Our view point is to assume that the cosmological constant is indeed invariant. And also done where we use an inflaton value due to use of a scale factor if we furthermore use g(t.t) as the variation of the time component of the metric tensor in Pre-Planckian Space-time up to the Planckian space-time initial values. In doing so, we come up with a polynomial expression for a minimum time step, we can call which leads to a development of the arrow of time, and the preservation of information, of essential type, in cosmological early universe dynamics. In doing so we delineate where Causal structure as outlined by Dowker is relevant to Space-time, which is integral to where we examine a nonsingular beginning of space-time, albeit with a very small initial radii, of the order or smaller than Planck’s length in radii. We show an inter relationship between the formation of the Arrow of time, and Causal structure, assuming developments which are from the setting of H = 0 in the Friedman equation as a starting point and systematically allows delineation of where we can meaningfully discuss creation of Causal structure.
Andrew Walcott Beckwith