New Conservation Law as to Hubble Parameter, Squared Divided by Time Derivative of Inflaton in Early and Late Universe, Compared with Discussion of HUP in Pre Planckian to Planckian Physics, and Relevance of Fifth Force Analysis to Gravitons and GW

Abstract

We use as given by Li and Koyama, as to using their idea of a fifth force. In doing so, we are assuming a force which is minus the spatial derivative of a scalar field. The scalar field we are using is one from Padmanabhan, and the problem is that the scalar field in the Padmanabhan representation is initially only dependent on time. The time component is stated to be in the Pre Planckian regime is proportional to a radial distance divided by the speed of light. The rephrasing of time as justified by stating that time in its initial configuration does not exist before the expansion of the universe and that we reintroduce time separately from a radial component divided by the speed of light upon entrance into Planckian space–time. In doing this we also refer to a new assumed conservation law which will give new structure as to inflationary expansion and its immediate aftermath. That of the Hubble “constant” divided by the ‘time derivative’ of the scalar field in the inflation regime and then a long time afterwards.