We examine dark-energy models in which a quintessence or a phantom field, $\varphi$, rolls near the vicinity of a local minimum or maximum, respectively, of its potential $V(\varphi )$. Under the approximation that $(1/V)(dV/d\varphi )\ll 1$, [although $(1/V)(d^{2}V/d{\varphi }^2)$ can be large], we derive a general expression for the equation-of-state parameter $w$ as a function of the scale factor for these models. The dynamics of the field depends on the value of $(1/V)(d^{2}V/d{\varphi }^2)$ near the extremum, which describes the potential curvature. For quintessence models, when $(1/V)(d^{2}V/d{\varphi }^2)<3/4$ at the potential minimum, the equation-of-state parameter $w(a)$ evolves monotonically, while for $(1/V)(d^{2}V/d{\varphi }^2)>3/4$, $w(a)$ has oscillatory behavior. For phantom fields, the dividing line between these two types of behavior is at $(1/V)(d^{2}V/d{\varphi }^2)=-3/4$. Our analytical expressions agree within 1% with the exact (numerically derived) behavior, for all of the particular cases examined, for both quintessence and phantom fields. We present observational constraints on these models.

We reexamine the evolution of thermal relic particle abundances for the case where the interaction rate depends on the particle velocities. For the case of Sommerfeld enhancement, we show that the standard analytic approximation, modified in a straightforward way, provides an estimate of the relic particle abundance that is accurate to within 10% (in comparison to less than 1% error for the non-Sommerfeld-enhanced case). We examine the effect of kinetic decoupling on relic particle abundances when the interaction rate depends on the velocity. For the case of pure p-wave annihilation, the effect of kinetic decoupling is an increase in the relic abundance, but the effect is negligible when the kinetic decoupling temperature is much less than the chemical decoupling temperature. For the case of Sommerfeld-enhanced s-wave annihilations, after kinetic decoupling occurs, annihilations continue to change the particle abundance down to arbitrarily low temperatures, until either matter domination begins or the Sommerfeld effect cuts off. We derive analytic approximations to give the final relic particle abundances for both of these cases.

We derive slow-roll conditions for thawing k-essence with a separable Lagrangian $p(X,\varphi )=F(X)V(\varphi )$. We examine the evolution of the equation of state parameter, $w$, as a function of the scale factor $a$, for the case where $w$ is close to $-1$. We find two distinct cases, corresponding to $X\approx 0$ and $F_X\approx 0$, respectively. For the case where $X\approx 0$ the evolution of $\varphi$ and hence $w$ is described by only two parameters, and $w(a)$ is model independent and coincides with similar behavior seen in thawing quintessence models. This result also extends to nonseparable Lagrangians where $X\approx 0$. For the case $F_X\approx 0$, an expression is derived for $w(a)$, but this expression depends on the potential $V(\varphi )$, so there is no model-independent limiting behavior. For the $X\approx 0$ case, we derive observational constraints on the two parameters of the model, $w_0$ (the present-day value of $w$), and the $K$, which parametrizes the curvature of the potential. We find that the observations sharply constrain $w_0$ to be close to $-1$, but provide very poor constraints on $K$.

The anapole moment is the only allowed electromagnetic moment for Majorana fermions. Fermionic dark matter acquiring an anapole can have a standard thermal history and be consistent with current direct detection experiments. In this paper, we calculate the collider monojet signatures of anapole dark matter and show that the current LHC results exclude anapole dark matter with mass less than 100 GeV, for an anapole coupling that leads to the correct thermal relic abundance.

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 nonoscillating 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.

We propose a simple dark energy model with the following properties: the model predicts a late-time dark radiation component that is not ruled out by current observational data, but which produces a distinctive time-dependent equation of state $w(z)$ for $z<3$. The dark energy field can be coupled strongly enough to standard model particles to be detected in colliders, and the model requires only modest additional particle content and little or no fine-tuning other than a new energy scale of order milli-electron volts.