The IR-resummed Effective Field Theory of Large Scale Structures

Abstract: We present a new method to resum the effect of large scale motions in the Effective Field Theory of Large Scale Structures. Because the linear power spectrum in $\Lambda$CDM is not scale free the effects of the large scale flows are enhanced. Although previous EFT calculations of the equal-time density power spectrum at one and two loops showed a remarkable agreement with numerical results, they also showed a 2% residual which appeared related to the BAO oscillations. We show that this was indeed the case, explain the physical origin and show how a Lagrangian based calculation removes this differences. We propose a simple method to upgrade existing Eulerian calculations to effectively make them Lagrangian and compare the new results with existing fits to numerical simulations. Our new two-loop results agrees with numerical results up to $k\sim 0.6 h/$Mpc to within 1% with no oscillatory residuals. We also compute power spectra involving momentum which is significantly more affected by the large scale flows. We show how keeping track of these velocities significantly enhances the UV reach of the momentum power spectrum in addition to removing the BAO related residuals. We compute predictions for the real space correlation function around the BAO scale and investigate its sensitivity to the EFT parameters and the details of the resummation technique.

• The paper introduces a novel resummation technique that mitigates BAO oscillations and sharpens power spectrum predictions.
• It translates Eulerian perturbative results into Lagrangian frameworks, reducing two-loop discrepancies to around 2%.
• The approach achieves 1% precision up to k ~ 0.6 h/Mpc and extends its applicability to momentum power spectra.

Overview of the IR-resummed Effective Field Theory of Large Scale Structures

The paper by Leonardo Senatore and Matias Zaldarriaga presents advancements in the Effective Field Theory of Large Scale Structures (EFTofLSS), focusing on a novel method to address the resummation of large-scale motions. These motions, significant in cosmologies governed by $\Lambda$CDM, substantially impact the power spectra of matter correlators, particularly due to enhanced effects from Baryon Acoustic Oscillations (BAO). The authors provide methodologies to mitigate these oscillatory residuals and improve the domain's calculation precision.

The research introduces an elegant technique to translate Eulerian perturbative results into their Lagrangian counterparts, addressing previous challenges in the equal-time density power spectrum accuracy due to long wavelength displacements. This transition is crucial in resolving 2% discrepancies observed at two-loop calculations, primarily associated with BAO effects in prior efforts. The authors leverage Lagrangian frameworks to extend the power spectrum calculations significantly, achieving convergence with numerical data up to $k \sim 0.6\,h\,\text{Mpc}^{-1}$ within a 1% error margin, with no residual BAO oscillations.

EFT resummation is implemented by formulating a convergently restructured problem through Lagrangian mappings, effectively tackling the displacement fields non-perturbatively while maintaining perturbative control over UV contributions and density perturbations. Theoretical consistency demands expansion truncation, restraining to $\delta$-like divergences while emphasizing important displacement-induced effects through an advanced matrix formulation. This enables nuanced treatment of IR resummation, refining the UV translations without introducing significant computational complexity.

Furthermore, the paper extends its analysis to momentum power spectra, where large-scale flows exert a substantially more profound impact. Herein, traditional Eulerian approaches fail to capture all the nuances introduced by IR modes, particularly when correlating unequal-time structures. The applied IR-resummed frameworks showcase an enhanced scope by fostering better approximations of these nuances, suggesting a potential paradigm shift in cosmological computations to incorporate the effects consistently across different perturbative orders.

Implications and Future Directions

The methodological advancements encapsulated within this paper strongly suggest a broader utility of EFTofLSS in refining cosmological observables' predictive accuracy while ensuring theoretical control over divergent structures. The removal of perturbative oscillations and enhanced accuracy levels position this approach for future explorations of non-linearities in complex cosmological models, particularly in regimes where traditional perturbative methods lack sufficiency.

The potential for extending these IR-resummed frameworks into high-z cosmological studies or more expansive unconvolved cosmological probes stands as a promising avenue for future research. Furthermore, adapting these techniques to redshift space distortions or stochastic halo biasing can further integrate observational cosmology with theoretical frameworks.

In conclusion, the IR-resummed EFTofLSS presented by Senatore and Zaldarriaga signifies a pivotal step forward in cosmological modeling, providing robust methodologies for precision cosmology's continued evolution. This research piece forms a foundation for upcoming theoretical endeavors, emphasizing the utility of non-linear techniques in the large-scale structure and particle physics communities.