Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed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 (08:00:37 CEST)

How to cite: Dorofeev, V. Inflation Model and Riemann Tensor on Non-associative Algebra. Preprints 2020, 2020090201. https://doi.org/10.20944/preprints202009.0201.v1. Dorofeev, V. Inflation Model and Riemann Tensor on Non-associative Algebra. Preprints 2020, 2020090201. https://doi.org/10.20944/preprints202009.0201.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.

## Keywords

inflation; gravity; compactification

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