M-theory cosmology, octonions, error correcting codes

We study M-theory compactified on twisted 7-tori with G₂-holonomy. The effective 4d supergravity has 7 chiral multiplets, each with a unit logarithmic Kähler potential. We propose octonion, Fano plane based superpotentials, codifying the error correcting Hamming (4, 7) 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 α-attractor models of inflation with 3α = 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=12α/Ne2 in the range 10⁻² ≳ r ≳ 10⁻³, to be explored by future cosmological observations.