Extending the conservation of energy-momentum tensor from flat to curved spacetime is the cornerstone of general relativity (GR). This law has previously been examined in Earth labs (flat cases), thus the successes of GR propose that this law may be valid in curved spacetimes. This means that GR disabilities may also be considered as a signal for abandoning the energy-momentum conservation law (EMCL) in curved spacetimes. Therefore, a first guess is to generalize GR by leaving EMCL and relating the divergence of energy-momentum tensor to the curvature tensors such as the divergence of Ricci scalar.

Hence, an initial outcome of this way of thinking is the possibility of extracting energy (spacetime) from the fabric of spacetime (the energy-momentum source). Such modifications of GR, including a non-minimal coupling between geometry and matter fields, started with the work of P. Rastall. The unimodular theory of gravity (originally coming back to Einstein), the uncertainty principle and particle production process during the evolution of the cosmos may also reinforce the idea of leaving EMCL in curved spacetime, motivating physicists to take the non-minimal couplings more seriously. There is also an attractive ideology claiming that spacetime and gravity are emergent phenomena that arise from other laws such as the thermodynamic laws meaning that the entropy definition, indeed the statistical theory employed to model the degrees of freedom distributed on a boundary, plays a crucial role in such viewpoints. On the other hand, it has repeatedly been claimed (firstly by Gibbs (1902)) that the entropy of systems including long-range interactions should be non-extensive. If this assertion is true, then gravitational phenomena should be described by generalized entropy definitions introduced in deformed statistics which are not necessarily extensive and additive in the way that Gibbs entropy is. In fact, the non-extensivity and the non-additivity of Bekenstein entropy, obtained by considering the Gibbs entropy (Srednicki (1993)), is another motivation to use generalized entropies and deformed statistics in order to model and study the gravitational phenomena.

This Special Issue is devoted to the consequences of considering non-minimal couplings, and also employing deformed statistics and generalized entropies in describing gravity, high energy physics, and their related cosmological and astrophysical outcomes. All original research articles and also review articles that address solutions to the current challenges of these fields such as dark energy and dark matter problems, fine-tuning and cosmological coincidence puzzles, inflation physics, H0 tension, the physics of black holes, the Sun and other compact objects, structure formation and its characteristics such as Jeans criterion and Chandrasekhar limit, the nature of holographic screen and spacetime, and etc., are welcome.

Potential topics include but are not limited to the following:

• The effects of (generalized entropies) non-minimal coupling on the structure formation in various scales
• The consequences of the use of generalized statistics (non-minimal coupling) on gravitational collapse
• The role of non-minimal coupling (generalized entropies) in the evolution of the universe
• Various motivations and origins for the existence of non-minimal coupling (generalized entropies)
• The effects of (generalized entropies) non-minimal coupling on the quantum features of gravitational systems
• The astrophysical implications of the existence of non-minimal coupling (generalized entropies), such as their effects on MHD equations
• Physical and mathematical properties of compact objects in the presence of non-minimal coupling
• Various properties of black holes, wormholes, and other objects in the formalism of generalized entropies
• The implications of (generalized entropies) non-minimal coupling on the predictions of quantum field theory in curved spacetime
• The quality and properties of gravitational waves in these viewpoints
• Relation between non-commutative spacetime and i) non-minimal coupling, and ii) the statistics met by the degrees of freedom distributed on boundary