A Possible Solution to the Horizon Problem: the Mad Era for Massless Scalar Theories of Gravity

Extensions of Einstein gravity which allow the gravitational constant G to change with time as the universe evolves may provide a resolution to the horizon problem without invoking a period of vacuum domination and without the subsequent entropy violation. In a cosmology for which the gravitational constant is not in fact constant, the universe may be older at a given temperature than in a standard Hot Big Bang universe; thus, larger regions of space could have come into causal contact at that temperature. This opens the possibility that large regions became smooth at some high temperature without violating causality. The extra aging of the universe can be accomplished by an early period with a large Planck mass, a period we call the MAD era (Modified Aging era or the Massively Aged and Detained era). We discuss in this paper theories of gravity in which the gravitational constant is replaced with a function of a scalar field. 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. In this paper, we examine scalar theories of gravity without a potential for the scalar field. We first consider the original BransDicke proposal and then address more general scalar theories. Solutions to the equations of motion for Brans-Dicke gravity during the radiation dominated era are presented. In particular, we study the evolution of the Brans-Dicke field Φ which determines the Planck mass at any given time, Φ(t) = mpl(t) . We find that, regardless of initial conditions for the Planck mass, it evolves towards an asymptotic value m̃pl = Φ̃ . The same asymptotic behavior is found in more general scalar theories. For both a Brans-Dicke cosmology and a more general scalar theory, the smoothness of the universe can be explained if the Planck mass is large at some high temperature Tc prior to matter-radiation equality: specifically, if m̃pl/Mo ∼ Tc/To, where Mo = 10 GeV is the Planck mass today and To is the temperature of the cosmic background radiation today. In a pure Brans-Dicke cosmology, an additional mechanism (e.g. a potential for Φ) is required to drive the Planck mass to the value Mo by today. In a more general scalar theory of gravity with variable Brans-Dicke parameter, the suggestion is made that the Planck mass may approach the value Mo more rapidly during the matter dominated era than in a Brans-Dicke cosmology. submitted to Physical Review D November 6, 1992 Alfred P. Sloan Foundation Fellow Presidential Young Investigator