标题： 扩展度量仿射$f(R)$引力在真空中的动态连接 显示英文标题

标题： Extended Metric-Affine $f(R)$ Gravity with Dynamical Connection in Vacuum

摘要： 我们通过补充所有与扭转和非度规性相关的偶宇称二次不变量，扩展了通常的真空度规仿射$f(R)$引力。 正如我们明确展示的那样，这种补充极大地改变了理论的状态，现在该理论在引力子之外还传播一个额外的标量自由度。 这个标量自由度具有几何起源，因为它与时空的扭转和非度规性有关。 所得的理论可以等价地写成一个无扭转的度规标量-张量理论，其势能项和动能项耦合分别取决于函数$f(R)$的选择以及二次不变量的无量纲参数。 显示英文摘要

摘要： We extend the usual vacuum Metric-Affine $f(R)$ Gravity by supplementing it with all parity even quadratic invariants in torsion and non-metricity. As we show explicitly this supplementation drastically changes the status of the Theory which now propagates an additional scalar degree of freedom on top of the graviton. This scalar degree of freedom has a geometric origin as it relates to spacetime torsion and non-metricity. The resulting Theory can be written equivalently as a metric and torsionless Scalar-Tensor Theory whose potential and kinetic term coupling depend on the choice of the function $f(R)$ and the dimensionless parameters of the quadratic invariants respectively.