The Planck value of the spectral index can be interpreted as ns = 1 − 2/N in terms of the number of e-foldings N . An appealing explanation for this phenomenological observation is provided by α-attractors: the inflationary predictions of these supergravity models are fully determined by the curvature of the Kähler manifold. We provide a novel formulation of α-attractors which only involves a single chiral superfield. Our construction involves a natural deformation of no-scale models, and employs these to construct a De Sitter plateau with an exponential fall-off. Finally, we show how analogous structures with a flat Kähler geometry arise as a singular limit of such α-scale models.

We continue developing cosmological models involving nilpotent chiral superfields, which provide a simple unified description of inflation and the current acceleration of the universe in the supergravity context. We describe here a general class of models with a positive cosmological constant at the minimum of the potential, such that supersymmetry is spontaneously broken in the direction of the nilpotent superfield S. In the unitary gauge, these models have a simple action where all highly non-linear fermionic terms of the classical Volkov-Akulov action disappear. We present masses for bosons and fermions in these theories. By a proper choice of parameters in this class of models, one can fit any possible set of the inflationary parameters n s and r, a broad range of values of the vacuum energy V 0 , which plays the role of the dark energy, and achieve a controllable level of supersymmetry breaking. This can be done without introducing light moduli, such as Polonyi fields, which often lead to cosmological problems in phenomenological supergravity.

We provide a unified description of cosmological α-attractors and late-time acceleration, in excellent agreement with the latest Planck data. Our construction involves two superfields playing distinctive roles: one is the dynamical field and its evolution determines inflation and dark energy, the other is nilpotent and responsible for a landscape of vacua and supersymmetry breaking. We prove that the attractor nature of the theory is enhanced when combining the two sectors: cosmological attractors are very stable with respect to any possible value of the cosmological constant and, interestingly, to any generic coupling of the inflationary sector with the field responsible for uplifting. Finally, as related result, we show how specific couplings generate an arbitrary inflaton potential in a supergravity framework with varying Kähler curvature.

We develop a new class of supergravity cosmological models where inflation is induced by terms in the Kähler potential which mix a nilpotent superfield S with a chiral sector Φ. As the new terms are non-(anti)holomorphic, and hence cannot be removed by a Kähler transformation, these models are intrinsically Kähler potential driven. Such terms could arise for example due to a backreaction of an anti-D3 brane on the string theory bulk geometry. We show that this mechanism is very general and allows for a unified description of inflation and dark energy, with controllable SUSY breaking at the vacuum. When the internal geometry of the bulk field is hyperbolic, we prove that small perturbative Kähler corrections naturally lead to α-attractor behaviour, with inflationary predictions in excellent agreement with the latest Planck data. * evanmc@physics.mcgill.ca † marco.scalisi@desy.de 1 After writing S in terms of the superspace coordinates, one can easily check that the scalar part is replaced by a bilinear fermion. This simply reflects that, in this case, supersymmetry is nonlinearly realized (see also the recent investigations [2]). One can then recover the original Volkov-Akulov action [3].arXiv:1609.00364v2 [hep-th]