Possible solution to the horizon problem: Modified aging in massless scalar theories of gravity.

Abstract

An early MAD (massively aged and detained) epoch during which the University becomes older than in the standard model is proposed as a possible new resolution to the horizon problem. This scenario differs from inflation in that there is no period of vacuum domination required and no entropy violation. Extensions of Einstein gravity which allow the Planck mass ${m}_{\mathrm{Pl}}$ to change with time as the Universe evolves may provide such a MAD resolution to the horizon problem: in a cosmology where the gravitational constant $G={m}_{\mathrm{Pl}}^{2}$ is not in fact constant, the Universe may be older at a given temperature than in the standard hot big bang model. Thus, larger regions of space could have come into causal contact at that temperature. This opens the possibility that large regions became smooth without violating causality. We discuss in this paper theories of gravity in which the gravitational constant is replaced with a function of a massless scalar field. We first consider the original Brans-Dicke proposal and then address more general scalar theories. However, this resolution to the smoothness problem can more generally be a feature of any physics which allows the Planck mass to vary with time. Solutions to the equations of motion during the radiation dominated era for Brans-Dicke gravity and more general massless scalar theories of gravity are presented. In particular, we study the evolution of the field $\ensuremath{\Phi}$ which determines the Planck mass at any given time, $\ensuremath{\Phi}(t)={m}_{\mathrm{Pl}}{(t)}^{2}$, in the absence of a potential for $\ensuremath{\Phi}$. We find that, regardless of initial conditions, the Planck mass evolves towards an asymptotic value ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{m}}_{\mathrm{Pl}}={\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\Phi}}}^{\frac{1}{2}}$. For both a Brans-Dicke cosmology and a more general scalar theory, our observable Universe could fit inside a region causally connected at some high temperature ${T}_{c}$ prior to matter-radiation equality if there is a large disparity between the early value of the Planck mass and the Planck mass today; specifically, our causality condition is that $\frac{{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{m}}_{\mathrm{Pl}}}{{m}_{\mathrm{Pl}}({T}_{0})}\ensuremath{\gtrsim}\frac{{T}_{c}}{{T}_{0}}$, where ${m}_{\mathrm{Pl}}({T}_{0})={M}_{0}={10}^{19}$ GeV is the Planck mass today and ${T}_{0}$ is the temperature of the cosmic background radiation today. Still, an additional mechanism is required to drive the Planck mass to the value ${M}_{0}$ before the Universe cools below a temperature of ${T}_{0}\ensuremath{\sim}2.74\ifmmode^\circ\else\textdegree\fi{}$ K. A mechanism capable of anchoring the Planck mass fast enough will necessarily accelerate the cosmological expansion and thus involves important dynamics. We suggest possible mechanisms to anchor the Planck mass and complete this MAD model.