New Model of Inflation that Predicts Natural Fermion Re-heating and a Dark-Energy energy-fraction of 75%

Abstract

We study a model cosmological solution of the coupled Einstein, electromagnetic (with source) and second-gravity \cite{Nash2010} equations that employs a flat universe Friedmann-\text{Lema{\^ ı}tre}-Robertson-Walker (FLRW) line element with scale factor $a = a(t)$ [comoving coordinates] for the Einstein sector. The solution of the coupled field equations yields a scale factor $a(t)$ that initially varies exponentially $a(t) = a(0) {e}^{H t}$. Exponential growth continues until the comoving time approaches the end of inflation, then $a(t)$ rapidly transitions to a power law dependence on $t$. Concomitant with the transition from inflation in this model is a natural re-heating and excitation of Standard Model degrees of freedom, and in particular of electrically charged quarks and leptons. No scalar inflaton field, or slow-roll potential is introduced to achieve these effects. This model is noteworthy in two respects. A plausible connection between the second-gravity \emph{unit} field $\mathbf{u}$ and Dark Energy, through the generalization of the photon wave function, is demonstrated, and a scenario is outlined that allocates a 75% fraction of the total energy of the Universe to Dark Energy. Secondly, we conjecture that an experimentally detectable substructure of the of the photon can be observed if the (quantized) unit field can be excited out of its ground state.