The Multiverse and Cosmic Procreation via Cofinsler Spaces -- or -- Being and Nothingness

TL;DR

This paper explores a scalar field theory on a Lorentzian Cofinsler manifold, proposing a multiverse model with branching de Sitter spaces, and discusses implications for matter, space quantization, inflation, and gravitons.

Contribution

It introduces a novel multiverse model based on a third-order Hamiltonian with branching FLRW spaces and continuous metrics, expanding the theoretical framework of cosmology.

Findings

Multiple vacuum solutions generate a multiverse with branching de Sitter spaces.

The metric remains continuous despite derivative discontinuities at branching points.

The formalism addresses the nature of matter and space before and after universe branching.

Abstract

In this paper I shall consider a scalar-scalar field theory with scalar field phi on a four-dimensional manifold M, and a Lorentzian Cofinsler function f on T*M. A particularly simple Lagrangian is chosen to govern this theory, and when f is chosen to generate FLRW metrics on M the Lagrangian becomes a function of phi and its first two time derivatives. The associated Hamiltonian is third-order, and admits infinitely many vacuum solutions. These vacuum solutions can be pieced together to generate a multiverse. This is done for those FLRW spaces with k>0. So when time, t, is less than zero we have a universe in which the t=constant spaces are 3-spheres with constant curvature k. As time passes through zero the underlying 4-space splits into an infinity of spaces (branches) with metric tensors that describe piecewise de Sitter spaces until some cutoff time, which will, in general, be different for different branches. After passing through the cutoff time all branches will return to their original 4-space in which the t=constant spaces are of constant curvature k, but will remain separate from all of the other branch universes. The metric tensor for this multiverse is everywhere continuous, but experiences discontinuous derivatives as the universe branches change between different de Sitter spaces. Some questions I address using this formalism are: what is the nature of matter when t<0; what happens to matter as time passes through t=0; and what was the universe doing before the multiple universes came into existence at t=0? The answers to these questions will help to explain the paper's title. I shall also briefly discuss a possible means of quantizing space, how inflation influences the basic cells that constitute space, and how gravitons might act.