Seven-Disk Manifold, alpha-attractors and B-modes

TL;DR

This paper connects M-theory compactifications on G_2 manifolds to alpha-attractor models in supergravity, predicting specific B-mode polarization signals in cosmology based on the geometry of the moduli space.

Contribution

It introduces a novel link between M-theory compactifications and alpha-attractor inflation models, deriving specific predictions for the tensor-to-scalar ratio based on moduli space geometry.

Findings

Predicts r ≈ 10^{-2} for 53 e-foldings from G_2 compactification.

Identifies specific alpha values (1 to 7) from supergravity models.

Connects moduli space geometry to observable cosmological parameters.

Abstract

Cosmological alpha-attractor models in \cN=1 supergravity are based on hyperbolic geometry of a Poincar\'e disk with the radius square {\cal R}^2=3\alpha. The predictions for the B-modes, r\approx 3\alpha {4\over N^2}, depend on moduli space geometry and are robust for a rather general class of potentials. Here we notice that starting with M-theory compactified on a 7-manifold with G_2 holonomy, with a special choice of Betti numbers, one can obtain d=4 \cN=1 supergravity with rank 7 scalar coset \Big[{SL(2)\over SO(2)}\Big]^7. In a model where these 7 unit size Poincar\'e disks have identified moduli one finds that 3 alpha =7. Assuming that the moduli space geometry of the phenomenological models is inherited from this version of M-theory, one would predict r \approx 10^{-2} for 53 e-foldings. We also describe the related maximal supergravity and M/string theory models leading to preferred values 3 alpha =1,2,3,4,5,6,7.