Inflation model and Riemann tensor on non-associative algebra

TL;DR

This paper explores a novel inflation model based on non-associative algebra, linking space reduction to inflation, and introduces a new gravitational constant derived from octonion algebra, with implications for early universe dynamics.

Contribution

It presents a new inflation framework using non-associative algebra and constructs a gravitational constant from octonion algebra, connecting algebraic structures to cosmological evolution.

Findings

Space reduction interpreted as inflation process.

Non-associativity leads to two-stage inflation.

Continuous link between Friedmann and inflationary stages.

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.