Accounting for the Origin of the Arrow of Time - Spontaneous Inflation or Toral Topology?

Abstract

The very early universe at or near the Big Bang was in an extremely `special? or `non-generic? state as implied by the existence of a thermodynamic arrow of time in the present universe. In this thesis, I present and compare two theories - one proposed by Carroll and Chen and the other by McInnes - that purport to explain the special initial conditions of our observable universe, and thus account for the origin of the arrow of time. The approaches adopted by both theories contrast starkly. Carroll and Chen first defined the most `natural? dynamical evolution of an arbitrary state of the universe before suggesting that our observable universe was a baby universe born out of spontaneous inflation; McInnes first considered the concept of `creation from nothing? in the context of string theory proposed by Ooguri, Vafa and Verlinde, then by studying the initial value problem of gravity, drew the conclusion, based on various theorems in differential geometry, that the `earliest? universe has to have the spatial topology of a flat torus so that the observable universe can possibly come into existence with an `inherited? arrow of time. I argue in preference of McInnes? approach (though not the theory in its entirety) over Carroll and Chen?s as it is qualified mathematically, has geometry playing a central role in its account and took into considerations the initial value problem of gravity, where the corresponding initial value constraints have yet to be taken into serious consideration by anyone else as possible sources to an explanation for the origin of the arrow of time.