We examine hilltop quintessence models, in which the scalar field is rolling near a local maximum in the potential, and w is close to -1. We first derive a general equation for the evolution of the scalar field in the limit where w is close to -1. We
solve this equation for the case of hilltop quintessence to derive w as a function of the scale factor; these solutions depend on the curvature of the potential near its maximum. Our general result is in excellent agreement (delta w < 0.5%) with all of the particular cases examined. It works particularly well (delta w < 0.1%) for the pseudo-Nambu-Goldstone Boson potential. Our expression for w(a) reduces to the previously-derived slow-roll result of Sen and Scherrer in the limit where the curvature goes to zero. Except for this limiting case, w(a) is poorly fit by linear evolution in a.
Oscillating scalar fields, with an oscillation frequency much greater than the expansion rate, have been proposed as models for dark energy. We examine these models, with particular emphasis on the evolution of the ratio of the oscillation frequency
to the expansion rate. We show that this ratio always increases with time if the dark energy density declines less rapidly than the background energy density. This allows us to classify oscillating dark energy models in terms of the epoch at which the oscillation frequency exceeds the expansion rate, which is effectively the time at which rapid oscillations begin. There are three basic types of behavior: early oscillation models, in which oscillations begin during the matter-dominated era, late oscillation models, in which oscillations begin after scalar-field domination, and non-oscillating models. We examine a representative set of models (those with power-law potentials) and determine the parameter range giving acceptable agreement with the supernova observations. We show that a subset of all three classes of models can be consistent with the observational data.
Observational limits on the high-energy neutrino background have been used to place general constraints on dark matter that annihilates only into standard model particles. Dark matter particles that annihilate into neutrinos will also inevitably bran
ch into electromagnetic final states through higher-order tree and loop diagrams that give rise to charged leptons, and these charged particles can transfer their energy into photons via synchrotron radiation or inverse Compton scattering. In the context of effective field theory, we calculate the loop-induced branching ratio to charged leptons and show that it is generally quite large, typically >1%, when the scale of the dark matter mass exceeds the electroweak scale, M_W. For a branching fraction >3%, the synchrotron radiation bounds on dark matter annihilation are currently stronger than the corresponding neutrino bounds in the interesting mass range from 100 GeV to 1 TeV. For dark matter masses below M_W, our work provides a plausible framework for the construction of a model for neutrinos only dark matter annihilations.
We demonstrate that as we extrapolate the current $Lambda$CDM universe forward in time, all evidence of the Hubble expansion will disappear, so that observers in our island universe will be fundamentally incapable of determining the true nature of th
e universe, including the existence of the highly dominant vacuum energy, the existence of the CMB, and the primordial origin of light elements. With these pillars of the modern Big Bang gone, this epoch will mark the end of cosmology and the return of a static universe. In this sense, the coordinate system appropriate for future observers will perhaps fittingly resemble the static coordinate system in which the de Sitter universe was first presented.
