M-theory cosmology, octonions, error correcting codes

Abstract

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 $$ r=12\alpha /{N}_e^2 $$ r = 12 α / N e 2 in the range 10−2 ≳ r ≳ 10−3, to be explored by future cosmological observations.

Tachyonic de Sitter Solutions of 10d Type II Supergravities

“…Such a realisation could match standard cosmological models described above, but alternative stringy approaches to cosmology have also been proposed (see e.g. [9–20] for a recent sample). Finding de Sitter solutions from string theory has been attempted for a long time, and the current situation is that it is difficult to build any well‐controlled example.…”

M-theory, black holes and cosmology

“…A nice feature of our cosmological models in [24] is that they describe a case of maximal supersymmetry spontaneously broken down to a minimal supersymmetry. These models will be tested by future cosmological observations, as we show in figure 1.…”

“…A short summary of the recent paper [24] suitable for this set-up is the following. We have proposed an expression for the effective N=1 4d supergravity following from M-theory/11d supergravity compactified on a manifold with G 2 structure.…”

“…The octonion superpotentials for models in [24] with G 2 holonomy and seven moduli have 14 terms in the form WO=12double-struckMijTiTj. The matrix double-struckMij for the simplest case WO for Cartan–Shouten–Coxeter octonion notations is double-struckMWO=(0−11001−1−10−110011−10−110001−10−110001−10−111001−10−1−11001−10…”

“…The fermion mass matrix in equation (4.3) at Minkowski vacua in cosmological models [24] can be brought to a diagonal form as shown in equations (4.5) and (4.6). Since it is a 7 × 7 matrix, its eigenvalues are invariant under the O (7) symmetry and its subgroups.…”