Why does the effective field theory of inflation work?

Understand

The effective field theory (EFT) of inflation has become the preferred method for computing cosmological correlation functions of the curvature fluctuation, $\zeta$.

• It makes explicit use of the soft breaking of time diffeomorphisms by the inflationary background to organize the operators expansion in the action of the Goldstone mode $\pi$ associated with this breaking.
• Despite its ascendancy, there is another method for calculating $\zeta$ correlators, involving the direct calculation of the so-called Horndeski action order by order in powers of $\zeta$ and its derivatives.
• The question we address in this work is whether or not the $\zeta$ correlators calculated in these seemingly different ways are in fact the same.