On the Statistical Equivalence of the Large-scale Structure

The upcoming generation of the large-scale structure (LSS) survey requires a very accurate description of LSS. However, it is challenging to model all relevant physical processes that eventually contribute to the statistical properties of an observed sample. Since not all physical degree-of-freedoms (DOFs) are equally interesting, there could exist some equivalent deterministic/stochastic processes that exactly reproduce the statistics of the observation. Particularly, for LSS,  a mathematically rigorous description of this statistical equivalence principle lead to a theory quite similar (but not the same) to the well-studied effective field theory (EFT). Unlike the EFT of LSS, which conceptually should work at realization level, our ‘equivalent dynamics’ is valid only statistically. Our formalism also provides a much clearer view for understanding the relationship between the effective approach and standard perturbation calculation.