  Boostless Bootstrap techniques have been applied by many in the literature to
compute pure scalar and graviton correlators. In this paper, we focus primarily
on mixed graviton and scalar correlators. We start by developing an EFT of
Inflation (EFToI) with some general assumptions, clarifying various subtleties
related to power counting. We verify explicitly the soft limits for mixed
correlators, showing how they are satisfied for higher derivative operators
beyond the Maldacena action. We clarify some confusion in the literature
related to the soft limits for operators that modify the power spectra of
gravitons or scalars. We then proceed to apply the boostless bootstrap rules to
operators that do not modify the power spectra. Towards the end, we give a
prescription that gives correlators for states that are Bogolyubov transforms
of the Bunch-Davies vacuum, directly once we have the correlator for the
Bunch-Davies vacuum. This enables us to bypass complicated in-in calculations
for Bogolyubov states.
