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We studyd= 4,$$ \mathcal{N} $$$N$≥ 5 supergravities and their deformation via candidate counterterms, with the purpose to absorb UV divergences. We generalize the earlier studies of deformation and twisted self-duality constraint to the case with unbroken local$$ \mathcal{H} $$$H$-symmetry in presence of fermions. We find that the deformed action breaks nonlinear local supersymmetry. We show that all known cases of enhanced UV divergence cancellations are explained by nonlinear local supersymmetry.

This result implies, in particular, that if$$ \mathcal{N} $$$N$= 5 supergravity at five loop will turn out to be UV divergent, the deformed theory will be BRST inconsistent. If it will be finite, it will be a consequence of nonlinear local supersymmetry and E7-type duality.

 

We investigate the two-stage inflation regime in the theory of hybrid cosmological  α-attractors. The spectrum of inflationary perturbations is compatible with the latest Planck/BICEP/Keck Array results, thanks to the attractor properties of the model. However, at smaller scales, it may have a very high peak of controllable width and position, leading to a copious production of primordial black holes (PBH) and generation of a stochastic background of gravitational waves (SGWB).

 

Abstract We discuss two-stage dilaton-axion inflation models [1] and describe α -attractor models with either exponential or polynomial approach to the plateau.We implement one of the models of primordial black hole production proposed in [2] in the α -attractor context, and develop its supergravity version. The predictions of this model following from its polynomial attractor properties are: n s and r are α -independent, r depends on the mass parameter μ defining the approach to the plateau. The tachyonic instability at the transition point between the two stages of inflation is proportional to the negative curvature of the hyperbolic space ℛ K = -2/3 α . Thereforethe masses of primordial black holes (PBHs) and the frequencies of small-scale gravitational waves (GWs) in this model show significant dependence on  α . 

A bstract It was argued in [1] that the Volkov-Akulov (VA) model as well as similar models in supergravity and the related KKLT model in string theory, suffer from tachyonic instabilities due to goldstino condensation. The authors of [1] constructed a specific model with two unconstrained interacting chiral superfields with linearly realized supersymmetry which has an unstable vacuum. They claimed that this model becomes equivalent to the VA model in the UV limit. We show that the UV limit of their model is discontinuous, and the vacuum instability of the model proposed in [1] is not relevant to the VA model, to related models in supergravity, and to the KKLT construction. 

Abstract Inflationary α -attractor models can be naturally implemented in supergravity with hyperbolic geometry. They have stable predictions for observables, such as n s = 1 - 2/ N e , assuming that the potential in terms of the original geometric variables, as well as its derivatives, are not singular at the boundary of the hyperbolic disk, or half-plane. In these models, the potential in the canonically normalized inflaton field φ has a plateau, which is approached exponentially fast at large φ . We call them exponential α-attractors . We present a closely related class of models, where the potential is not singular, but its derivative is singular at the boundary. The resulting inflaton potential is also a plateau potential, but it approaches the plateau polynomially. We call them polynomial α-attractors . Predictions of these two families of attractors completely cover the sweet spot of the Planck/BICEP/Keck data. The exponential ones are on the left, the polynomial are on the right. 

Abstract We discuss implications of the latest BICEP/Keck data release for inflationary models, with special emphasis on the cosmological attractors which can describe all presently available inflation-related observational data. These models are compatible with any value of the tensor to scalar ratio r , all the way down to r  = 0. Some of the string theory motivated models of this class predict 10 -3  ≤  r  ≤ 10 -2 . The upper part of this range can be explored by the ongoing BICEP/Keck observations.