Complementary Roles of Distance and Growth Probes in Testing Time-Varying Dark Energy

TL;DR

This paper analyzes how distance and growth measurements differently constrain time-varying dark energy, revealing that growth data can provide additional independent information beyond traditional distance probes, especially at high precision.

Contribution

It introduces an information-based framework to compare the sensitivities of distance and growth probes to dark energy evolution, highlighting the complementary roles of these observables.

Findings

Distance data mainly constrain a single information mode.

Growth measurements can activate additional information modes at high precision.

Next-generation surveys like Euclid will require percent-level growth precision to access new information.

Abstract

Distance measurements have long provided the primary observational constraints on the expansion history of the Universe and the properties of dark energy. However, because such observables depend on cumulative line-of-sight integrals over the Hubble rate, their sensitivity to time-dependent features of the dark energy equation of state is intrinsically limited. In this work, we examine this limitation from an information-based perspective using the eigenvalue structure of the Fisher information matrix constructed from distance, expansion rate, and growth observables. We show that distance and expansion-rate data generically produce a strongly hierarchical Fisher spectrum dominated by a single information mode, reflecting an irreducible loss of sensitivity to temporal variations in dark energy. This behavior can be traced directly to the integrated kernel structure of geometric observables. Growth measurements, by contrast, respond through differential dynamics and can introduce additional independent information directions. Using both controlled mock data and survey-like configurations representative of next-generation experiments, we find that the impact of growth information depends not only on its nominal precision but also on the structure of the data covariance. In simplified mock setups, growth measurements can partially activate a second information direction even at moderate precision. In Euclid-like configurations, however, the information remains effectively one-dimensional until growth precision reaches the percent level, below which a second mode emerges rapidly. These results clarify the complementary roles of distance and growth probes and provide a model-independent criterion for assessing the physical content of cosmological constraints on dynamical dark energy.