A Dynamical Solution to the Problem of a Small Cosmological Constant and Late-time Cosmic Acceleration

TL;DR

In the theories considered, the dynamics causes the scalar field to lock automatically into a negative pressure state at the onset of matter domination such that the present epoch is the earliest possible time consistent with nucleosynthesis restrictions when it can start to dominate.

Abstract

Increasing evidence suggests that most of the energy density of the universe consists of a dark energy component with negative pressure, a ``cosmological constant" that causes the cosmic expansion to accelerate. In this paper, we address the puzzle of why this component comes to dominate the universe only recently rather than at some much earlier epoch. We present a class of theories based on an evolving scalar field where the explanation is based entirely on internal dynamical properties of the solutions. In the theories we consider, the dynamics causes the scalar field to lock automatically into a negative pressure state at the onset of matter-domination such that the present epoch is the earliest possible time, consistent with nucleosynthesis restrictions, when it can start to dominate.

Figures (3)

• Figure 1: A plot of $g(y)$ vs. $y$ (see Eq. (3) for definition) indicating the points discussed in the text. R corresponds to the attractor solution during the radiation-dominated epoch; S is the de Sitter attractor at the onset of matter-domination; and K is the attractor as $k$-essence dominates. For our range of $g(y)$, there is no dust-like attractor solution at $y=y_D$.
• Figure 2: The ratio of $k$-essence energy density, $\rho_k$, to the density in radiation and matter, $\rho_m$, vs. red shift. At the present epoch (dashed line), $\Omega_k \approx 0.7$.
• Figure 3: The $k$-essence equation-of-state vs. red shift. The three attractors in the radiation-, matter-, and $k$-essence-dominated epochs are evident. At the present epoch, $w_k \approx -0.77$.