Soft theorems for boosts and other time symmetries

I will derive new classes of soft theorems for theories in which time symmetries (i.e., symmetries that involve the transformation of time, an example of which are Lorentz boosts) are spontaneously broken. The soft theorems involve unequal-time correlation functions with the insertion of a soft Goldstone in the far past. I will discuss explicit examples, which include the effective theory of a relativistic superfluid and inflationary cosmology. I will then discuss how in certain cases these unequal-time identities capture information at the level of observables that cannot be seen purely in terms of equal-time correlators of the field alone.