M-theory, black holes and cosmology.

Area of Science:

• Theoretical Physics
• String Theory
• Cosmology

Background:

• Discussions on M-theory, string theory, and supergravity relevant to Michael J. Duff's interests.
• Exploration of STU black hole entropy and its mathematical connections.

Purpose of the Study:

• To describe relations between STU black hole entropy, Cayley hyperdeterminant, Bhargava cube, and triality symmetry.
• To present M-theory cosmology models inspired by Duff's work, utilizing octonions and error-correcting codes.

Main Methods:

• Investigating mathematical relationships between physical concepts.
• Applying octonions and Hamming error-correcting codes to M-theory cosmology models.
• Analyzing fermion mass eigenvalues and their relation to the exceptional Jordan eigenvalue problem.

Main Results:

• A connection is established between STU black hole entropy, the Cayley hyperdeterminant, the Bhargava cube, and a three-qubit triality symmetry.
• M-theory cosmology models involving seven qubits, octonions, and Hamming codes are described, with implications for cosmic microwave background missions.
• Puzzling relations are shown between fermion mass eigenvalues, the exceptional Jordan eigenvalue problem, and black hole entropy.

Conclusions:

• The study highlights intricate connections between diverse areas of theoretical physics and mathematics.
• The developed models offer potential benchmarks for future cosmic microwave background observations.
• The underlying symmetries of these cosmological models are illustrated using the root system of E7.