Using the first law of thermodynamics, we propose a relation between the system entropy ( S) and its IR ( L) and UV ([equation]) cutoffs. In addition, applying this relation to the apparent horizon...

In this paper, we study the viability and stability of anisotropic compact stars in the context of $$f({\mathcal {Q}})$$f ( Q ) theory, where $${\mathcal {Q}}$$Q is non-metricity scalar. We use Finch–Skea solutions to investigate the physical properties of compact stars. To determine the values of unknown constants, we match internal spacetime with the exterior region at the boundary surface. Furthermore, we study the various physical quantities, including effective matter variables, energy conditions and equation of state parameters inside the considered compact stars. The equilibrium and stability states of the proposed compact stars are examined through the Tolman–Oppenheimer–Volkoff equation, causality condition, Herrera cracking approach and adiabatic index, respectively. It is found that viable and stable compact stars exist in $$f({\mathcal {Q}})$$f ( Q ) theory as all the necessary conditions are satisfied.

We explore the thermodynamic analysis at the apparent horizon in the framework of Rastall theory of gravity. We take different entropies such as the Bakenstein, logarithmic corrected, power law...

The cosmic expansion phenomenon is being studied through the interaction of newly proposed dark energy models (Tsallis, Rényi and Sharma-Mittal holographic dark energy (HDE) models) with cold dark matter in the framework of loop quantum cosmology. We investigate different cosmic implications such as equation of state parameter, squared sound speed and cosmological plane (${\omega }_d$ - ${\omega }_d^{\prime }$ , ${\omega }_d$ and ${\omega }_d^{\prime }$ represent the equation of state (EoS) parameter and its evolution, respectively). It is found that EoS parameter exhibits quintom like behavior of the universe for all three models of HDE. The squared speed of sound represents the stable behavior of Rényi HDE and Sharma-Mittal HDE at the latter epoch while unstable behavior for Tsallis HDE. Moreover, ${\omega }_d$ - ${\omega }_d^{\prime }$ plane lies in the thawing region for all three HDE models.