M-theory Cosmology, Octonions, Error Correcting Codes

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 Kähler 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.

63 pages, 25 figures, v2: comments added, typos fixed, v3: improved formulation presented in Sec.7 and refs added. The new formulation does not change inflationary predictions, but the potentials for decoupled heavy modes are simplified compared with the ones in the previous versions

References in corpus (13)

• The Standard Model Higgs boson as the inflaton
• Planck, LHC, and $\alpha$-attractors
• Simple Finite Non-Abelian Flavor Groups
• E_7 and the tripartite entanglement of seven qubits
• Seven-Disk Manifold, alpha-attractors and B-modes
• Strings, black holes, the tripartite entanglement of seven qubits and the Fano plane
• Inflation from Nilpotent Kähler Corrections
• Four curious supergravities
• Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes
• A new N=1 AdS4 Vacuum of Maximal Supergravity
• A second look at gauged supergravities from fluxes in M-theory
• Probing the origin of our Universe through cosmic microwave background constraints on gravitational waves
• Mass Production of Type IIA dS Vacua

Cited by in corpus (13)

• Hybrid cosmological attractors
• BICEP/Keck and Cosmological Attractors
• Polynomial $\alpha$-attractors
• Narain CFTs and Quantum Codes at Higher Genus
• $\alpha$-attractor inflation: Models and predictions
• IIB String Theory and Sequestered Inflation
• Conjugation Matters. Bioctonionic Veronese Vectors and Cayley-Rosenfeld Planes
• M-theory, Black Holes and Cosmology
• Listening to Celestial Algebras
• Supersymmetric $d{S}_n$ solutions for $n\ge 5$ in $D=11$ supergravity
• Complementary signatures of $\alpha -$attractor inflation in CMB and cosmic string Gravitational Waves
• Inflationary $\alpha$-Attractor From Type IIB/F Theory
• Sequestered Inflation