Entropy applications in cosmology: spacetime thermodynamics, holographic dark energy, entropic gravity and beyond - a review
Entropy has emerged as a key concept at the intersection of gravity, quantum theory, and cosmology, revealing deep connections between geometry, information, and thermodynamics. The realization that black holes are thermodynamic systems, characterized by an entropy proportional to their horizon area, has provided evidence that spacetime itself may possess a microscopic structure. Since then, entropy has acquired a central role across quantum field theory, holography, quantum gravity, and cosmology. In this review, we present a unified account of entropy in gravitational and cosmological contexts. We first survey entropy in gravitational systems, focusing on black-hole thermodynamics, entropy bounds, the holographic principle, entanglement entropy, and the area law, together with the main corrections and generalizations arising from quantum field theory, generalized uncertainty principles, modified statistics, and extended theories of gravity. We then discuss three conceptually distinct ways in which entropy is employed in cosmology. The first is through the spacetime-thermodynamics conjecture, in which gravitational dynamics emerge from thermodynamic relations applied to cosmological horizons, and generalized entropy forms consequently lead to modified cosmological evolution. The second is the holographic approach, in which entropy bounds constrain the vacuum energy of the Universe, giving rise to the holographic dark energy scenario and its various extensions. The third is entropic gravity, where gravity is interpreted as an emergent phenomenon of entropic origin, leading to interesting cosmological phenomenology. By reviewing the theoretical foundations and cosmological implications of these entropic frameworks, we aim to clarify the role of entropy, discuss open issues and outline directions toward a deeper thermodynamic and informational understanding of gravity and cosmology.