Exploring the Expansion History of the Universe

TL;DR

The paper addresses reconstructing the universe's expansion history from distance-redshift data, highlighting Type Ia supernovae as a key probe. It analyzes the limitations of the conventional linear $w(z)$ parametrization and introduces a new two-parameter form $w(a)=w_0+w_a(1-a)$ that remains well-behaved across redshift, enabling accurate mapping of $H(z)$ and $a(t)$ and connecting to conformal time. It also investigates conformal-time representations and extends the framework to beyond-dark-energy scenarios, including braneworld and Chaplygin gas models, with explicit observational forecasts for SNAP and Planck. The work emphasizes model-independent reconstruction of cosmic expansion, enabling tests of gravity and high-energy theories while guiding future observational strategies to distinguish dark energy dynamics from alternative explanations.

Abstract

Exploring the recent expansion history of the universe promises insights into the cosmological model, the nature of dark energy, and potentially clues to high energy physics theories and gravitation. We examine the extent to which precision distance-redshift observations can map out the history, including the acceleration-deceleration transition, and the components and equations of state of the energy density. We consider the ability to distinguish between various dynamical scalar field models for the dark energy, as well as higher dimension and alternate gravity theories. Finally, we present a new, advantageous parametrization for the study of dark energy.

Figures (3)

• Figure 1: Mapping the expansion history through the supernova magnitude-redshift relation can distinguish the dark energy explanation for the accelerating universe from alternate theories of gravitation, high energy physics, or higher dimensions. All three models take an $\Omega_M=0.3$, flat universe but differ on the form of the Friedmann expansion equation.
• Figure 2: Mapping the density history with SNAP can clearly show both the current accelerating phase and the transition to the matter dominated, decelerating epoch. At high redshifts all models obey the matter dominated slope 3 law, but deviation from this -- the sign of dark energy or alternative gravity -- is clearly visible for $z<2$.
• Figure 3: The conformal horizon scale characterizes the dynamics. The negative slope part of the curve allows comoving wavelengths to expand outside the horizon, or alternately represents $aH=\dot a$ increasing, i.e. $\ddot a>0$ -- the signature of inflation or acceleration. The dashed blue lines show that SNAP will map the accelerating phase, the transition, and into the matter dominated, decelerating phase of the past universe.