Beyond Two Parameters: Revisiting Dark Energy with the Latest Cosmic Probes

TL;DR

The paper investigates whether a four-parameter dynamical dark energy (DDE) model can be constrained by current cosmological data. It constrains the EoS $w_{ m de}(a) = w_0 + (w_m - w_0)\mathcal{G}(a)$ with transition scale factor $a_t$ and steepness $\Delta_{ m de}$ using Planck 2018 CMB, DESI DR2 BAO, and three SNeIa compilations (PantheonPlus, DESY5, Union3) via Cobaya MCMC and CAMB with PPF perturbations. The main findings are that $a_t$ is generally unconstrained, while $w_0$ and $w_m$ show quintessence and phantom tendencies respectively for several dataset combinations; $\Delta_{ m de}$ is constrained only in a subset of combos. In some cases, the 4PDE model improves the fit (negative $\Delta \chi^2$) but Bayesian evidence often disfavors the extra complexity, with notable exception for the CMB+DESI+DESY5 dataset, which shows moderate evidence in favor of 4PDE. Overall, the results indicate that richer DDE parametrizations can capture subtler late-time dynamics and motivate further exploration with upcoming surveys.

Abstract

Dark energy (DE) models with many free parameters are often considered excessive, as constraining all parameters poses a significant challenge. On the other hand, such models offer greater flexibility to probe the DE sector in more detail. With the rapid advancement of astronomical surveys and the availability of diverse datasets, it is timely to examine whether current combined observations can effectively constrain an extended parameter space in DE models. This article investigates a four-parameter dynamical dark energy (DDE) model that spans a broad region of the universe's expansion history through four key parameters: the present-day value of the DE equation of state ($w_0$), its initial value ($w_m$), the scale factor depicting transition from $w_m$ to $w_0$ occurs ($a_t$), and the steepness of this transition ($Δ_{\rm de}$). We constrain the model using CMB data from Planck, BAO from DESI DR2, and three distinct compilations of Type Ia Supernovae: PantheonPlus, DESY5, and Union3. Our results show that constraining all four parameters remains difficult: $a_t$ is not constrained by any dataset, while the remaining three parameters can be constrained only when all observational probes are combined (with the exception of DESY5). The results further show that DE has a quintessential nature at present ($w_0 > -1$), while $w_m$ is negative, indicating a phantom-like behaviour at early times. Interestingly, despite its larger parameter space, the proposed DDE model is preferred over the $Λ$CDM scenario, based on both $Δχ^2$ and Bayesian evidence, for certain combined datasets, particularly CMB+BAO+DESY5 and CMB+BAO+Union3.

Figures (9)

• Figure 1: Evolution of $w_{\mathrm{de}}(a)$ for different sets of values of $a_{\mathrm{t}}$ and $\Delta_{\mathrm{de}}$, with the parameters $w_0$ and $w_{\mathrm{m}}$ fixed to $-0.8$ and $-1.2$, respectively.
• Figure 2: Evolution of $\frac{\rho_{\mathrm{de}}(a)}{\rho_{\mathrm{de}}(a_0)}$ for different sets of values for $n_{\mathrm{steps}}$, $a_{\mathrm{t}}$, and $\Delta_{\mathrm{de}}$, where the integral steps are set to $n_{\mathrm{steps}} = 4$, $100$, and $500$, respectively. The parameters $w_0$ and $w_{\mathrm{m}}$ are fixed to $-0.8$ and $-1.2$, respectively.
• Figure 3: Theoretical prediction demonstrating the impact on the CMB TT power spectrum when varying different dark energy equation-of-state parameters (see the legends), while keeping the other EoS parameters fixed to the values $w_0 = -0.8$, $w_{\rm m} = -2.2$, $\log_{10}(\Delta_{\mathrm{de}}) = -0.2$, and $\log_{10}(a_\mathrm{t}) = -1$. Other cosmological parameters are fixed to the Planck 2018 best-fit values.
• Figure 4: One-dimensional posterior distributions and two-dimensional marginalized contours for $H_0$ and the four model parameters, as obtained from the CMB+PantheonPlus, CMB+Union3, and CMB+DESY5 dataset combinations.
• Figure 5: One-dimensional posterior distributions and two-dimensional marginalized contours for $H_0$ and the four model parameters, as obtained from the CMB+DESI, CMB+DESI+PantheonPlus, CMB+DESI+Union3, and CMB+DESI+DESY5 dataset combinations.