  If time-translations are spontaneously broken, so are boosts. This symmetry
breaking pattern can be non-linearly realized by either just the Goldstone
boson of time translations, or by four Goldstone bosons associated with time
translations and boosts. In this paper we extend the Effective Field Theory of
Multifield Inflation to consider the case in which the additional Goldstone
bosons associated with boosts are light and coupled to the Goldstone boson of
time translations. The symmetry breaking pattern forces a coupling to curvature
so that the mass of the additional Goldstone bosons is predicted to be equal to
$\sqrt{2}H$ in the vast majority of the parameter space where they are light.
This pattern therefore offers a natural way of generating self-interacting
particles with Hubble mass during inflation. After constructing the general
effective Lagrangian, we study how these particles mix and interact with the
curvature fluctuations, generating potentially detectable non-Gaussian signals.
