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Title: On the symmetries of cosmological perturbations

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Abstract: The space of inflationary models is vast, containing wide varieties of mechanisms, symmetries, and spectra of particles. Consequently, the space of observational signatures is similarly complex. Hence, it is natural to look for boundaries of the space of models and their signatures.

In the first part of the talk, I’ll prove three theorems about the possible symmetries of cosmological correlators. First, correlation functions of scalar metric fluctuations are uniquely characterized by the soft theorems that generalize Maldacena’s consistency relations and are free from ambiguity under field redefinitions. Second, whatever the particle content and interactions, when the standard soft theorems apply, invariance under de Sitter boosts is only possible if all connected correlators vanish identically, i.e. if the theory is free. Third, conformal invariance is the largest set of linearly realized (bosonic) symmetries of the correlators of any single scalar, irrespectively of any soft theorems or particle content.

In the second part of the talk I’ll discuss some ongoing work on describing cosmological perturbations from “the boundary”, without explicit reference to the time evolution in the “bulk” for popular models of inflation where boost are broken by some condensate.

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