论文标题
伪变异和f（t）重力的额外自由度
Pseudoinvariance and the extra degree of freedom in f(T) gravity
论文作者
论文摘要
远程平行性重力的非线性概括需要修改五局场的局部洛伦兹变换下的伪变量。因此，该程序导致局部伪创变的丧失和其他自由度的出现（D.O.F.）。 F（t）重力的约束结构表明存在一个额外的D.O.F.与GR相比，该GR应该描述四局方向的某些方面。本文的目的是更好地了解此额外的D.O.F.的性质。通过一种玩具模型，该模型模仿了F（t）重力的基本特征。我们发现，具有局部旋转伪变量的拉格朗日L的非线性修饰产生了两种类型的解决方案。在一种情况下，原始的量规不变变量 - 电触觉中的度量标准的类似物 - 像由（非形式的）拉格朗日l统治时一样演变；这些解决方案的特征是其Lagrangian的（可选）常数值，这是额外的D.O.F.的表现。在另一种情况下，解决方案确实包含针对原始量规变量的新动力学，但额外的D.O.F.没有实现，因为拉格朗日在壳上仍然不变。回到f（t）重力，第一种情况包括解决方案，其中扭转标量t是常数，在初始条件（额外的d.o.f.）中选择，并且预计该度量的新动态没有新的动力学。后一种情况涵盖了表现出真正修改重力的那些解决方案； t不是一个常数，但是在洛伦兹转换下（仅根据时间而定），它（壳上）是不变的。两种F（t）溶液在平坦的FLRW宇宙中举例说明。最后，我们提出了一个具有旋转不变性的高阶拉格朗日的玩具模型[类似于f（r）重力]，并得出了其约束结构和D.O.F.的约束结构和数量。
Nonlinear generalizations of teleparallel gravity entail the modification of a Lagrangian that is pseudoinvariant under local Lorentz transformations of the tetrad field. This procedure consequently leads to the loss of the local pseudoinvariance and the appearance of additional degrees of freedom (d.o.f.). The constraint structure of f(T) gravity suggests the existence of one extra d.o.f. when compared with GR, which should describe some aspect of the orientation of the tetrad. The purpose of this article is to better understand the nature of this extra d.o.f. by means of a toy model that mimics essential features of f(T) gravity. We find that the nonlinear modification of a Lagrangian L possessing a local rotational pseudoinvariance produces two types of solutions. In one case the original gauge-invariant variables -- the analogue of the metric in teleparallelism -- evolve like when governed by the (nondeformed) Lagrangian L; these solutions are characterized by a (selectable) constant value of its Lagrangian, which is the manifestation of the extra d.o.f. In the other case, the solutions do contain new dynamics for the original gauge-invariant variables, but the extra d.o.f. does not materialize because the Lagrangian remains invariant on-shell. Coming back to f(T) gravity, the first case includes solutions where the torsion scalar T is a constant, to be chosen at the initial conditions (extra d.o.f.), and no new dynamics for the metric is expected. The latter case covers those solutions displaying a genuine modified gravity; T is not a constant, but it is (on-shell) invariant under Lorentz transformations depending only on time. Both kinds of f(T) solutions are exemplified in a flat FLRW universe. Finally, we present a toy model for a higher-order Lagrangian with rotational invariance [analogous to f(R) gravity] and derive its constraint structure and number of d.o.f.
