Search Results (12)

This article presents a novel mathematical formalism for advanced manifold–metric pairs, enhancing the frameworks of geometry and topology. We construct various D-dimensional manifolds and their associated metric spaces using functional methods, with a focus on integrating concepts from mathematical physics, field theory, topology, algebra, probability, and statistics. Our methodology employs rigorous mathematical construction proofs and logical foundations to develop generalized manifold–metric pairs, including homogeneous and isotropic expanding manifolds, as well as probabilistic and entropic variants. Key results include the establishment of metrizability for topological manifolds via the Urysohn Metrization Theorem, the formulation of higher-rank tensor metrics, and the exploration of complex and quaternionic codomains with applications to cosmological models like the expanding spacetime. By combining spacetime generalized sets with information-theoretic and probabilistic approaches, we achieve a unified framework that advances the understanding of manifold–metric interactions and their physical implications. Full article

In previous works, entropic gravity and ungravity have been considered as possible solutions to the dark energy and dark matter problems. To test the viability of these models, modifications to planetary orbits are calculated for ungravity and different models of entropic gravity. Using the gravitational sector of unparticles, an equation for the contribution to the effect of orbital precession is obtained. We conclude that the estimated values for the ungravity parameters from planetary orbits are inconsistent with the values needed for the cosmological constant. The same ideas are explored for entropic gravity arising from a modified entropy–area relationship. Full article

We provide a short review of the recent developments in entropic cosmology based on two thermodynamic laws of the apparent horizon, namely the first and the second laws of thermodynamics. The first law essentially provides the change in entropy of the apparent horizon during the cosmic evolution of the universe; in particular, it is expressed by $TdS=-d\left(\rho V\right)+WdV$ (where W is the work density and other quantities have their usual meanings). In this way, the first law actually links various theories of gravity with the entropy of the apparent horizon. This leads to a natural question—“What is the form of the horizon entropy corresponding to a general modified theory of gravity?”. The second law of horizon thermodynamics states that the change in total entropy (the sum of horizon entropy + matter fields’ entropy) with respect to cosmic time must be positive, where the matter fields behave like an open system characterised by a non-zero chemical potential. The second law of horizon thermodynamics importantly provides model-independent constraints on entropic parameters. Finally, we discuss the standpoint of entropic cosmology on inflation (or bounce), reheating and primordial gravitational waves from the perspective of a generalised entropy function. Full article

We explicitly calculate the value of the cosmological constant, $\mathsf{\Lambda }$, based on the recently developed theory connecting entropic gravity with quantum events induced by transactions, called transactional gravity. We suggest a novel interpretation of the cosmological constant and rigorously show its inverse proportionality to the squared radius of the causal universe $\mathsf{\Lambda }~R_U^{-2}$. Full article

In spirit of the recently proposed four-parameter generalized entropy of apparent horizon, we investigate inflationary cosmology where the matter field inside of the horizon is dominated by a scalar field with a power law potential (i.e., the form of ${\varphi }^n$ where $\varphi$ is the scalar field under consideration). Actually without any matter inside of the horizon, the entropic cosmology leads to a de-Sitter spacetime, or equivalently, an eternal inflation with no exit. Thus in order to achieve a viable inflation, we consider a minimally coupled scalar field inside the horizon, and moreover, with the simplest quadratic potential. It is well known that the ${\varphi }^2$ potential in standard scalar field cosmology is ruled out from inflationary perspective as it is not consistent with the recent Planck 2018 data; (here it may be mentioned that in the realm of “apparent horizon thermodynamics”, the standard scalar field cosmology is analogous to the case where the entropy of the apparent horizon is given by the Bekenstein–Hawking entropy). However, the story becomes different if the horizon entropy is of generalized entropic form, in which case, the effective energy density coming from the horizon entropy plays a significant role during the evolution of the universe. In particular, it turns out that in the context of generalized entropic cosmology, the ${\varphi }^2$ potential indeed leads to a viable inflation (according to the Planck data) with a graceful exit, and thus the potential can be made back in the scene. Full article

By employing Tsallis’ extensive but non-additive $\delta$-entropy, we formulate the first two laws of thermodynamics for gravitating systems. By invoking Carathéodory’s principle, we pay particular attention to the integrating factor for the heat one-form. We show that the latter factorizes into the product of thermal and entropic parts, where the entropic part cannot be reduced to a constant, as is the case in conventional thermodynamics, due to the non-additive nature of $S_{\delta }$. The ensuing two laws of thermodynamics imply a Tsallis cosmology, which is then applied to a radiation-dominated universe to address the Big Bang nucleosynthesis and the relic abundance of cold dark matter particles. It is demonstrated that the Tsallis cosmology with the scaling exponent $\delta$∼1.499 (or equivalently, the anomalous dimension $\Delta$∼0.0013) consistently describes both the abundance of cold dark matter particles and the formation of primordial light elements, such as deuterium ${}^{2}H$ and helium ${}^{4}He$. Salient issues, including the zeroth law of thermodynamics for the $\delta$-entropy and the lithium ${}^{7}Li$ problem, are also briefly discussed. Full article

Kaniadakis statistics is a widespread paradigm to describe complex systems in the relativistic realm. Recently, gravitational and cosmological scenarios based on Kaniadakis ($\kappa$-deformed) entropy have been considered, leading to generalized models that predict a richer phenomenology comparing to their standard Maxwell–Boltzmann counterparts. The purpose of the present effort is to explore recent advances and future challenges of Gravity and Cosmology in Kaniadakis statistics. More specifically, the first part of the work contains a review of $\kappa$-entropy implications on Holographic Dark Energy, Entropic Gravity, Black hole thermodynamics and Loop Quantum Gravity, among others. In the second part, we focus on the study of Big Bang Nucleosynthesis in Kaniadakis Cosmology. By demanding consistency between theoretical predictions of our model and observational measurements of freeze-out temperature fluctuations and primordial abundances of ${}^{4}He$ and D, we constrain the free $\kappa$-parameter, discussing to what extent the Kaniadakis framework can provide a successful description of the observed Universe. Full article

The spacetime is basically curved and dynamical. Thus our knowledge of universe must be extended to a dynamical curved spacetime to understand the nature of the universe. The field theory in the curved spacetime has shown that the evolution of spacetime involving the field in the curved spacetime leads to particle creation. From another perspective, by employing thermodynamics to cosmology, we can learn about the source of current entropy content associated with the universe. From the quantum thermodynamics, it is clear that the inner friction stemming from the quantum fluctuations of the field can produce the entropy. Using this approach, the particle creation due to the expansion of spacetime beginning from the vacuum is shown as an entropic increase. Considering an asymptotically flat Robertson-Walker spacetime, the particle creation entropy is evaluated. Each special scale factor can be used to characterize the cosmic parameters. Thus, the dependence of particle creation entropy on the field parameters and the cosmic parameters allows us to recover information from the underlying structure of the spacetime. Also, by adding an entropy production, indicating the mutual information between created particle and spacetime, to this particle creation entropy, the well-known entanglement measure can obtained to investigate the entanglement of created particles. In fact, the entanglement entropy, measuring the mixedness of the primary state, is affected from the creation and the correlation of the particle. Full article

We derive the thermodynamic products, in particular the area (or entropy) products of ${\mathcal{H}}^{\pm }$ for a wide variety of black holes (BHs) in anti-de Sitter (AdS) space. We show by explicit and exact calculations that, for this class of BHs, more complicated functions of the event horizon area and Cauchy horizon area are indeed mass-independent. This mass-independent results indicate that they could turn out to be a “universal” quantity provided that they depend only on the quantized angular momentum, quantized charges, and cosmological constant, etc. Furthermore, these area (or entropy) product relations for several classes of BHs in AdS space gives us strong indication to understanding the nature of non-extremal BH entropy (both inner and outer) at the microscopic level. Moreover, we compute the famous Cosmic Censorship Inequality (which requires Cosmic-Censorship hypothesis) for these classes of BHs in AdS space. Local thermodynamic stability has been discussed for these BHs and under certain conditions, these classes of BHs displayed second order phase transition. The super-entropic BH does not provide any kind of second order phase transition. Full article

We formulate the basic framework of thermodynamical entropic force cosmology which allows variation of the gravitational constant G and the speed of light c. Three different approaches to the formulation of the field equations are presented. Some cosmological solutions for each framework are given and one of them is tested against combined observational data (supernovae, BAO, and CMB). From the fit of the data, it is found that the Hawking temperature numerical coefficient γ is two to four orders of magnitude less than usually assumed on the geometrical ground theoretical value of O(1) and that it is also compatible with zero. In addition, in the entropic scenario, we observationally test that the fit of the data is allowed for the speed of light c growing and the gravitational constant G diminishing during the evolution of the universe. We also obtain a bound on the variation of c to be Δc / c ∝ 10^-5 > 0 , which is at least one order of magnitude weaker than the quasar spectra observational bound. Full article

We performed an in depth analysis of the subjects of entropy and the second law of thermodynamics and how they are treated in astrophysical systems. These subjects are retraced historically from the early works on thermodynamics to the modern statistical mechanical approach and analyzed in view of specific practices within the field of astrophysics. As often happens in discussions regarding cosmology, the implications of this analysis range from physics to philosophy of science. We argue that the difficult question regarding entropy and the second law in the scope of cosmology is a consequence of the dominating paradigm. We further demonstrate this point by assuming an alternative paradigm, not related to thermodynamics of horizons, and successfully describing entropic behavior of astrophysical systems. Full article

The dark energy problem is studied based on the approach associated with the cosmological term in General Relativity that is considered as a dynamic quantity. It is shown that a quantum field theory of the Early Universe (Planck scales) and its limiting transition at low energy play a significant role. Connection of this problem with Verlinde’s new (entropic) approach to gravity is revealed within the frame of such statement as well as the Generalized Uncertainty Principle (GUP) and Extended Uncertainty Principle (EUP). The implications from the obtained results are presented, and a more rigorous statement of the Concordance Problem in cosmology is treated. Full article