Future Supernovae observations as a probe of dark energy

TL;DR

The paper assesses how future Type Ia SN data, especially from the SNAP mission, can constrain dark energy by advocating a direct parameterization of the equation of state $w_{\phi}(z)$ and by comparing fitting approaches for the luminosity-distance relation. It evaluates a variety of scalar-field dark energy models, showing SNAP could distinguish many of them from ΛCDM, particularly when aided by external $Ω_m$ priors and controlled systematics. Through simulations and fit-quality analyses, the authors find that a linear $w_{\phi}$ expansion (with fixed $Ω_m$) often provides the best balance between bias and variance, though model oscillations can challenge reconstruction. The study also investigates how experimental design, priors, and curvature affect the ability to detect evolution in $w_{\phi}$, concluding that SNAP offers a powerful probe of dark energy with complementary probes potentially enhancing the results.

Abstract

We study the potential impact of improved future supernovae data on our understanding of the dark energy problem. We carefully examine the relative utility of different fitting functions that can be used to parameterize the dark energy models, and provide concrete reasons why a particular choice (based on a parameterization of the equation of state) is better in almost all cases. We discuss the details of a representative sample of dark energy models and show how future supernova observations could distinguish among these. As a specific example, we consider the proposed ``SNAP'' satellite which is planned to observe around 2000 supernovae. We show how a SNAP-class data set taken alone would be a powerful discriminator among a family of models that would be approximated by a constant equation of state for the most recent epoch of cosmic expansion. We show how this family includes most of the dark energy models proposed so far. We then show how an independent measurement of $Ω_{\rm m}$ can allow SNAP to probe the evolution of the equation of state as well, allowing further discrimination among a larger class of proposed dark energy models. We study the impact of the satellite design parameters on this method to distinguish the models and compare SNAP to alternative measurements. We establish that if we exploit the full precision of SNAP it provides a very powerful probe.

Figures (20)

• Figure 1: The Calán Tololo (open circles) and SCP data points (solid circles). The curves correspond to the theoretical models discussed in section \ref{['models']}.
• Figure 2: The relative magnitude with respect to a cosmology with $\Omega_{\rm m}=0.3$ and $\Omega_\Lambda=0.7$. The SNAP data points are simulated with this cosmology. The solid triangles are the binned data points with errorbars from the SNAP type specifications as in table \ref{['tab:snap']}. We have not plotted the data in the redshift interval $z=0-0.2$ for the SNAP experiment. On the left the Calán/Tololo (open circles) and SCP data points (solid circles) are not binned and in the right figure they are. The curves correspond to the theoretical models discussed in section \ref{['models']} and the key to this curves is the same as in fig.\ref{['fig:wall']}. The thick dot-short dash line is a cosmological constant model with $\Omega_\Lambda = 0.6$ and the thick short dash - long dash line a model with $\Omega_\Lambda = 0.8$. The thick long dash line is the "Standard Cold Dark Matter" model with $\Omega_{\rm m} = 1.0$, which is clearly ruled out by the current data.
• Figure 3: On the left the pure exponential potential Wetterich:88Ratra:88Peebles:88Wetterich:95Ferreira:97Ferreira:98Copeland:98 which is an example for a slow roll dark energy model and on the right the exponential with a polynomial prefactor as proposed inAS:00 which gives rise to a local minimum in which the field is trapped.
• Figure 4: The evolution of the densities relative to the critical density for the trapped minimum modelAS:00. The long dashed line is $\Omega_{\rm r}$, the energy density in the radiation, the dotted line $\Omega_{\rm m}$, for the matter fields, and the solid line $\Omega_\phi$, the dark energy contribution.
• Figure 5: The redshift evolution of equation of state factor $w_\phi = p_\phi/ \rho_\phi$ for the discussed models. The thin short dash line is the trapped minimum model, the thin dot - short dash line is from the brane inspired potential, the thin short dash - long dash line from the potential which involves two exponentials, the thick short dashed line from the periodic potential, the thick long dashed line from the pure exponential, the thick solid line from the Pseudo Nambu-Gotu Boson potential, the thin solid line from the Supergravity inspired potential, the thin long dashed line from the exponential tracker solution (underneath $w=-1$), and the thick dotted line from the inverse tracker.