论文标题
迈向量子重力现象学的彩虹几何形状的几何解释
Towards a geometrical interpretation of rainbow geometries for quantum gravity phenomenology
论文作者
论文摘要
在文献中，有几篇论文在变形的运动学与非平地（动量依赖性）度量之间建立了对应关系。在这项工作中，我们详细研究了由哈密顿量变形的轨迹与从cotangent束中的几何形状获得的轨迹之间的轨迹之间的关系，发现当汉密尔顿在动量空间中的平方距离鉴定时，这两种轨迹都是同时发生的。此外，遵循cotangent束几何形状的自然结构，我们构建了时空曲率张量，从中我们获得了广义的爱因斯坦方程。由于在动量差异性（动量坐标的变化）下，该指标并不是不变的，我们注意到，为了保持保守的爱因斯坦张量（从同样的一般相对论中），出现了特权的动量基础，因此出现了一个全新的结果，在没有时空的情况下无法找到这种长期弯曲的情况，这使得这种长期存在的几个几个几个几个几个几个几个的态度。之后，我们在不断扩展的宇宙中考虑了地球运动和Raychaudhuri方程，并展示了如何构建爱因斯坦方程的真空解决方案。最后，我们对我们框架的现象学含义发表评论。
In the literature, there are several papers establishing a correspondence between a deformed kinematics and a nontrivial (momentum dependent) metric. In this work, we study in detail the relationship between the trajectories given by a deformed Hamiltonian and the geodesic motion obtained from a geometry in the cotangent bundle, finding that both trajectories coincide when the Hamiltonian is identified with the squared distance in momentum space. Moreover, following the natural structure of the cotangent bundle geometry, we construct the space-time curvature tensor, from which we obtain generalized Einstein equations. Since the metric is not invariant under momentum diffeomorphisms (changes of momentum coordinates) we note that, in order to have a conserved Einstein tensor (in the same sense of general relativity), a privileged momentum basis appears, a completely new result that cannot be found in absence of space-time curvature, which settles a long standing ambiguity of this geometric approach. After that, we consider in an expanding universe the geodesic motion and the Raychaudhuri's equations, and we show how to construct vacuum solutions to the Einstein equations. Finally, we make a comment about the possible phenomenological implications of our framework.
