Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Inflation Model and Riemann Tensor on Non-Associative Algebra

Version 1 : Received: 7 September 2020 / Approved: 9 September 2020 / Online: 9 September 2020 (11:05:46 CEST)

How to cite: Dorofeev, V. Inflation Model and Riemann Tensor on Non-Associative Algebra. Preprints 2020, 2020090208 (doi: 10.20944/preprints202009.0208.v1). Dorofeev, V. Inflation Model and Riemann Tensor on Non-Associative Algebra. Preprints 2020, 2020090208 (doi: 10.20944/preprints202009.0208.v1).

Abstract

In this article the reduction of a $n$-dimensional space to a $k$-dimensional space is considered as a reduction of $N^n$ states to $N^k$ states, where $N$ stands for the number of single-particle states per unit of spatial length. It turns out, this space reduction could be understood as another definition of inflation. It is shown that the introduction of the non-associativity of the algebra of physical fields in a homogeneous space leads to a nonlinear equation, the solutions of which can be considered as two-stage inflation. Using the example of reduction $T\times R^7$ to $T\times R^3$, it is shown that there is a continuous cross-linking of the Friedmann and inflationary stages of algebraic inflation at times $10^{-15}$ with the number of baryons $10^{80}$ in the Universe. In this paper, we construct a new gravitational constant based on a nonassociative octonion algebra.

Subject Areas

Inflation; gravity; compactification

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