The Effective Field Theory of Large Scale Structures at Two Loops (1310.0464v2)

Abstract: Large scale structure surveys promise to be the next leading probe of cosmological information. It is therefore crucial to reliably predict their observables. The Effective Field Theory of Large Scale Structures (EFTofLSS) provides a manifestly convergent perturbation theory for the weakly non-linear regime of dark matter, where correlation functions are computed in an expansion of the wavenumber k of a mode over the wavenumber associated with the non-linear scale k_nl. Since most of the information is contained at high wavenumbers, it is necessary to compute higher order corrections to correlation functions. After the one-loop correction to the matter power spectrum, we estimate that the next leading one is the two-loop contribution, which we compute here. At this order in k/k_nl, there is only one counterterm in the EFTofLSS that must be included, though this term contributes both at tree-level and in several one-loop diagrams. We also discuss correlation functions involving the velocity and momentum fields. We find that the EFTofLSS prediction at two loops matches to percent accuracy the non-linear matter power spectrum at redshift zero up to k~0.6 h/Mpc, requiring just one unknown coefficient that needs to be fit to observations. Given that Standard Perturbation Theory stops converging at redshift zero at k~0.1 h/Mpc, our results demonstrate the possibility of accessing a factor of order 200 more dark matter quasi-linear modes than naively expected. If the remaining observational challenges to accessing these modes can be addressed with similar success, our results show that there is tremendous potential for large scale structure surveys to explore the primordial universe.

• The paper demonstrates that two-loop corrections in EFTofLSS match the non-linear matter power spectrum to percent-level accuracy up to k ~0.6 h/Mpc.
• It employs counterterms and renormalization techniques to systematically incorporate short-scale physics beyond standard perturbation theory.
• These advances enable surveys to probe cosmological parameters and early universe physics with significantly increased dark matter modes.

Overview of "The Effective Field Theory of Large Scale Structures at Two Loops"

The paper "The Effective Field Theory of Large Scale Structures at Two Loops" presents significant advancements in understanding the distribution of matter in the Universe, particularly focusing on the weakly non-linear regime. The authors employ the framework of the Effective Field Theory of Large Scale Structures (EFTofLSS) to compute the two-loop corrections to the matter power spectrum, improving upon the predictive power necessary for analyzing data from large-scale structure surveys in cosmology.

EFTofLSS allows the incorporation of non-linear effects, typically elusive in standard perturbation theory (SPT), by systematically expanding the relevant quantities in the ratio of the wavenumber, $k$, to a non-linear scale characterized by $\Lambda$. At this order of expansion, the inclusion of certain counterterms accounts for unresolved short-scale physics, notably extending the predictive accuracy from leading one-loop (positional only) to more precise two-loop calculations.

Key Results

The authors have determined that the EFTofLSS predictions at two loops yield a match to the non-linear matter power spectrum at redshift zero with percent-level accuracy up to $k \sim 0.6 \, h \, \text{Mpc}^{-1}$, utilizing just one free parameter that must be estimated from observations or simulations. The results highlight a notable increase in the number of accessible dark matter modes compared to SPT, which traditionally experiences a breakdown around $k \sim 0.1 \, h \, \text{Mpc}^{-1}$.

Techniques and Methodology

The EFTofLSS framework diverges from traditional approach by incorporating additional terms in the equations of motion for matter overdensities which encode the impact of short-distance physics through parameters like speed of sound and viscosity. By calculating beyond one-loop, specifically at two loops, the authors demonstrate how previously inaccessible corrections can now be systematically incorporated through counterterms, ensuring both the cancellation of divergences and the robustness of predictions at sub-percent level precision.

Their methodology involves a detailed assessment of scaling universes, where the linear power spectrum behaves as a power-law across different wavenumber domains. This setup provides insight into estimating the contribution of various loop orders and counterterm significance by dimensional analysis, substantially verifying that the higher-order terms previously ignored materially influence the calculations.

The authors also navigate through complications such as potential divergences and counterterm degeneracies by rigorously employing renormalization techniques. This also brings attention to the unique non-local-in-time nature of EFTofLSS, requiring integration along the fluid trajectory, a thoughtful incorporation in these complex perturbative calculations.

Implications and Future Directions

The paper posits that large-scale structure surveys can harness these methods to significantly probe the primordial universe and improve constraints on cosmological parameters notably involving the inflationary model, neutrino masses, and dark energy dynamics. The results of this paper underscore the importance of adapting the EFTofLSS to encompass baryonic physics and halo clustering to achieve a more comprehensive understanding.

Future developments should focus on extending the two-loop framework of EFTofLSS to three-loop computations and applying this understanding to analyze cosmological N-body simulations further. Moreover, enhancing the practical implementation and interpretation of these theoretical insights in active surveys like DESI and Euclid would provide a pathway to unleash the vast potential of cosmological data in testing the fundamentals of cosmology and gravitational theory.

In summary, the authors present a substantial advancement in the field of cosmological perturbation theory by proving the practical efficacy of EFTofLSS in predicting the matter power spectrum at two loops with a substantial improvement in the reach of accessible modes. This advancement opens new avenues for large-scale surveys to vastly improve cosmological constraints, particularly those linked to the physics of the early universe.