Is Dark Energy Changing? Probing the Universe's Expansion with present and future astronomical probes

TL;DR

Is Dark Energy Changing? probes whether the DE EoS $w(a)$ deviates from $-1$ by employing a general Padé parametrization that unifies several DE forms, including CPL, and tests both flat and curved universes using current cosmological probes and mock GW standard sirens from the Einstein Telescope. The authors constrain three Padé-based DE forms, Padé-I, SPadé-I, and Padé-II, across data combinations with and without GW data, finding the strongest dynamical DE signals for Padé-II, especially when CMB priors are included; GW data tighten constraints and can reduce significance in some cases. Bayesian evidence suggests all Padé models remain close to $\Lambda$CDM, with SPadé-I sometimes mildly preferred by information criteria, but no model is decisively favored. The work highlights Padé-II as a compelling dynamical-DE candidate and demonstrates the potential of future GW standard sirens to sharpen cosmological constraints, motivating further analyses with full CMB likelihoods and upcoming surveys.

Abstract

This study explores the possibility of a time-varying dark energy (DE) equation of state (EoS) deviating from -1. We employ a comprehensive dataset of usual astronomical probes (Type Ia supernovae, baryon acoustic oscillations, Big Bang nucleosynthesis, Hubble data, and Planck 2018 CMB) alongside future mock gravitational wave (GW) distance measurements from the Einstein Telescope. We utilize the Pad'e approximation, a versatile framework encompassing well-known DE models like constant EoS, Chevallier-Polarski-Linder parametrization and other time-evolving DE parametrizations. Within Pad'e parametrization, we examine three specific forms (Pad'e-I, SPad'e-I, Pad'e-II) applied to both spatially flat and non-flat universes. Pad'e-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 dataset of standard probes (including CMB) with Pad'e-II in a flat universe, we find a strong preference (6.4σ) for a dynamical (time-varying) DE EoS. This preference remains significant (4.7σ) even when incorporating future GW data. Non-Flat Universe: In a non-flat universe, the combined standard datasets (without or with CMB) also indicate dynamical DE EoS at a high confidence level (6.2σ and 6.4σ, respectively). The addition of GW data slightly reduces the evidence (3.8σ and 5.1σ, respectively), but the preference persists. These results collectively suggest a robust case for dynamical DE in the dark sector. While a non-flat universe is not strongly favored, Pad'e-II hints at a possible closed universe when CMB data is included (with or without GW data).

Figures (8)

• Figure 1: Redshift distribution of the SN, $H(z)$ and GW samples using the normalized histogram description. Note that in the redshift regions $(3--4)$ and $(4--5)$ only the GW data are present, in particular, only a few data points of the GW sample are in the latter region, and hence the vertical bar in this redshift region is barely visible.
• Figure 2: One-dimensional marginalized posterior distributions and two-dimensional joint contours at $1\sigma$ and $2\sigma$ considering some of the model parameters are shown for flat Padé-I using the combined datasets SN+BAO+BBN+$H(z)$, SN+BAO+BBN+$H(z)$+GW, SN+BAO+BBN+$H(z)$+CMB and SN+BAO+BBN+$H(z)$+CMB+GW. The solid lines through $w_1 =0$ and $w_2 = 0$ correspond to the $\Lambda$CDM cosmology, which is also considered as the fiducial model for generating the GW mock dataset.
• Figure 3: One-dimensional marginalized posterior distributions and two-dimensional joint contours at $1\sigma$ and $2\sigma$ considering some of the model parameters are shown for flat SPadé-I using the combined datasets SN+BAO+BBN+$H(z)$, SN+BAO+BBN+$H(z)$+GW, SN+BAO+BBN+$H(z)$+CMB and SN+BAO+BBN+$H(z)$+CMB+GW. The solid line through $w_2 = 0$ corresponds to the $\Lambda$CDM cosmology, which is also considered as the fiducial model for generating the GW mock dataset.
• Figure 4: One-dimensional marginalized posterior distributions and two-dimensional joint contours at $1\sigma$ and $2\sigma$ considering some of the model parameters are shown for flat Padé-II using the combined datasets SN+BAO+BBN+$H(z)$, SN+BAO+BBN+$H(z)$+GW, SN+BAO+BBN+$H(z)$+CMB and SN+BAO+BBN+$H(z)$+CMB+GW. The solid lines through $w_1 =0$ and $w_2 = 0$ correspond to the $\Lambda$CDM cosmology, which is also considered as the fiducial model for generating the GW mock dataset.
• Figure 5: One-dimensional marginalized posterior distributions and two-dimensional joint contours at $1\sigma$ and $2\sigma$ considering some of the model parameters are shown for non-flat Padé-I using the combined datasets SN+BAO+BBN+$H(z)$, SN+BAO+BBN+$H(z)$+GW, SN+BAO+BBN+$H(z)$+CMB and SN+BAO+BBN+$H(z)$+CMB+GW. The solid lines through $w_1 =0$ and $w_2 = 0$ correspond to the $\Lambda$CDM cosmology, which is also considered as the fiducial model for generating the GW mock data set.