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Boostless Bootstrap techniques have been applied by many in the literature tocompute pure scalar and graviton correlators. In this paper, we focus primarilyon mixed graviton and scalar correlators. We start by developing an EFT ofInflation (EFToI) with some general assumptions, clarifying various subtletiesrelated to power counting. We verify explicitly the soft limits for mixedcorrelators, showing how they are satisfied for higher derivative operatorsbeyond the Maldacena action. We clarify some confusion in the literaturerelated to the soft limits for operators that modify the power spectra ofgravitons or scalars. We then proceed to apply the boostless bootstrap rules tooperators that do not modify the power spectra. Towards the end, we give aprescription that gives correlators for states that are Bogolyubov transformsof the Bunch-Davies vacuum, directly once we have the correlator for theBunch-Davies vacuum. This enables us to bypass complicated in-in calculationsfor Bogolyubov states.

Mixed Graviton and Scalar Bispectra in the EFT of Inflation: Soft Limits and Boostless Bootstrap