Ab Initio Estimates of the Size of the Observable Universe

TL;DR

This paper combines multiverse, anthropic, and renormalization group arguments to derive an approximate equation for the proton charge, predicting the universe's age, size, and cosmological constant with close agreement to observed values.

Contribution

It introduces a novel theoretical framework linking fundamental constants to cosmological parameters without adjustable parameters.

Findings

Derived an equation predicting the proton charge within 8% of observed value.

Predicted universe's age and size within 17% of observed values.

Unified multiple theoretical approaches to explain cosmological observations.

Abstract

When one combines multiverse predictions by Bousso, Hall, and Nomura for the observed age and size of the universe in terms of the proton and electron charge and masses with anthropic predictions of Carter, Carr, and Rees for these masses in terms of the charge, one gets that the age of the universe should be roughly the inverse 64th power, and the cosmological constant should be around the 128th power, of the proton charge. Combining these with a further renormalization group argument gives a single approximate equation for the proton charge, with no continuous adjustable or observed parameters, and with a solution that is within 8% of the observed value. Using this solution gives large logarithms for the age and size of the universe and for the cosmological constant that agree with the observed values within 17%.