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

On page 17 of a book on Modified Gravity by Li and Koyama there is a discussion of how to obtain a Fifth force by a force proportional to minus the spatial derivative of a scalar field. If the scalar field say for an inflaton , as presented by Padmanabhan only depends upon time, of course this means no scalar field contributing to a fifth force Our proposal in the neighborhood of Planck time is to turn the time into being equal to r/[constant times c]. This in pre Planck time where we could specify a fifth force as to breaking down a causal barrier as to initiating a inflationary expansion. For the scalar field, we initially have this r dependence in place of time, whereas our scalar field, and resultant treatment of an effective potential may allow for a transition from a presumed stationary state to inflation