The existence of light particles with spin during inflation is prohibited by the Higuchi bound. This conclusion can be evaded if one considers states with a sizeable coupling with the inflaton foliation, since this breaks the de Sitter isometries. The action for these states can be constructed within the Effective Field Theory of Inflation, or using a CCWZ procedure. Light particles with spin have prescribed couplings with soft inflaton perturbations, which are encoded in consistency relations. We study the phenomenology of light states with spin 2. These mix with the graviton changing the tensor power spectrum and can lead to sizeable tensor non-Gaussianities. They also give rise to a scalar bispectrum and trispectrum with a characteristic angle-dependent non-Gaussianity.

We point out that tensor consistency relations-i.e. the behavior of primordial correlation functions in the limit a tensor mode has a small momentum-are more universal than scalar consistency relations. They hold in the presence of multiple scalar fields and as long as anisotropies are diluted exponentially fast. When de Sitter isometries are approximately respected during inflation this is guaranteed by the Higuchi bound, which forbids the existence of light particles with spin: De Sitter space can support scalar hair but no curly hair. We discuss two indirect ways to look for the violation of tensor consistency relations in observations, as a signature of models in which inflation is not a strong isotropic attractor, such as solid inflation: (a) Graviton exchange contribution to the scalar four-point function; (b) Quadrupolar anisotropy of the scalar power spectrum due to super-horizon tensor modes. This anisotropy has a well-defined statistics which can be distinguished from cases in which the background has a privileged direction.

We study graviton non-Gaussianities in the EFT of Inflation. At leading (second) order in derivatives, the graviton bispectrum is fixed by Einstein gravity. There are only two contributions at third order. One of them breaks parity. They come from operators that directly involve the foliation: we then expect sizable non-Gaussianities in three-point functions involving both gravitons and scalars. However, we show that at leading order in slow roll the parity-odd operator does not modify these mixed correlators. We then identify the operators that can affect the graviton bispectrum at fourth order in derivatives. There are two operators that preserve parity. We show that one gives a scalar-tensor-tensor three-point function larger than the one computed in Maldacena, 2003 [1] if M2PAs/Λ2≫ 1 (where Λ is the scale suppressing this operator and As the amplitude of the scalar power spectrum). There are only two parity-odd operators at this order in derivatives.

We study generalized disformal transformations, including derivatives of the metric, in the context of the Effective Field Theory of Inflation. All these transformations do not change the late-time cosmological observables but change the coefficients of the operators in the action: some couplings are effectively redundant. At leading order in derivatives and up to cubic order in perturbations, one has 6 free functions that can be used to set to zero 6 of the 17 operators at this order. This is used to show that the tensor three-point function cannot be modified at leading order in derivatives, while the scalar-tensor-tensor correlator can only be modified by changing the scalar dynamics. At higher order in derivatives there are transformations that do not affect the Einstein-Hilbert action: one can find 6 additional transformations that can be used to simplify the inflaton action, at least when the dynamics is dominated by the lowest derivative terms. We also identify the leading higher-derivative corrections to the tensor power spectrum and bispectrum.

We argue that isotropic scalar fluctuations in solid inflation are adiabatic in the super-horizon limit. During the solid phase this adiabatic mode has peculiar features: constant energy-density slices and comoving slices do not coincide, and their curvatures, parameterized respectively by ζ and R, both evolve in time. The existence of this adiabatic mode implies that Maldacena's squeezed limit consistency relation holds after angular average over the long mode. The correlation functions of a long-wavelength spherical scalar mode with several short scalar or tensor modes is fixed by the scaling behavior of the correlators of short modes, independently of the solid inflation action or dynamics of reheating.

We demonstrate that there are theories that exhibit spontaneous scalarization in the strong gravity regime while having General Relativity with a constant scalar as a cosmological attractor. We identify the minimal model that has this property and discuss its extensions.

We investigate the degree to which the Cosmic Microwave Background (CMB) can be used to constrain primordial non-Gaussianity coming from the presence of spinning particles coupled to the inflaton. We compute the T T T and T T T T correlation functions arising from the exchange of a particle with spin s and generic mass, and the corresponding signal-to-noise ratios for a cosmic-variance-limited CMB experiment. We show that already with Planck data one could improve the theoretical bounds on the amplitude of these primordial templates by an order of magnitude. We particularly emphasize the fact that the trispectrum could be sizable even if the bispectrum is not, making it a prime observable to explore the particle content during inflation.

We propose a mechanism that generates a naturally light dark energy field (with Hubble scale mass), starting from a theory with exclusively high scale (Planckian) couplings. It is derived from the clockwork model, with O(100) scalar fields interacting among themselves as well as with a 4-form field strength. We explicitly embed our model in type IIA supergravity. We also give an alternative interpretation in a braneworld set-up.