The Supersymmetric Effective Field Theory of Inflation

Abstract

We construct the Supersymmetric Effective Field Theory of Inflation, that is the most general theory of inflationary fluctuations when time-translations and supersymmetry are spontaneously broken. The non-linear realization of these invariances allows us to define a complete SUGRA multiplet containing the graviton, the gravitino, the Goldstone of time translations and the Goldstino, with no auxiliary fields. Going to a unitary gauge where only the graviton and the gravitino are present, we write the most general Lagrangian built out of the fluctuations of these fields, invariant under time-dependent spatial diffeomorphisms, but softly-breaking time diffeomorphisms and gauged SUSY. With a suitable Stückelberg transformation, we introduce the Goldstone boson of time translation and the Goldstino of SUSY. No additional dynamical light field is needed. In the high energy limit, larger than the inflationary Hubble scale for the Goldstino, these fields decouple from the graviton and the gravitino, greatly simplifying the analysis in this regime. We study the phenomenology of this Lagrangian. The Goldstino can have a non-relativistic dispersion relation. Gravitino and Goldstino affect the primordial curvature perturbations at loop level. The UV modes running in the loops generate three-point functions which are degenerate with the ones coming from operators already present in the absence of supersymmetry. Their size is potentially as large as corresponding to f equil., orthog. NL ∼ 1 or, for particular operators, even 1. The non-degenerate contribution from modes of order H is estimated to be very small.

Higher spin supersymmetry at the cosmological collider: sculpting SUSY rilles in the CMB

“…In the supersymmetric context, this would be joined with contributions from additional interactions. This requires careful consideration of the gravity multiplet, as is the focus of the supersymmetric EFT of inflation [42]. We postpone this analysis to future work.…”

“…The on-shell supersymmetry of the higher spin sector can then be used in conjunction with the effective field theory of inflation to dictate the couplings of higher spin fermions and bosons to primordial perturbations. This is distinct from the supersymmetric EFT of inflation [42] in that we do not focus on the gravity multiplet, but instead on the higher spin supermultiplets.…”

Gravitational production of superheavy dark matter and associated cosmological signatures

“…The existence of such dark matter may originate from supersymmetry breaking theories [17], string inspired models [18][19][20][21] or Kaluza-Klein theory of extra dimension [3,4,22].…”

Constrained superfields and applications

“…Let us close this part with a comment on the gravitino mass. We see that in both the models of [25] and of [61], the relation of the gravitino mass to the vacuum energy is not as transparent as in standard supergravity. We would like to stress that the first time models with this property were constructed in superspace was in [26], in the context of the goldstino brane, where an independent gravitino mass term was introduced.…”