论文标题
弗里德曼·莱梅特尔·罗伯逊·沃克（Friedmann Lemaitre Robertson Walker）几何的协变时间线元素
Covariant Space Time Line Elements in the Friedmann Lemaitre Robertson Walker Geometry
论文作者
论文摘要
大多数量子重力理论都按照普朗克长度（LP）的顺序量化时空。其中一些理论，例如环路量子重力（LQG），预测这种差异可以通过在天文长度距离的行进粒子上通过Lorentz的不变性（LIV）表现出来。但是，关于LIV的报告是有争议的，空间差异仍然可以与Lorentz的不变性兼容。在这里，通过应用协变量几何不确定性原理（GEUP）作为对FRW几何形状中的地理学的约束，是否可以通过应用协证的几何不确定性原理（GEUP）来与洛伦兹的不变性兼容。计算与不确定性原理兼容的时空元素是针对以Friedmann Lemaitre Robertson Walker解决通用相对论（FLRW或FRRW度量）代表的同质的各向同性扩展宇宙的计算。得出了二次适当时空元素元素的通用表达式，与普朗克长度平方成正比，并取决于两个贡献。第一个与能量时间不确定性有关，第二个取决于哈勃函数。结果与预期长度顺序的时空量化一致，根据量子重力理论，以及对假定LIV的实验限制。
Most quantum gravity theories quantize space time on the order of Planck length (lp). Some of these theories, such as loop quantum gravity (LQG), predict that this discreetness could be manifested through Lorentz invariance violations (LIV) over travelling particles at astronomical length distances. However, reports on LIV are controversial, and space discreetness could still be compatible with Lorentz invariance. Here, it is tested whether space quantization on the order of Planck length could still be compatible with Lorentz invariance through the application of a covariant geometric uncertainty principle (GeUP) as a constraint over geodesics in FRW geometries. Space time line elements compatible with the uncertainty principle are calculated for a homogeneous, isotropic expanding Universe represented by the Friedmann Lemaitre Robertson Walker solution to General Relativity (FLRW or FRW metric). A generic expression for the quadratic proper space time line element is derived, proportional to Planck length squared, and dependent on two contributions. The first is associated to the energy time uncertainty, and the second depends on the Hubble function. The results are in agreement with space-time quantization on the expected length orders, according to quantum gravity theories, and within experimental constraints on putative LIV.
