Quantum Entanglement of Fermions- Antifermions Pair Creation modes in Non-commutative Bianchi I Space-time

Bianchi type I cyclic cosmology from Lie-algebraically deformed phase space

We study the effects of noncommutativity, in the form of a Lie-algebraically deformed Poisson commutation relations, on the evolution of a Bianchi type I cosmological model with a positive cosmological constant. The phase space variables turn out to correspond to the scale factors of this model in $x$, $y$ and $z$ directions. According to the conditions that the structure constants (deformation parameters) should satisfy, we argue that there are two types of noncommutative phase space with Lie-algebraic structure. The exact classical solutions in commutative and type I noncommutative cases are…

Generalized uncertainty principle in Bianchi type I quantum cosmology

We study a quantum Bianchi type I model in which the dynamical variables of the corresponding minisuperspace obey the generalized Heisenberg algebra. Such a generalized uncertainty principle has its origin in the existence of a minimal length suggested by quantum gravity and sting theory. We present approximate analytical solutions to the corresponding Wheeler-DeWitt equation in the limit where the scale factor of the universe is small and compare the results with the standard commutative and noncommutative quantum cosmology. Similarities and differences of these solutions are also discussed.

非交换广义不确定性原理框架下的 Mixmaster 宇宙动力学

Dynamics of the Mixmaster Universe in a non-commutative Generalized Uncertainty Principle framework

本文在非交换广义不确定性原理框架下研究Mixmaster宇宙动力学，通过引入形变Poisson括号推导BKL映射，发现非交换GUP方案将标准BKL映射的混沌遍历行为转化为准周期轨道，使宇宙尺度因子呈现依赖初始条件的振荡行为。

Poisson-Lie plurals of Bianchi cosmologies and Generalized Supergravity Equations

Poisson-Lie T-duality and plurality are important solution generating techniques in string theory and (generalized) supergravity. Since duality/plurality does not preserve conformal invariance, the usual beta function equations are replaced by Generalized Supergravity Equations containing vector $\mathcal{J}$. In this paper we apply Poisson-Lie T-plurality on Bianchi cosmologies. We present a formula for the vector $\mathcal{J}$ as well as transformation rule for dilaton, and show that plural backgrounds together with this dilaton and $\mathcal{J}$ satisfy the Generalized Supergravity Equation…

A Twisted ${\mathcal C}^{\star}$-algebra formulation of Quantum Cosmology with application to the Bianchi I model

A twisted ${\mathcal C}^\star $- algebra of the extended (noncommutative) Heisenberg-Weyl group has been constructed which takes into account the Uncertainty Principle for coordinates in the Planck length regime. This general construction is then used to generate an appropriate Hilbert space and observables for the noncommutative theory which, when applied to the Bianchi I Cosmology, leads to a new set of equations that describe the quantum evolution of the universe. We find that this formulation matches theories based on a reticular Heisenberg-Weyl algebra in the bouncing and expanding region…

Bianchi II and VII$_{h=0}$ Models Revisited Via The Euclidean-Signature Semi Classical Method

We apply in a novel fashion a modified semi-classical method to the Bianchi II and VII$_{h=0}$ models when a cosmological constant, aligned electromagnetic field and stiff matter are present. Additionally we study the non-commutative quantum Bianchi II models when an aligned electromagnetic field is included. Through the use of the Euclidean-signature semi classical method we find a plethora of new solutions to these model's corresponding Lorentzian signature Wheeler DeWitt equations which we can interpret qualitatively. These new solutions for the aforementioned models involving matter source…

广义相对论修正理论研究：微分几何方法

The Study on Modified Theories of General Relativity: A Differential Geometric Approach

本文基于微分几何方法系统研究多种修正引力理论，涵盖f(Q)、f(R, L_m)、f(Q, T)和f(T)等模型，通过参数化、MCMC约束、宇宙学分析及虫洞解等手段，探讨暗能量、暗物质等问题的替代理论方案。