March 12, 2020

Answered by: Jonathan Gorard

Are your models consistent with inflationary cosmology?

Absolutely! The structure of the Wolfram model allows for both local and global variation in spacetime dimensionality; indeed, one of the more subtle mathematical points regarding our derivation of the Einstein field equations is that, at least up to a certain level of granularity, it is not possible to distinguish between local spacetime curvature and a local change in effective spacetime dimension. Therefore, if the initial condition for the universe is a spatial hypergraph with abnormally high vertex connectivity (e.g. a complete graph), then we can interpret this as corresponding to an arbitrarily large number of initial spatial dimensions. If the update rules exhibit the property of being asymptotically dimensionality preserving, then they will eventually cause the effective dimensionality of space to converge to some fixed, finite value.

Thinking about such a universe from the point of view of its causal structure, we can see that it therefore starts off with an arbitrarily large value for the speed of light (since the causal graph is arbitrarily densely connected, allowing information propagation at abnormally high speeds), which then converges down to a much lower value at late times. This makes such a universe compatible with a so-called “VSL” or “variable speed of light” cosmology; VSL cosmologies are known to yield similar observational consequences to standard inflationary models, and, in particular, allow for valid solutions to the horizon and flatness problems of ΛCDM cosmology.