Search for Isocurvature with Large-scale Structure: A Forecast for Euclid and MegaMapper using EFTofLSS

Isocurvature perturbations with a blue power spectrum are one of the natural targets for the future large scale structure observations which are probing shorter length scales with greater accuracy. We present a Fisher forecast for the Euclid and MegaMapper (MM) experiments in their ability to detect blue isocurvature perturbations. We construct the theoretical predictions in the EFTofLSS and bias expansion formalisms at quartic order in overdensities which allows us to compute the power spectrum at one loop order and bispectrum at tree level and further include theoretical error at the next to leading order for the covariance determination. We find that Euclid is expected to provide at least a factor of few improvement on the isocurvature spectral amplitude compared to the existing Planck constraints for large spectral indices while MM is expected to provide about 1 to 1.5 order of magnitude im provement for a broad range of spectral indices. We find features that are specific to the blue isocurvature scenario including the leading parametric degeneracy being with the Laplacian bias and a UV sensitive bare sound speed parameter.