Abstract
The proposed cyclic universes model based on the split division algebras accounts for the inflation, the Big Bang, gravity, dark energy, dark matter, the standard model, and the masses of all elementary particles. The split algebras (complex quaternion and complex octonion) as the Furey model generate the fixed spacetime dimension number for the observable universe with the fixed 4-dimensional spacetime (4D) standard model particles and the oscillating spacetime dimension number for the oscillating universes (hidden or dark energy) with the oscillation between 11D and 11D through 10D and between 10D and 10D through 4D. 11D has the lowest rest mass, the highest speed of light, and the highest vacuum energy, while 4D has the highest rest mass, the lowest (observed) speed of light, and zero vacuum energy. In the cyclic universes model, the universes start with the positive-energy and the negative-energy 11D membrane-antimembrane dual universes from the zero-energy inter-universal void, and are followed by the transformation of the 11D membrane-antimembrane dual universes into the 10D string-antistring dual universes and the external dual gravities as in the Randall-Sundrum model, resulting in the four equal and separate universes consisting of the positive-energy 10D universe, the positive-energy external gravity, the negative-energy 10D universe, and the negative-energy external gravity. Under the fixed spacetime dimension number, the positive-energy 10D universe is transformed into 4D standard model particles through the inflation and the Big Bang. Dark matter is the right-handed neutrino, exactly five times of baryonic matter in total mass in the universe. Under the oscillating spacetime dimension number, the other three universes oscillate between 10D and 10D through 4D, resulting in the hidden universes when D > 4 and dark energy (the maximum dark energy = 3/4 = 75%) when D = 4. Eventually, all four universes return to the 10D universes.
Highlights
Cosmology explains the origin, evolution and ultimate fate of the entire universe [1]
Under the fixed spacetime dimension number, the combination of 4-dimensional spacetime (4D) derived from complex quaternion and the standard model particles derived from complex octonion generates the fixed 4D standard model particle to account for the observable universe
Under the oscillating spacetime dimension number [8], the combination of 4D particle derived from complex quaternion and 10 dimensional spacetime (10D) string and 11D membrane derived from complex octonion through Lie superalgebra [9] [10] [11] generates the oscillating spacetime dimension number between 11D membrane and 11D membrane through 10D string and between 10D particle and 10D particle through 4D particle to account for the oscillating universes as hidden or dark energy [12] [13]. 11D has the lowest rest mass, the highest speed of light, and the highest vacuum energy, while 4D has the highest rest mass, the lowest speed of light, and zero vacuum energy
Summary
Evolution and ultimate fate of the entire universe [1]. Cosmology must be able to account for the well-established phenomena, such as the inflation, the Big Bang, gravity, dark energy, dark matter, baryonic matter, the standard model particles (leptons, quarks, gauge bosons, and the Higgs boson), and the masses of all elementary particles. This paper proposes the cyclic universes model based on the split division algebras to account for all well-established phenomena, the simple relation between 4D and the internal symmetry in the standard model for the observable universe, and the oscillating dimension number among different spacetime dimensions for the reversible cyclic universes model. The proposed cyclic universes model based on the split division algebras accounts for the inflation, the Big Bang, gravity, dark energy, dark matter, the standard model, and the masses of all elementary particles.
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