f(T) cosmology with nonzero curvature

We investigate exact and analytic solutions in [Formula: see text] gravity within the context of a Friedmann–Lemaître–Robertson–Walker background space with nonzero spatial curvature. For the power-law theory [Formula: see text] we find that the field equations admit an exact solution with a linear scalar factor for negative and positive spatial curvature. That Milne-like solution is asymptotic behavior for the scale factor near the initial singularity for the model [Formula: see text]. The analytic solution for that specific theory is presented in terms of Painlevé series for [Formula: see text]. Moreover, from the value of the resonances of the Painlevé series we conclude that the Milne-like solution is always unstable while for large values of the independent parameter, the field equations provide an expanding universe with a de Sitter expansion of a positive cosmological constant. Finally, the presence of the cosmological term [Formula: see text] in the studied [Formula: see text] model plays no role in the general behavior of the cosmological solution and the universe immerge in a de Sitter expansion either when the cosmological constant term [Formula: see text] in the [Formula: see text] model vanishes.

Deep neural networks for climate relation extraction

<p>Climate data composes of time series and space series with unknown. These unknown series contains complex co-variation relations of climate data. The extraction of these relations is essential for further revealing the complex representations between time series and space series in climate data. As an important application, through extracting these co-variation relations, we can further predict the change of climate to provide early warning for natural disasters, e.g., Greenhouse effect. Hence, it is a challenge to explore the relations between climate data. To address this, this work propose a deep neural network. Based on Brenier theorem, the loss function is derived. Since Brenier theorem rigorously proves that the data distribution in background space is consistent with the data distribution in the feature space with greatest probability, ensuring that the relations extracted from the latent space are as close to that of in background space as possible. Then, the parameters of time series consisting of eight variables are encoded by the first hidden-layer in the proposed model. The remaining two hidden-layers encode the latitude and longitude in spatial series, respectively. Experimental results show that the proposed method outperforms the state-of-the-art methods with respect to climate relations extracted. Hence, the proposed method is considered a good alternative in capturing relations between climate variables, as well as, between carbon dioxide (CO2) and surface temperature</p>

Rotating frame effects and potential on a relativistic scalar particle in Kaluza–Klein theory

The effects of uniform rotation on a relativistic scalar particle that interacts with a Cornell-type potential in background space–time described by the Kaluza–Klein theory are analyzed and the gravitational analogue of the Aharonov–Bohm effect is observed. Furthermore, linear confinement of a relativistic scalar particle was also discussed. We see a coupling between the angular velocity of the rotating frame [Formula: see text] and the angular momentum eigenvalue [Formula: see text] which shows the Sagnac-type effect.

New Anisotropic Exact Solution in Multifield Cosmology

In the case of two-scalar field cosmology, and specifically for the Chiral model, we determine an exact solution for the field equations with an anisotropic background space. The exact solution can describe anisotropic inflation with a Kantowski–Sachs geometry and can be seen as the anisotropic analogue of the hyperbolic inflation. Finally, we investigate the stability conditions for the exact solution.

Dynamics in Interacting Scalar-Torsion Cosmology

In a spatially flat Friedmann–Lemaître–Robertson–Walker background space, we consider a scalar-torsion gravitational model which has similar properties to the dilaton theory. This teleparallel model is invariant under a discrete transformation similar to the Gasperini–Veneziano duality transformation. Moreover, in the gravitational action integral, we introduce the Lagrangian function of a pressureless fluid source which is coupled to the teleparallel dilaton field. This specific gravitational theory with interaction in the dark sector of the universe was investigated by using methods of the dynamical system analysis. We calculate that the theory provides various areas of special interest for the evolution of the cosmological history. Inflationary scaling solutions and the de Sitter universe are recovered. Furthermore, we calculate that there exist an attractor which provides a stable solution where the two fluid components, the scalar field and the pressureless matter, contribute in the cosmological fluid. This solution is of special interest because it can describe the present epoch. Finally, the qualitative evolution of the cosmographic parameters is discussed.

Regularization ambiguity and van der Waals black hole in 2 + 1 dimensions

Charged black holes in a ($$2+1$$ 2 + 1 )-dimensional anti-de Sitter space-time suffer from some limitations such as the ambiguity in the definition of the mass and the bad short distance behavior. In this paper we present a way to resolve such issues. By extending the parameter space of the BTZ geometry, we properly identify the integration constants in order to remove the conical singularity sitting at the origin. In such a way we obtain a well defined Minkowski limit and horizons also in the case of de Sitter background space. On the thermodynamic side, we obtain a proper internal energy, by invoking the consistency with the Area Law, even if the mass parameter does not appear in the metric coefficients. As a further improvement, we show that it is sufficient to assume a finite size of the electric charge to obtain a short scale regular geometry. The resulting solution, generalizing the charged BTZ metric, is dual to a van der Waals gas.

The Quantum Regularization of Singular Black-Hole Solutions in Covariant Quantum Gravity

An excruciating issue that arises in mathematical, theoretical and astro-physics concerns the possibility of regularizing classical singular black hole solutions of general relativity by means of quantum theory. The problem is posed here in the context of a manifestly covariant approach to quantum gravity. Provided a non-vanishing quantum cosmological constant is present, here it is proved how a regular background space-time metric tensor can be obtained starting from a singular one. This is obtained by constructing suitable scale-transformed and conformal solutions for the metric tensor in which the conformal scale form factor is determined uniquely by the quantum Hamilton equations underlying the quantum gravitational field dynamics.

Quantum gravity for dummies

Dirac noted in his first paper on quantum electrodynamics [Proc. Roy. Soc. A 114, 243 (1927)] that, “The theory is non-relativistic only on account of the time being counted throughout as a c-number [classically], instead of being treated symmetrically with the space coordinates.” His suggestion for a relativistic theory of quantum mechanics is carried out here by describing the atom in configuration space as the action integral of a Lagrangian. Atomic structure is described with discrete coordinates in Minkowski space, while the atom itself resides in the curved space-time continuum of the gravitational field, the background space of quantum gravity. Although it does not meet the more ambitious goals of a string theory or loop quantum gravity, it is the first successful theory. In other words, it is the first theory to describe how gravitational fields interact with quanta at the microscopic level. This paper is dedicated to the thousands of theoretical physicists who have defended nonrelativistic theory since its inception in 1926 without questioning its limitations even as it lost touch with reality and became ever more difficult to believe.

Integrability and cosmological solutions in Einstein-æther-Weyl theory

We consider a Lorentz violating scalar field cosmological model given by the modified Einstein-æther theory defined in Weyl integrable geometry. The existence of exact and analytic solutions is investigated for the case of a spatially flat Friedmann–Lemaître–Robertson–Walker background space. We show that the theory admits cosmological solutions of special interests. In addition, we prove that the cosmological field equations admit the Lewis invariant as a second conservation law, which indicates the integrability of the field equations.

Vacuum expectation values in nontrivial background space from three types of UV improved Green’s functions

We evaluate the quantum expectation values in nonsimply connected spaces by using UV improved Green’s functions proposed by Padmanabhan, Abel, and Siegel. It is found that the results from these three types of Green’s functions behave similarly under changes of scales, but have minute differences. Prospects in further applications are briefly discussed.