Poincaré invariance is a well-tested symmetry of nature and sits at the core of our description of relativistic particles and gravity. At the same time, in most systems Poincaré invariance is not a symmetry of the ground state and is hence broken spontaneously. This phenomenon is ubiquitous in cosmology where Lorentz boosts are spontaneously broken by the existence of a preferred reference frame in which the universe is homogeneous and isotropic. This motivates us to study scattering amplitudes without requiring invariance of the interactions under Lorentz boosts. In particular, using on-shell methods and assuming massless, relativistic and luminal particles of any spin, we show that the allowed interactions around Minkowski spacetime are severely constrained by unitarity and locality in the form of consistent factorization. The existence of an interacting massless spin-2 particle enforces (analytically continued) three-particle amplitudes to be Lorentz invariant, even those that do not involve a graviton, such as cubic scalar couplings. We conjecture this to be true for all n-particle amplitudes. Also, particles of spin S > 2 cannot self-interact nor can be minimally coupled to gravity, while particles of spin S > 1 cannot have electric charge. Given the growing evidence that free gravitons are well described by massless, luminal relativistic particles, our results imply that cubic graviton interactions in Minkowski must be those of general relativity up to a unique Lorentz-invariant higher-derivative correction of mass dimension 9. Finally, we point out that consistent factorization for massless particles is highly IR sensitive and therefore our powerful flat-space results do not straightforwardly apply to curved spacetime.

Gravitational interferometers and cosmological observations of the cosmic microwave background offer us the prospect to probe the laws of gravity in the primordial universe. To study and interpret these datasets we need to know the possible graviton non-Gaussianities. To this end, we derive the most general tree-level three-point functions (bispectra) for a massless graviton to all orders in derivatives, assuming scale invariance. Instead of working with explicit Lagrangians, we take a bootstrap approach and obtain our results using the recently derived constraints from unitarity, locality and the choice of vacuum. Since we make no assumptions about de Sitter boosts, our results capture the phenomenology of large classes of models such as the effective field theory of inflation and solid inflation. We present formulae for the infinite number of parity-even bispectra. Remarkably, for parity-odd bispectra, we show that unitarity allows for only a handful of possible shapes: three for graviton-graviton-graviton, three for scalar-graviton-graviton and one for scalar-scalar-graviton, which we bootstrap explicitly. These parity-odd non-Gaussianities can be large, for example in solid inflation, and therefore constitute a concrete and well-motivated target for future observations.

In a recent paper [1], three-particle interactions without invariance under Lorentz boosts were constrained by demanding that they yield tree-level four-particle scattering amplitudes with singularities as dictated by unitarity and locality. In this brief note, we show how to obtain an independent verification and consistency check of these boostless bootstrap results using BCFW momentum shifts. We point out that the constructibility criterion, related to the behaviour of the deformed amplitude at infinite BCFW parameter z, is not strictly necessary to obtain non-trivial constraints for the three-particle interactions.

The effect of spatial curvature on primordial perturbations is controlled by Ω K,0 /c 2 s , where Ω K,0 is today's fractional density of spatial curvature and c s is the speed of sound during inflation. Here we study these effects in the limit c s 1. First, we show that the standard cosmological soft theorems in flat universes are violated in curved universes and the soft limits of correlators can have non-universal contributions even in single-clock inflation. This is a consequence of the fact that, in the presence of spatial curvature, there is a gap between the spectrum of residual diffeomorphisms and that of physical modes. Second, there are curvature corrections to primordial correlators, which are not scale invariant. We provide explicit formulae for these corrections to the power spectrum and the bispectrum to linear order in curvature in single-clock inflation. We show that the large-scale CMB anisotropies could provide interesting new constraints on these curvature effects, and therefore on Ω K,0 /c 2 s , but it is necessary to go beyond our linear-order treatment.

We derive parity-even graviton bispectra in the Effective Field Theory of Inflation (EFToI) to all orders in derivatives. Working in perturbation theory, we construct all cubic interactions that can contribute to tree-level graviton bispectra, showing that they all come from EFToI operators containing two or three powers of the extrinsic curvature and its covariant derivatives: all other operators can be removed by field redefinitions or start at higher-order in perturbations. For operators cubic in the extrinsic curvature, where the single-clock consistency relations are satisfied without a correction to the graviton two-point function, we use the Manifestly Local Test (MLT) to efficiently extract the effects of evolving graviton fluctuations to the end of inflation. Despite the somewhat complicated nature of the bulk interactions, the final boundary correlators take a very compact form. For operators quadratic in the extrinsic curvature, the leading order bispectra are a sum of contact and single exchange diagrams, which are tied together by spatial diffeomorphisms, and to all orders in derivatives we derive these bispectra by computing the necessary bulk time integrals. For single exchange diagrams we exploit factorisation properties of the bulk-bulk propagator for massless gravitons and write the result as a finite sum over residues. Perhaps surprisingly, we show these single exchange contributions have only total-energy poles and also satisfy the MLT.