Hamiltonian formalism for nonlocal gravity models

Nonlocal gravity models are constructed to explain the current acceleration of the universe. These models are inspired by the infrared correction appearing in Einstein–Hilbert action. Here, we develop the Hamiltonian formalism of a nonlocal model by considering only terms to quadratic order in Riemann tensor, Ricci tensor and Ricci scalar. We show how to count degrees of freedom using Hamiltonian formalism including Ricci tensor and Ricci scalar terms. In this model, we have also worked out with a choice of a nonlocal action which has only two degrees of freedom equivalent to GR. Finally, we find the existence of additional constraints in Hamiltonian required to remove the ghosts in our full action. We also compare our results with that of obtained using Lagrangian formalism.

Comparing Quantum Gravity Models: String Theory, Loop Quantum Gravity, and Entanglement Gravity versus SU(∞)-QGR

In a previous article we proposed a new model for quantum gravity (QGR) and cosmology, dubbed SU(∞)-QGR. One of the axioms of this model is that Hilbert spaces of the Universe and its subsystems represent the SU(∞) symmetry group. In this framework, the classical spacetime is interpreted as being the parameter space characterizing states of the SU(∞) representing Hilbert spaces. Using quantum uncertainty relations, it is shown that the parameter space—the spacetime—has a 3+1 dimensional Lorentzian geometry. Here, after a review of SU(∞)-QGR, including a demonstration that its classical limit is Einstein gravity, we compare it with several QGR proposals, including: string and M-theories, loop quantum gravity and related models, and QGR proposals inspired by the holographic principle and quantum entanglement. The purpose is to find their common and analogous features, even if they apparently seem to have different roles and interpretations. The hope is that this exercise provides a better understanding of gravity as a universal quantum force and clarifies the physical nature of the spacetime. We identify several common features among the studied models: the importance of 2D structures; the algebraic decomposition to tensor products; the special role of the SU(2) group in their formulation; the necessity of a quantum time as a relational observable. We discuss how these features can be considered as analogous in different models. We also show that they arise in SU(∞)-QGR without fine-tuning, additional assumptions, or restrictions.

The holographic c-theorem and infinite-dimensional Lie algebras

We discuss a non-dynamical theory of gravity in three dimensions which is based on an infinite-dimensional Lie algebra that is closely related to an infinite-dimensional extended AdS algebra. We find an intriguing connection between on the one hand higher-derivative gravity theories that are consistent with the holographic c-theorem and on the other hand truncations of this infinite-dimensional Lie algebra that violate the Lie algebra structure. We show that in three dimensions different truncations reproduce, up to terms that do not contribute to the c-theorem, Chern-Simons-like gravity models describing extended 3D massive gravity theories. Performing the same procedure with similar truncations in dimensions larger than or equal to four reproduces higher derivative gravity models that are known in the literature to be consistent with the c-theorem but do not have an obvious connection to massive gravity like in three dimensions.

Gravity Models with Nonlinear Symmetry Realization

Validity of three gravity models with non-linear realization of conformal symmetry previously discussed in literature is addressed. Two models are found to be equivalent up to a change of coset coordinates. It was found that models contain ghost degrees of freedom that may be excluded by an introduction of an additional symmetry to the target space. One model found to be safe in early universe. The others found to lack spin-2 degrees of freedom and to have peculiar coupling to matter degrees of freedom.

Investigation of the Relations Between Foreign Trade and Characteristics of Environmental Quality: Existing Approaches and Approbation of Gravity Modeli

The purpose of this study is for the author to summarize approaches and methods for assessing availability, identifying forms and types of relations between characteristics of environmental quality and international trade, and also to test the gravity theory of trade as such a method (on the example of the Republic of Belarus).The author has investigated modern economic works devoted to the study of the influence of trade liberalization on environmental pollution, the pollution haven hypothesis, the environmental Kuznets curve, the Porter hypothesis, etc., as well as the studies aimed at confirming or refuting these hypotheses, has systematized modern approaches to assessing the relations between trade and environmental indicators.Based on the panel data for the period from 1995 to 2019, the author has constructed the gravity models of trade (separately for export and import) of the Republic of Belarus with the EAEU partner countries and neighboring countries (Lithuania, Latvia, Poland, Ukraine), taking into account the environmental impact (the carbon dioxide emissions as the proxy variable of pollution). The simulation results have confirmed the theoretical provisions of the gravity theory. In addition, a significant effect of an increase in carbon dioxide emissions of countries – trade partners of the Republic of Belarus on its imports has been revealed.

Primordial big bang nucleosynthesis and generalized uncertainty principle

The Generalized Uncertainty Principle (GUP) naturally emerges in several quantum gravity models, predicting the existence of a minimal length at Planck scale. Here, we consider the quadratic GUP as a semiclassical approach to thermodynamic gravity and constrain the deformation parameter by using observational bounds from Big Bang Nucleosynthesis and primordial abundances of the light elements $${}^4 He, D, {}^7 Li$$ 4 H e , D , 7 L i . We show that our result fits with most of existing bounds on $$\beta $$ β derived from other cosmological studies.