Beyond $Λ$CDM with Low and High Redshift Data: Implications for Dark Energy

TL;DR

The paper tackles the H0 tension and possible deviations from ΛCDM by reconstructing the late-time Hubble parameter H(z) from low-redshift data using a Padé cosmography approach and enforcing Planck ΛCDM behavior at high redshift through a matching redshift z_match. It derives the dark-energy evolution via 3H^2(z) = ρ_m0(1+z)^3 + ρ_DE0 f(z) and finds ρ_DE(z) exhibits a minimum with ρ_DE,min < 0, effectively signaling a negative cosmological constant plus an evolving DE component. Including Planck high-z H(z) constraints shifts the inferred H0 downward and makes the negative minimum in ρ_DE(z) more pronounced for certain z_match and Ω_m0 values, while the low-z reconstruction alone shows oscillations and phantom crossing around the present. The results imply a nontrivial DE sector compatible with a small negative Λ, with observable implications for structure formation and CMB, and motivate future joint likelihood analyses to self-consistently determine z_match and test predictions with upcoming data.

Abstract

Assuming that the Universe at higher redshifts (z \sim 4 and beyond) is consistent with LCDM model as constrained by the Planck measurements, we reanalyze the low redshift cosmological data to reconstruct the Hubble parameter as a function of redshift. This enables us to address the H_0 and other tensions between low z observations and high z Planck measurement from CMB. From the reconstructed H(z), we compute the energy density for the "dark energy" sector of the Universe as a function of redshift without assuming a specific model for dark energy. We find that the dark energy density has a minimum for certain redshift range and that the value of dark energy at this minimum is negative. This behavior can most simply be described by a negative cosmological constant plus an evolving dark energy component. We discuss possible theoretical and observational implications of such a scenario.

Figures (4)

• Figure 1: Low data redshift analysis without inclusion of high redshift CMB data from Planck. Left-Top: Reconstructed Hubble parameter $H(z)$ from various low-redshift data sets. The black dashed line is for best fit values whereas the inner and outer lines denote $1\sigma$ and $2\sigma$ contours. The thin shaded region is reconstructed $H(z)$ behaviour from Planck-2018 measurements. Right-Top: Comparison of our reconstructed $H(z)$ using Pade approximant and the best fit $H(z)$ for $\Lambda$CDM by Planck-2018. Bottom: Reconstructed dark energy density as a function of redshift. The horizontal line $f(z)=1$ is for $\Lambda$CDM.
• Figure 2: Reconstructed Hubble parameter $H(z)$ behavior employing both low redshift and CMB Planck data sets, see the text for details. The left one is based on Planck $H(z)$ data at $z=4,5,6$ and right one is for $z=6,7,8$. The dashed line is for mean and inner and outer regions are for $68\%$ and $95\%$ confidence regions. The thin shaded region is reconstructed $H(z)$ behaviour from Planck-2018 measurements.
• Figure 3: Reconstructed $f(z)$. The top ones for PL1 whereas the bottom ones are PL2. In each case, left ones are for $\Omega^{(0)}_{m} = 0.3$ and right ones are for $\Omega^{(0)}_{m} = 0.32$. The different regions and lines are same as in Fig.\ref{['fig:hqplot']}.
• Figure 4: Reconstructed $f(z)$. The mean $f(z)$ is plotted from the MCMC chains. The top one is without $H_{0}$ data as well as without taking Planck points for $H(z)$ for higher redshifts. The middle one is without $H_{0}$ data but taking Planck points for $H(z)$ for higher redshifts. The bottom one is taking both the $H_{0}$ data and Planck Points for $H(z)$ for higher redshifts. The rest of the low redshift data as mentioned in the text are taken in all plots. Planck points for $H(z)$ are for PL1 and $\Omega^{(0)}_{m} =0.3$ is assumed.