Bimetric Convergence

Abstract

If the early universe obeys constructivist principles, there is a dual or multiple definition of dimensionality – in the first epoch – giving it an upper and lower bound.  Various theories of gravity have been suggested which are bimetric, in having a dual definition in their formulation.  In this brief letter, we explore a scenario where D is delimited initially, on both the upper and lower end of the spectrum, and later converges toward familiar values.  Spacetime in the local universe appears to be 4-d at this time, but some theories suggest it is lower-dimensional at the outset or in the microscale, and some say it may be higher-dimensional at vast distances or in an earlier epoch.  Both options might be true simultaneously.  So if we admit the possibility that spacetime is bimetric and study what happens if we leave D open-ended at both extremes initially, in the Planck epoch, we can better understand why reality has the nature it does today.