Based on an analytically continued Riemannian foliated quantum gravity super-Hamiltonian, known as branch cut quantum gravity (BCQG) we propose a novel approach to investigating the effects of noncommutative geometry on a minisuperspace of variables, influencing the acceleration behavior of the Universe’s wave function and the cosmic scale factor. Noncommutativity is introduced through a deformation of the conventional Poisson algebra, enhanced with a symplectic metric. The resulting symplectic manifold provides a natural setting that enables an isomorphism between canonically conjugate dual vector spaces, spanning the BCQG cosmic scale factor and its complementary quantum counterpart. Using this formulation, we describe the dynamic evolution of the Universe’s wave function, the cosmic scale factor, and its complementary quantum image. Our results strongly suggest that the noncommutative algebra induces late-time accelerated growth of the wave function, the Universe’s scale factor, and its complementary quantum counterpart, offering a new perspective on explaining the accelerating cosmic expansion rate and the inflationary period. In contrast to the inflationary model, where inflation requires a remarkably fine-tuned set of initial conditions in a patch of the Universe, analytically continued non-commutative foliated quantum gravity captures short and long scales, driving the evolutionary dynamics of the Universe through a reconfiguration of the primordial cosmic content of matter and energy. This reconfiguration is encapsulated into a quantum field potential, which leads to the generation of relic gravitational waves, a topic for future investigation. Graphical representations and contour plots indicate a characteristic torsion (or twist) deformation of spacetime geometry. This result introduces new speculative elements regarding the reconfiguration of matter and energy as a driver of spacetime torsion deformation, generating relic gravitational waves and serving as an alternative topological mechanism for the Universe’s acceleration. However, these assumptions require further investigation.

中文翻译：

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非交换解析连续叶状量子引力中的加速宇宙


基于分析连续的黎曼叶状量子引力超哈密顿量，称为分支切割量子引力 （BCQG），我们提出了一种新的方法来研究非交换几何对变量的小超空间的影响，影响宇宙波函数和宇宙比例因子的加速行为。非交换性是通过传统泊松代数的变形引入的，并通过对称度量进行了增强。由此产生的对称流形提供了一个自然设置，可以在规范共轭双向量空间之间实现同构，跨越 BCQG 宇宙比例因子及其互补量子对应物。使用这个公式，我们描述了宇宙波函数、宇宙比例因子及其互补量子图像的动态演化。我们的结果强烈表明，非交换代数诱导了波函数、宇宙的比例因子及其互补量子对应物的后期加速增长，为解释加速的宇宙膨胀速率和膨胀期提供了新的视角。与膨胀模型相反，膨胀模型需要在宇宙的一块中进行一组非常精细的初始条件，而分析连续的非交换叶状量子引力捕获了短尺度和长尺度，通过物质和能量的原始宇宙含量的重新配置来驱动宇宙的进化动力学。这种重构被封装成量子场势，这导致了遗留引力波的产生，这是未来研究的主题。 图形表示和等值线图表示时空几何的特征性扭转（或扭曲）变形。这一结果引入了关于物质和能量的重新配置作为时空扭转变形驱动因素的新推测因素，产生遗留引力波并作为宇宙加速的替代拓扑机制。但是，这些假设需要进一步调查。