Model independent constraints on dark energy evolution from low-redshift observations

TL;DR

The paper develops a model-independent cosmographic framework using a $P_{22}$ Padé approximation for the normalized Hubble parameter $E(z)$ to constrain late-time cosmic expansion with low-redshift data. It finds tensions with $ abla Λ$CDM, requiring phantom-like or phantom-crossing dark energy and indicating that no single dark-energy model can explain the entire 0≤z≤2 range; statefinder diagnostics and sound-speed analyses further challenge both canonical scalar-field and barotropic dark-sector scenarios. The analysis yields a model-independent $H_0$ around $72.6$ km s$^{-1}$ Mpc$^{-1}$, with tensions with Planck depending on dataset combinations, and shows that including $H(z)$ data is crucial for reconciling some parameters with Planck. Overall, the work demonstrates the utility of Padé-based cosmography in discriminating late-time cosmologies and highlights the need for more complex or multiple-dark-energy descriptions to fit the full set of low-redshift observations.

Abstract

Knowing the late time evolution of the Universe and finding out the causes for this evolution are the important challenges of modern cosmology. In this work, we adopt a model-independent cosmographic approach and approximate the Hubble parameter considering the Pade approximation which works better than the standard Taylor series approximation for $z>1$. With this, we constrain the late time evolution of the Universe considering low-redshift observations coming from SNIa, BAO, $H(z)$, $H_{0}$ , strong-lensing time-delay as well as the Megamaser observations for angular diameter distances. We confirm the tensions with $Λ$CDM model for low-redshifts observations. The present value of the equation of state for the dark energy has to be phantom-like and for other redshifts, it has to be either phantom or should have a phantom crossing. For lower values of $Ω_{m0}$, multiple phantom crossings are expected. This poses serious challenges for single, non-interacting scalar field models for dark energy. We derive constraints on the {\it statefinders} $(r,s)$ and these constraints show that a single dark energy model cannot fit data for the whole redshift range $0\leq z\leq 2$: in other words, we need multiple dark energy behaviors for different redshift ranges. Moreover, the constraint on sound speed for the total fluid of the Universe, and for the dark energy fluid (assuming them being barotropic), rules out the possibility of a barotropic fluid model for unified dark sector and barotropic fluid model for dark energy, as fluctuations in these fluids are unstable as $c_{s}^2 < 0$ due to constraints from low-redshift observations.

Figures (7)

• Figure 1: The percentage difference ($\Delta$) between the actual model (see text) and fitted model as a function of redshift. Dashed line is fourth order Taylor Series Expansion and solid line is for $P_{22}$.
• Figure 2: Reconstructed $H(z)$ using observational data (see text). The solid lines are for using $q_{0}, j_{0}, s_{0}, l_{0}$ as parameters and the dashed lines are for using $P_{1}, P_{2}, Q_{1}, Q_{2}$ as parameters. In both cases, the innermost line is for the best fit case and the other two sets are for $68\%$ and $95\%$ confidence level.
• Figure 3: The likelihoods for different cosmographic parameters and $r_{d}$ as well as the confidence contours in different parameter space. For each contour, the deep shaded region is for $68\%$ confidence level and light shaded region is for $95\%$ confidence level.
• Figure 4: Reconstructed $w_{eff}$ as a function of redshift $z$. Pink shaded region is for model independent study in this paper. The red shaded region is for $\Lambda$CDM model as constrained by Planck-2015. The horizontal line is for $w_{eff} = -1/3$. The deep shaded and light shaded regions are for $68\%$ and $95\%$ confidence level.
• Figure 5: Reconstructed equation of state for dark energy $w_{DE}(z)$ taking values of $\Omega_{m0}$ =0.28(upper left), 0.30(upper right), 0.31(lower) respectively. Contour shadings are the same as in Figure 4.