Revising the Halofit Model for the Nonlinear Matter Power Spectrum (1208.2701v2)

Abstract: Based on a suite of state-of-the-art high-resolution $N$-body simulations, we revisit the so-called halofit model (Smith et al. 2003) as an accurate fitting formula for the nonlinear matter power spectrum. While the halofit model has been frequently used as a standard cosmological tool to predict the nonlinear matter power spectrum in a universe dominated by cold dark matter, its precision has been limited by the low-resolution of $N$-body simulations used to determine the fitting parameters, suggesting the necessity of improved fitting formula at small scales for future cosmological studies. We run high-resolution $N$-body simulations for 16 cosmological models around the Wilkinson Microwave Anisotropy Probe (WMAP) best-fit cosmological parameters (1, 3, 5, and 7 year results), including dark energy models with a constant equation of state. The simulation results are used to re-calibrate the fitting parameters of the halofit model so as to reproduce small-scale power spectra of the $N$-body simulations, while keeping the precision at large scales. The revised fitting formula provides an accurate prediction of the nonlinear matter power spectrum in a wide range of wavenumber ($k \leq 30h$\,Mpc$^{-1}$) at redshifts $0 \leq z \leq 10$, with 5% precision for $k\leq1 h$ Mpc$^{-1}$ at $0 \leq z \leq 10$ and 10% for $1 \leq k\leq 10 h$ Mpc$^{-1} $ at $0 \leq z \leq 3$. We discuss the impact of the improved halofit model on weak lensing power spectra and correlation functions, and show that the improved model better reproduces ray-tracing simulation results.

• The paper recalibrates the Halofit model using high-resolution N-body simulations to achieve 5% precision for k ≤ 1 h/Mpc and 10% for 1 ≤ k ≤ 10 h/Mpc.
• The paper extends the model’s applicability to wavenumbers up to 30 h/Mpc and redshifts up to 10, ensuring more reliable cosmological predictions.
• The paper demonstrates improved reproduction of weak lensing and CMB lensing signals, which is critical for upcoming cosmic shear surveys.

Revising the Halofit Model for the Nonlinear Matter Power Spectrum

The paper conducted by Takahashi et al. addresses the limitations of the Halofit model, originally proposed by Smith et al. (2003), for the nonlinear matter power spectrum. The Halofit model has been a significant tool in cosmology for predicting the nonlinear matter power spectrum in universes dominated by cold dark matter (CDM). However, the necessity for an updated fitting formula, particularly at small scales, has become apparent due to the limitations imposed by the low resolution of the $N$-body simulations that underpinned the original model's parameters.

Methodology

The authors employed a suite of state-of-the-art, high-resolution $N$-body simulations across 16 cosmological models based on the Wilkinson Microwave Anisotropy Probe (WMAP) best-fit parameters, including variations in the dark energy equation of state. These simulations facilitated a recalibration of the Halofit model's fitting parameters to enhance its accuracy on small scales while maintaining precision at larger scales.

Key Findings

1. Enhanced Precision: The revised model provides predictions of the nonlinear matter power spectrum with 5% precision for wavenumbers $k \leq 1\,h\,\text{Mpc}^{-1}$ over redshifts $0 \leq z \leq 10$ and 10% precision for $1 \leq k \leq 10\,h\,\text{Mpc}^{-1}$ at redshifts $0 \leq z \leq 3$.
2. Broader Applicability: The revised formula applies effectively over a broad range of wavenumbers ($k \leq 30\,h\,\text{Mpc}^{-1}$) and redshifts, providing a more reliable tool for precision cosmological studies.
3. Impact on Weak Lensing and CMB Lensing: The improved Halofit model more accurately reproduces weak lensing power spectra and correlation functions compared to the original model, which is critical for analyzing future cosmic shear measurements from surveys like Subaru Hyper Suprime-Cam and the Large Synoptic Survey Telescope.

Implications

The recalibrated Halofit model holds substantial implications for both practical and theoretical cosmology. Practically, the enhanced accuracy of the model on small scales will significantly improve the reliability of cosmic shear studies, thereby refining constraints on cosmological parameters such as the matter density parameter and the amplitude of density fluctuations. Theoretically, the paper demonstrates the importance of high-resolution $N$-body simulations in improving cosmological models and may guide future theoretical developments to incorporate smaller scale phenomena and additional cosmological effects like those from baryonic physics and massive neutrinos.

Future Directions

Further research could extend upon this work by integrating the effects of baryonic feedback and massive neutrinos, both known to impact the matter power spectrum at small scales. As computational capabilities grow, more sophisticated simulations that cover a diverse set of cosmological parameters could further enhance these revisions. Moreover, applying this revised model to observational data from upcoming surveys will be crucial in testing its accuracy and utility in real-world cosmological applications.

This research constitutes a significant step forward in improving the precision of theoretical templates for the nonlinear matter power spectrum, which is essential for the advancement of modern cosmology and for maximizing the scientific return from next-generation cosmological surveys.