We present a general framework where the effective field theory of single field inflation is extended by the inclusion of operators with mass dimension 3 and 4 in the unitary gauge. These higher dimensional operators introduce quartic and sextic corrections to the dispersion relation. We study the regime of validity of this extended effective field theory of inflation and the effect of these higher dimensional operators on CMB observables associated with scalar perturbations, such as the speed of sound, the amplitude of the power spectrum and the tensor-to-scalar ratio. Tensor perturbations remain instead, unaltered.

In general relativity producing a regular bounce entails violation of Null Energy Condition for a dynamical source in the model. That generically indicates existence of ghosts or other instabilities. However, in cuscuton modification of gravity, the correspondence between a background bounce and violation of Null Energy Condition for dynamical sources is broken. Cuscuton action, modifies equations of motion in Infra Red limit allowing the background to go through a regular bounce phase. At the same time, since it does not contain any dynamical degrees of freedom, it does not lead to ghosts or other instabilities. Here, we present a toy scenario of a regular bouncing cosmology and prove this claim. Our model is presented as a proof of concept at this point and does not aim to explain observations in late time cosmology.

We demonstrate that in some regions of parameter space, modified dispersion relations can lead to highly populated excited states, which we dub as "super-excited" states. In order to prepare such super-excited states, we invoke dispersion relations that have negative slope in an interim sub-horizon phase at high momenta. This behaviour of quantum fluctuations can lead to large corrections relative to the Bunch-Davies power spectrum, which mimics highly excited initial conditions. We identify the Bogolyubov coefficients that can yield these power spectra. In the course of this computation, we also point out the shortcomings of the gluing method for evaluating the power spectrum and the Bogolyubov coefficients. As we discuss, there are other regions of parameter space, where the power spectrum does not get modified. Therefore, modified dispersion relations can also lead to so-called "calm excited states". We conclude by commenting on the possibility of obtaining these modified dispersion relations within the Effective Field Theory of Inflation.

Reconstructing the expansion history of the Universe from type Ia supernovae data, we fit the growth rate measurements and put modelindependent constraints on some key cosmological parameters, namely, Ω m , γ, and σ 8 . The constraints are consistent with those from the concordance model within the framework of general relativity, but the current quality of the data is not sufficient to rule out modified gravity models. Adding the condition that dark energy density should be positive at all redshifts, independently of its equation of state, further constrains the parameters and interestingly supports the concordance model.

Abstract. This paper presents the first derivation of the quadratic action for curvature perturbations, ζ, within the framework of cuscuton gravity. We study the scalar cosmological perturbations sourced by a canonical single scalar field in the presence of cuscuton field. We identify ζ as comoving curvature with respect to the source field and we show that it retains its conservation characteristic on super horizon scales. The result provides an explicit proof that cuscuton modification of gravity around Friedmann-Lemaitre-Robertson-Walker (FLRW) metric is ghost free. We also investigate the potential development of other instabilities in cuscuton models. We find that in a large class of these models, there is no generic instability problem. However, depending on the details of slow-roll parameters, specific models may display gradient instabilities.