$α$-Attractors: Planck, LHC and Dark Energy

Abstract: We develop four-parameter supergravity models of inflation and dark energy, constrained so that ${\delta\rho\over \rho}$, $n_s$ and the cosmological constant $\Lambda $ take their known observable values, but where the mass of gravitino $m_{3/2}$ and the tensor-to-scalar ratio $r$ are free parameters. We focus on generalized cosmological $\alpha$-attractor models, with logarithmic Kahler potentials, a nilpotent goldstino and spontaneously broken supersymmetry at the de Sitter minimum. The future data on B-modes will specify the parameter $\alpha$, measuring the geometry of the Kahler, manifold. The string landscape idea for dark energy is supported in these models via an incomplete cancellation of the universal positive goldstino and negative gravitino contribution. The scale of SUSY breaking M related to the mass of gravitino in our models is a controllable parameter, independent on the scale of inflation, it will be constrained by LHC data and future collider Energy-frontier experiments.