M-theory Cosmology, Octonions, Error Correcting Codes

TL;DR

This paper explores M-theory compactifications on twisted 7-tori with G2-holonomy, utilizing octonion-based superpotentials linked to error correcting codes to model Minkowski vacua and inflationary scenarios with testable predictions for B-mode polarization.

Contribution

It introduces novel superpotentials based on octonions and error correcting codes for M-theory compactifications, connecting string theory with cosmological inflation models.

Findings

Constructed Minkowski vacua with flat directions using octonion-inspired superpotentials.

Developed inflation models with specific alpha parameters predicting observable B-mode signals.

Predicted a range of tensor-to-scalar ratios (r) accessible to future cosmological experiments.

Abstract

We study M-theory compactified on twisted 7-tori with $G_2$-holonomy. The effective 4d supergravity has 7 chiral multiplets, each with a unit logarithmic K\"ahler potential. We propose octonion, Fano plane based superpotentials, codifying the error correcting Hamming (7,4) code. The corresponding 7-moduli models have Minkowski vacua with one flat direction. We also propose superpotentials based on octonions/error correcting codes for Minkowski vacua models with two flat directions. We update phenomenological $\alpha$-attractor models of inflation with $3\alpha=7,6,5,4,3,1$, based on inflation along these flat directions. These inflationary models reproduce the benchmark targets for detecting B-modes, predicting 7 different values of $r = 12\alpha/N_{e}^{2}$ in the range $10^{-2}\gtrsim r \gtrsim 10^{-3}$, to be explored by future cosmological observations.