The dark side of curvature

TL;DR

This paper discusses the challenges and limitations of geometrical tests in cosmology for distinguishing dark energy properties from spatial curvature, emphasizing the importance of high-redshift measurements and parameterization.

Contribution

It highlights the practical difficulties in breaking the degeneracy between dark energy and curvature using current and upcoming surveys, and underscores the need for high-redshift data and parameterized models.

Findings

High-redshift measurements (z ≈ 2) are crucial for resolving degeneracies.

Combining H(z) and d_A(z) helps but is limited by statistical and model assumptions.

Parameterization of w(z) is essential for disentangling dark energy from curvature.

Abstract

Geometrical tests such as the combination of the Hubble parameter H(z) and the angular diameter distance d_A(z) can, in principle, break the degeneracy between the dark energy equation of state parameter w(z), and the spatial curvature Omega_k in a direct, model-independent way. In practice, constraints on these quantities achievable from realistic experiments, such as those to be provided by Baryon Acoustic Oscillation (BAO) galaxy surveys in combination with CMB data, can resolve the cosmic confusion between the dark energy equation of state parameter and curvature only statistically and within a parameterized model for w(z). Combining measurements of both H(z) and d_A(z) up to sufficiently high redshifts around z = 2 and employing a parameterization of the redshift evolution of the dark energy equation of state are the keys to resolve the w(z)-Omega_k degeneracy.