Constraints on Dark Energy from the Observed Expansion of our Cosmic Horizon

Abstract

Within the context of standard cosmology, an accelerating universe requires the presence of a third `dark' component of energy, beyond matter and radiation. The available data, however, are still deemed insufficient to distinguish between an evolving dark energy component and the simplest model of a time-independent cosmological constant. In this paper, we examine the cosmological expansion in terms of observer-dependent coordinates, in addition to the more conventional co-moving coordinates. This procedure explicitly reveals the role played by the radius R_h of our cosmic horizon in the interrogation of the data. (In Rindler's notation, R_h coincides with the `event horizon' in the case of de Sitter, but changes in time for other cosmologies that also contain matter and/or radiation.) With this approach, we show that the interpretation of dark energy as a cosmological constant is clearly disfavored by the observations. Within the framework of standard Friedman-Robertson-Walker cosmology, we derive an equation describing the evolution of R_h, and solve it using the WMAP and Type Ia supernova data. In particular, we consider the meaning of the observed equality (or near equality) R_h(t_0) ~ ct_0, where t_0 is the age of the Universe. This empirical result is far from trivial, for a cosmological constant would drive R_h(t) towards ct (where t is the cosmic time) only once--and that would have to occur right now. Though we are not here espousing any particular alternative model of dark energy, for comparison we also consider scenarios in which dark energy is given by scaling solutions, which simultaneously eliminate several conundrums in the standard model, including the `coincidence' and `flatness' problems, and account very well for the fact that R_h(t_0) ~ ct_0.