General constraints on Tsallis holographic dark energy from observational data

We investigate Tsallis holographic dark energy (THDE) model in light of modern observations of supernovae, Hubble parameter measurements, data for baryon acoustic oscillations and fluctuations of matter density. The dark energy density for THDE model is written as ${\rho }_d=3C^2/L^{4-2\gamma }$ where $C$ and $\gamma$ are some constants. Scale $L$ is infrared cut-off length for which we use the event horizon. For analysis of type Ia supernovae (SNeIa) data Pantheon+ samples are involved. Dark Energy Spectroscopic Instrument (DESI) 2024 measurements serves as source of data about ratios between sound horizon $r_d$ and Hubble ($d_H$) or volume averaged ($d_V$) distances. The updated dataset of Hubble parameter for various redshift is also used in our analysis. Finally we consider the dependence of matter density fluctuations in past from redshift. The standard strategy of ${\chi }^2$ minimizing allows to estimate the optimal values of parameters (${\Omega }_{de}$ and $H_0$) for some fixed values of $C$ and $\gamma$. One note that best-fit values for parameters $H_0$ from Hubble parameter and SNeIa data are more close than in standard $\Lambda$CDM model for some $C$ and $\gamma$ although problem of Hubble tension remains unsolved. The combined data analysis also gives slightly better results in comparison with standard cosmology. We include in our consideration the possible interaction between matter and holographic component and estimate the acceptable interval of model parameters in this case.