The accelerated expansion in the early universe is both a blessing and a curse. On one hand, the strong gravitational fields provide a high-energy environment which probes the universe on the most fundamental length scales. On the other hand, any signatures of new physics are rapidly diluted away, leaving behind only a faint imprint of long wavelength fluctuations on the primordial matter distribution from which our universe grows.

By applying modern field theory techniques (effective field theory, scattering amplitudes) to the cosmological correlators, we can learn about sources of primordial non-Gaussianity in the early Universe and extend the high energy frontier beyond what is possible with terrestial colliders. In particular, developing consistency conditions such as unitarity and locality of the interactions present during inflation can then be used as theoretical priors to improve the constraining power of our measurements.

The S matrix program of the 60s dreamed of using a number of physically motivated assumptions to determine field theory scattering amplitudes: such as unitarity (correctly normalized probabilities), analyticity (causality), polynomial boundedness (locality), and crossing symmetry. While a unique determination of amplitudes from these principles alone has proven overly-ambitious, these assumptions still provide (in some cases highly non-trivial) inequalities which bound our amplitudes. This is the same spirit behind the recent success enjoyed by the conformal boostrap in applying e.g. unitarity and crossing symmetry to determine the validity of certain spectra and OPE coefficients.

From an EFT perspective, we do not expect an IR effective theory to satisfy these properties (having integrated out degrees of freedom, an EFT is expected to break down beyond some UV cutoff). However, by assuming the existence of a local, analytic UV completion (which we may know little or nothing else about), it is possible to derive corresponding bootstrap constraints on the IR EFT. EFTs which do not satisfy these so-called `positivity bounds' are therefore not consistent with a local UV completion in the standard Wilsonian sense, which can lead to incredibly powerful results regarding the UV behaviour of strongly coupled theories.

It is well known that General Relativity (GR) does not admit a local UV completion (processes like black hole formation lead to UV/IR mixing). However, the question remains open in massive theories of gravity: is it (even in principle) possible to integrate in new dof to provide a local, analytic UV completion (in the traditional Wilsonian sense)?

This question may be answered by considering the behaviour of scattering amplitudes in the IR, even at tree level, as these must satisfy a number of non-trivial positivity conditions (derived from the desired properties of the UV completion).
The answer is clearly interesting either way: if massive gravity satisfies the conditions necessary for UV completion which GR has failed, then understanding why grants important insights into UV structure of gravitational theories; and if it does not, then this points us firmly towards a non-local completion such as classicalization.

A related question is whether scalar or vector Galileons (which naturally arise in the decoupling limit of massive gravity) can admit local, analytic UV completions. Better understanding these features of spin-2 field theories will teach us important lessons about gravity (both GR and its possible massive extensions), as well as lower spin theories (such as the Galileon).

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