Consistency Relations in Effective Field Theory
  The consistency relations in large scale structure relate the lower-order
correlation functions with their higher-order counterparts. They are direct
outcome of the underlying symmetries of a dynamical system and can be tested
using data from future surveys such as Euclid. Using techniques from standard
perturbation theory (SPT), previous studies of consistency relation have
concentrated on continuity-momentum (Euler)-Poisson system of an ideal fluid.
We investigate the consistency relations in effective field theory (EFT) which
adjusts the SPT predictions to account for the departure from the ideal fluid
description on small scales. We provide detailed results for the 3D density
contrast $\delta$ as well as the {\em scaled} divergence of velocity
$\bar\theta$. Assuming a $\Lambda$CDM background cosmology, we find the
correction to SPT results becomes important at $k \gtrsim 0.05 \rm h/Mpc$ and
that the suppression from EFT to SPT results that scales as square of the wave
number $k$, can reach $40\%$ of the total at $k \approx 0.25\rm h/Mpc$ at
$z=0$. We have also investigated whether effective field theory corrections to
models of primordial non-Gaussianity can alter the squeezed limit behaviour,
finding the results to be rather insensitive to these counterterms. In
addition, we present the EFT corrections to the squeezed limit of the
bispectrum in redshift space which may be of interest for tests of theories of
modified gravity.
