Robertson-Walker几何中的最小长度宇宙
Minimum Length Universe in a Robertson Walker Geometry
AI总结：
该研究通过扩散马尔可夫场实现最小长度宇宙，推导出修正的Friedmann方程及宇宙学常数表达式，并发现减速参数q可取更高值，从而无需暗物质即可解释宇宙加速膨胀。
摘要：
一个最小长度宇宙通过扩散马尔可夫场得以实现。要求由这类场生成的时空变换下固有时泛函的不变性，为我们提供了许多添加到Christoffel联络、运动方程和Friedmann方程中的新项。在Robertson-Walker（RW）度规下，我们得到了依赖于物种的能量密度演化，现在它既是定义扩散场的参数的函数，也是RW尺度因子的函数。这些数学推导引出了时间扩散、宇宙膨胀加速度和宇宙膨胀速度之间的关系，并推导出宇宙学常数作为最小长度和Higgs机制的标量场期望值的函数。该理论为我们提供了一种将Hubble参数与其扩散的最小长度'等效'联系起来的方法，以及一种用减速参数q表示有效状态方程的方法。我们发现，在不引入暗物质物种的情况下，q可以取一系列更高的值，并且宇宙根据q的值处于真空主导或物质主导的时期。
英文摘要：
A minimum length universe is enforced via a diffusive Markovian field. Requiring the invariance of the proper time functional under spacetime transformations generated by such fields provides us with many new terms added to the Christoffel Connection, Equations of Motion, and Friedmann Equation. Under the Robertson-Walker (RW) metric, we obtain species-specific energy-density evolution, now a function of both the parameters defining the diffusive fields as well as the RW scale factor. The math leads us to a relationship between temporal diffusion, universe expansion acceleration, and the speed of universe expansion, along with a derivation of the cosmological constant as a function of both minimum length and the scalar field expectation value of the Higgs mechanism. The theory gives us a means of relating the Hubble parameter to its diffusive ML 'equivalent', and a means to express the effective equation of state in terms of the deceleration parameter, q. We find that q can take on a range of higher values without invoking the need for a dark matter species, and that the universe inhabits a vacuum or matter dominated regime as a function of q.
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