Non-Gaussian Covariance of the Matter Power Spectrum in the Effective Field Theory of Large Scale Structure

TL;DR

The paper addresses the non-Gaussian covariance of the matter power spectrum at one loop, comparing Standard Perturbation Theory and the EFT of Large-Scale Structure with seven leading EFT operators. It develops the first full one-loop covariance calculation in the Eulerian EFT framework and introduces FnFast to efficiently evaluate the required diagrams, including UV counterterms via the stress tensor. By comparing to two N-body simulations (Li et al. and Blot et al.), it extracts an effective combination of EFT coefficients and demonstrates dataset-dependent outcomes: the Li data benefit from a single EFT parameter extending the reliable range to about $k_i+k_j\sim0.3\,h\mathrm{Mpc}^{-1}$, whereas Blot data show no improvement over SPT. The results emphasize the impact of systematic uncertainties in simulations on covariance modeling and motivate improved numerical and analytic control for precision cosmology.

Abstract

We compute the non-Gaussian contribution to the covariance of the matter power spectrum at one-loop order in Standard Perturbation Theory (SPT), and using the framework of the effective field theory (EFT) of large scale structure (LSS). The complete one-loop contributions are evaluated for the first time, including the leading EFT corrections that involve seven independent operators, of which four appear in the power spectrum and bispectrum. We compare the non-Gaussian part of the one-loop covariance computed with both SPT and EFT of LSS to two separate simulations. In one simulation, we find that the one-loop prediction from SPT reproduces the simulation well to $k_i + k_j \sim$ 0.25 h/Mpc, while in the other simulation we find a substantial improvement of EFT of LSS (with one free parameter) over SPT, more than doubling the range of $k$ where the theory accurately reproduces the simulation. The disagreement between these two simulations points to unaccounted for systematics, highlighting the need for improved numerical and analytic understanding of the covariance.

Figures (6)

• Figure 1: Several representative slices through $k$-space showing our results for the Li et al. simulation covariance data. We show the covariance normalized to the power spectra, but fits are performed to the pure covariance data. Moreover, the Gaussian part of the covariance has been subtracted. The one-loop SPT contributions are evaluated with the cutoff $\Lambda =10$ h/Mpc. The thickness of the solid purple line represents the uncertainty from the fit parameter $c_*$, and from varying the power spectrum and bispectrum coefficients by $50\%$. Vertical dotted lines bound the region of $k_j$ values that were included in the fit for a slice at $k_i$. Any agreement between the EFT and the data to the right of the vertical lines is not coming from fitting but from the EFT prediction with the measured parameters.
• Figure 2: Same as Figure \ref{['li']} but with the Blot et al. data. We find that these data are well fit by the one-loop SPT zero-parameter prediction, and there is no significant improvement from the EFT.
• Figure 3: Tree-level SPT contributions to the trispectrum, represented diagrammatically.
• Figure 4: One-loop SPT contributions to the trispectrum, represented diagrammatically.
• Figure 5: Leading EFT contributions to the trispectrum, represented diagrammatically.