In the present article, models of traversable wormholes within the f (R, T ) modified gravity theory are investigated. We have presented some wormhole models, developed from various hypothesis for the substance of their matter, i.e. various relationships with their components of pressure (lateral and radial). The solutions found for the shape functions of the wormholes produced complies with the required metric conditions. The suitability of solution is examined by exploring null, strong and dominant energy conditions. It is surmised that the normal matter in the throat may pursue the energy conditions yet the gravitational field exuding from the adjusted gravity hypothesis support the appearance of the non-standard geometries of wormholes.

This paper explores the interacting Tsallis holographic dark energy (THDE) model in a non-flat universe following an infrared cutoff as the apparent horizon. The equation of state (EoS) and the deceleration parameter of THDE model are determined to understand the cosmological evolution for interacting THDE model in the non-flat universe. By applying the statefinder [Formula: see text] parameter-pairs diagnostic and [Formula: see text] pair dynamical analysis for the derived THDE model, we plot the evolutionary trajectories for different cases of Tsallis parameter [Formula: see text] and interaction term [Formula: see text] and also, for spatial curvature [Formula: see text], [Formula: see text] and [Formula: see text] corresponding to flat, open and closed universes, respectively, in the framework of Planck 2018 base cosmology results VI-LCDM observational data.

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In this work, we propose a new dark energy (DE) model by applying the Barrow entropy and the holographic principle, with a time scale as IR cut-off. Analyzing the conformal time as well as universe’s age as infrared cut-offs, we explore the cosmological importance of the suggested DE models and examine the universe evolution filled with the proposed DE applicants and a pressure-less matter. We observe that the equation of state, deceleration, the density parameters can present adequate nature, and these models may also explain the late-time acceleration though the proposed models are unstable except for some values of Barrow exponent [Formula: see text]. Furthermore, we mention the consequences of the presence of interaction among the universe sectors.

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In this research, we construct Kaniadakis holographic dark energy (KHDE) model within a nonflat Universe by considering the Friedmann–Robertson–Walker (FRW) metric with open and closed spatial geometries. The Kaniadakis entropy is indeed a one-parameter generalization of the classical Boltzmann–Gibbs–Shannon entropy which emerges from a coherent and self-consistent relativistic statistical theory. We therefore investigate cosmic evolution by employing the density parameter of the dark energy (DE), the equation-of-state (EoS) parameter and the deceleration parameter (DP). The transition from decelerated to accelerated expanding phase for the KHDE Universe is explained through dynamical behavior of DP. With the classification of matter- and DE-dominated epochs, we find that the Universe thermal history can be defined through the KHDE scenario, and moreover, a phantom regime is experienceable. The model parameters are constrained by applying the newest [Formula: see text] data cases of [Formula: see text] measurements, over the redshift span [Formula: see text], and the distance modulus measurement of the recent Union [Formula: see text] data set of type Ia supernovae. The classical stability of KHDE model has also been addressed.

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