Prospects for probing the dark energy via supernova distance measurements

TL;DR

The paper tackles how to probe dark energy with Type Ia supernova distances and, if present, reconstruct a quintessence scalar-field potential $V(\phi)$. It derives reconstruction equations that express $V(\phi)$ and $d\phi/dz$ in terms of the observable coordinate distance $r(z)$ and its derivatives in a flat universe with matter density parameter $\Omega_M$. Feasibility is assessed by Monte Carlo simulations of SN Ia data, showing that reconstruction is limited by the second-derivative term $d^2 r/dz^2$; with luminosity-distance errors at the 2% level and $z_{\max}\sim 1$, evolving $w_X(z)$ can be distinguished from constant $w_X$, and all constant $w_X=-N/3$ models with $N=0..3$ can be ruled out at $>99.9\%$ confidence. The study concludes that SN Ia distances offer a promising route to characterize dark energy, while highlighting challenges such as distance-systematics, optimal redshift sampling, and the reduced information content at $z\gtrsim 0.8$.

Abstract

Distance measurements to Type Ia supernovae (SNe Ia) indicate that the Universe is accelerating and that two-thirds of the critical energy density exists in a dark-energy component with negative pressure. Distance measurements to SNe Ia can be used to distinguish between different possibilities for the dark energy, and if it is an evolving scalar field, to reconstruct the scalar-field potential. We derive the reconstruction equations and address the feasibility of this approach by Monte-Carlo simulation.