Transitioning late-time cosmology with the Hubble parameterization

TL;DR

This work investigates late-time cosmology in Rastall gravity using a logarithmic H(z) parameterization $H^2(z)=H_0^2[(1+z)^3 A+B+\eta\log(1+z)]$, constrained by Planck CMB priors, DESI-BAO, and Union 3.0 SN Ia data. It compares traditional MCMC with deep-learning approaches (ANN, MDN, MNN) via the CoLFI package and finds strong agreement, with MNN yielding posteriors close to MCMC. The joint analysis gives $H_0=66.945\pm1.094$ and a transition redshift $z_t\approx0.685$, while the current deceleration parameter is $q_0\approx-0.595$ and $q\to-1$ as $z\to-1$, signaling sustained acceleration. Statefinder diagnostics yield $(r,s)\approx(0.114,0.270)$, i.e., ΛCDM–like late-time behavior with SEC violation; overall the results indicate Rastall gravity can account for late-time acceleration without dark energy, and ML methods provide efficient, reliable parameter inference.

Abstract

We investigate a late-time cosmological model for a homogeneous and isotropic space-time in the Rastall theory. We explore the observational constraints on the Hubble parameter by using the latest cosmological datasets such as cosmic microwave background radiation (Planck), baryon acoustic oscillations (DESI) and Type Ia Supernovae (Union 3.0). As a result, we explicitly demonstrate that the specific redshift transition occurs, namely, there happens a phase shift in the evolution of the universe from the initial deceleration era to the current accelerating phase of the cosmological scenario. Furthermore, we show that with the latest dataset of DESI-BAO clubbed with CC, CMB, and Union 3.0, the current value of the Hubble parameter is estimated as $H_0 = 66.945 \pm 1.094$, which can be compatible with the available observations.

Figures (11)

• Figure 1: Contour based on the model parameters with $1\sigma$ and $2\sigma$ confidence levels for CC, Pantheon, BAO, and joint datasets.
• Figure 2: Contour based on the model parameters with $1\sigma$ and $2\sigma$ confidence levels for CC, Union 3.0, CMB, DESI, and joint datasets.
• Figure 3: Observational investigation of the Rastall theory based cosmology under ANN model: (a) contours drawn from $H(z)$ data for $A$, $\eta$, and $H_{0}$$1\sigma$ and $2\sigma$, (b) relationship in between steps as well as best-fit values within $1 \sigma$ error of model parameters (where the solid black line and Grey-shaded parts display the best-fit values, while the red circle with error bars), and (c) graphical presentation of losses regarding the training and validation sets. Here, the training set consists of 2000 samples whereas the validating set contains 500 samples.
• Figure 4: Cosmological quantities in the Rastall theory under MDN model. The legends of (a), (b), and (c) are the same as Fig. 3.
• Figure 5: Cosmological quantities in the Rastall theory under MNN model. The legends of (a), (b), and (c) are the same as Fig. 3.