Is Dark Energy Changing? Probing the Universe’s Expansion with Present and Future Astronomical Probes

Abstract This study explores the possibility of a time-varying dark energy (DE) equation of state (EoS) deviating from −1. We employ a comprehensive data set of the usual astronomical probes (Type Ia supernovae, baryon acoustic oscillations, Big Bang nucleosynthesis, Hubble data, and Planck 2018 cosmic microwave background (CMB)) alongside future mock gravitational wave (GW) distance measurements from the Einstein Telescope. We utilize the Padé approximation, a versatile framework encompassing well-known DE models such as constant EoS, Chevallier–Polarski–Linder parameterization, and other time-evolving DE parameterizations. Within the Padé parameterization, we examine three specific forms (Padé-I, SPadé-I, Padé-II) applied to both spatially flat and nonflat universes. Padé-II exhibits particularly interesting features in terms of the evidence of dynamical DE at many standard deviations. Our results can be summarized as follows. Flat universe: when analyzing the combined data set of standard probes (including CMB) with Padé-II in a flat universe, we find a strong preference (6.4 σ ) for a dynamical (time-varying) DE EoS. This preference remains significant (4.7 σ ) even when incorporating future GW data. Nonflat universe: in a nonflat universe, the combined standard data sets (without or with CMB) also indicate a dynamical DE EoS at a high confidence level (6.2 σ and 6.4 σ , respectively). The addition of GW data slightly reduces the evidence (3.8 σ and 5.1 σ , respectively), but the preference persists. These results collectively suggest a robust case for dynamical DE in the dark sector. While a nonflat universe is not strongly favored, Padé-II hints at a possible closed universe when CMB data are included (with or without GW data).