Observational constraints on New Tsallis holographic energy in Rastall theory

TL;DR

This work tests New Tsallis holographic dark energy (NTHDE) within Rastall gravity against current background cosmology data. By solving the modified Friedmann equations with the Rastall parameter $\gamma$ and the non-extensive deformation parameter $\delta$, and using the NTHDE energy density on the apparent horizon, the authors perform a Markov Chain Monte Carlo analysis with DESI DR2 BAO, PantheonPlus SNe Ia, $H(z)$ measurements, and a BBN prior on $\omega_b$. They find best-fit values $\delta \approx 1.52$ and $\gamma \approx 0.1018$, with $\Omega_D$ capable of mimicking the ΛCDM dark-energy density today, though Bayesian evidence and AIC mildly favor ΛCDM. The NTHDE in Rastall gravity provides a viable alternative at the background level, reproducing the expansion history while predicting measurable deviations in $H(z)$ and the evolution of $\Omega_m(z)$ and $\Omega_D(z)$ at intermediate redshifts, offering testable signatures for upcoming surveys.

Abstract

The cosmological implications of New Tsallis holographic dark energy (NTHDE) in Rastall theory have been studied. Using the data set that includes DESI BAO (DR2), PantheonPlus SNe Ia, H(z) measurements, and BBN and the MCMC analysis, the key cosmological and model-specific parameters are constrained. The result is compared with that of the ΛCDM model indicating that in addition to providing a viable dynamical dark energy framework, predictions for H(z) are slightly more consistent with intermediate-redshift observations. Generally, the model remains compatible with current data and offers testable deviations from ΛCDM for upcoming surveys. It is also seen that when the energy density of quantum fields in vacuum, exposed by NTHDE, is combined with the Rastall correction term to the general relativity, a plausible candidate for dynamical dark energy is obtained that mimic the current value of the dark energy density parameter reported in the ΛCDM model. The latter cannot be repeated by NTHDE alone. The study also confirms previous theoretical and observational constraints on the Rastall parameter obtained by focusing on the thermodynamics, early universe, pulsars, and the early-type galaxies.

Figures (6)

• Figure 1: Corner plot showing the marginalized posterior distributions and two-dimensional confidence contours ($68\%$ and $95\%$ CL) for the main cosmological parameters of the NTHDE model, obtained from the combined dataset (SN Ia+Cepheid, $H(z)$, DESI BAO, and BBN).
• Figure 2: Corner plot showing the marginalized posterior distributions and two-dimensional confidence contours ($68\%$ and $95\%$ CL) for the main cosmological parameters of the NTHDE and $\Lambda$CDM models, obtained from the combined dataset (SN Ia+Cepheid, $H(z)$, DESI BAO, and BBN).
• Figure 3: Hubble parameter $H(z)$ as a function of redshift for the NTHDE (solid line) and $\Lambda$CDM (dashed line) models, compared with observational data points.
• Figure 4: Deceleration parameter $q(z)$ for NTHDE and $\Lambda$CDM models as a function of redshift.
• Figure 5: Matter and dark energy density parameters as functions of redshift for NTHDE (solid lines) and $\Lambda$CDM (dashed lines).