the matter power spectrum.
• Neutrino Mass Impact: It is shown that massive neutrinos systematically reduce the matter power spectrum, primarily due to their free-streaming effect. This suppression is not constant across scales and redshifts but varies, showing a distinctive spoon-shaped feature where the suppression peaks in the non-linear regime.
• Comparison with HALOFIT: Traditional models like HALOFIT are found to overestimate the suppression by up to 10%, particularly in the strongly non-linear regime at $k \sim 1$ Mpc. The results show that most existing constraints on neutrino masses remain unaffected as they stem from linear or mildly non-linear probes. However, HALOFIT does not fully account for neutrino effects, especially non-linear clustering and back-reaction phenomena.
• Improved Fitting Formula: The authors propose an improved fitting formula, modifying HALOFIT to better predict the non-linear power spectrum with massive neutrinos. The adjustment considers back-reaction effects and the increase in free-streaming suppression amplitude, effectively decreasing the discrepancy for future surveys.

Implications and Future Directions

The findings have significant implications for both theoretical and observational cosmology. The improved understanding of neutrino effects on the non-linear matter power spectrum is crucial for precise cosmological surveys, including galaxy clustering, weak lensing, and the Lyman-alpha forest. Future observations aim to achieve accuracy levels capable of constraining neutrino masses to a few tenths of eV, making the paper's empirical corrections to existing models vital.

The paper also suggests further exploration of N-body simulations with more accurate neutrino models to refine predictions. The development of statistical frameworks to accurately compare simulation results with observational data is necessary, given the precision required for upcoming cosmological probes. The integration of more sophisticated physical processes, such as baryonic feedback, could also be an avenue for future research to minimize discrepancies on smaller, non-linear scales.

In summary, this paper provides a crucial enhancement to the modeling of the non-linear matter power spectrum by addressing the complexities introduced by massive neutrinos. It sets a foundation for improved accuracy in cosmological analyses, thereby benefitting future surveys aiming to explore the universe's structure. The path forward involves further refinement and incorporation of these findings into broader cosmological models.