  Using an effective field theory approach to inflation, we examine novel
properties of the spectrum of inflationary tensor fluctuations, that arise when
breaking some of the symmetries or requirements usually imposed on the dynamics
of perturbations. During single-clock inflation, time-reparameterization
invariance is broken by a time-dependent cosmological background. In order to
explore more general scenarios, we consider the possibility that spatial
diffeomorphism invariance is also broken by effective mass terms or by
derivative operators for the metric fluctuations in the Lagrangian. We
investigate the cosmological consequences of the breaking of spatial
diffeomorphisms, focussing on operators that affect the power spectrum of
fluctuations. We identify the operators for tensor fluctuations that can
provide a blue spectrum without violating the null energy condition, and
operators for scalar fluctuations that lead to non-conservation of the comoving
curvature perturbation on superhorizon scales even in single-clock inflation.
In the last part of our work, we also examine the consequences of operators
containing more than two spatial derivatives, discussing how they affect the
sound speed of tensor fluctuations, and showing that they can mimic some of the
interesting effects of symmetry breaking operators, even in scenarios that
preserve spatial diffeomorphism invariance.
