Principal Shapes and Squeezed Limits in the Effective Field Theory of Large Scale Structure

Abstract

We apply an orthogonalization procedure on the effective field theory of large scale structure (EFT of LSS) shapes, relevant for the angle-averaged bispectrum and non-Gaussian covariance of the matter power spectrum at one loop. Assuming natural-sized EFT parameters, this identifies a linear combination of EFT shapes - referred to as the principal shape - that gives the dominant contribution for the whole kinematic plane, with subdominant combinations suppressed by a few orders of magnitude. For the covariance, our orthogonal transformation is in excellent agreement with a principal component analysis applied to available data. Additionally we find that, for both observables, the coefficients of the principal shapes are well approximated by the EFT coefficients appearing in the squeezed limit, and are thus measurable from power spectrum response functions. Employing data from N-body simulations for the growth-only response, we measure the single EFT coefficient describing the angle-averaged bispectrum with $\mathcal{O}(10\%)$ precision. These methods of shape orthogonalization and measurement of coefficients from response functions are valuable tools for developing the EFT of LSS framework, and can be applied to more general observables.

18+10 pages, 5 figures

References in corpus (4)

• The Effective Field Theory of Cosmological Large Scale Structures
• The Bispectrum in the Effective Field Theory of Large Scale Structure
• Separate Universe Simulations
• On Soft Limits of Large-Scale Structure Correlation Functions

Cited by in corpus (9)

• BOSS Correlation Function Analysis from the Effective Field Theory of Large-Scale Structure
• The BOSS bispectrum analysis at one loop from the Effective Field Theory of Large-Scale Structure
• Limits on primordial non-Gaussianities from BOSS galaxy-clustering data
• Limits on Clustering and Smooth Quintessence from the EFTofLSS
• Taming redshift-space distortion effects in the EFTofLSS and its application to data
• BOSS full-shape analysis from the EFTofLSS with exact time dependence
• Consistency Relations in Effective Field Theory
• Baryonic effects in the Effective Field Theory of Large-Scale Structure and an analytic recipe for lensing in CMB-S4
• New tests of dark sector interactions from the full-shape galaxy power spectrum