论文标题
宇宙常数作为边界术语
The cosmological constant as a boundary term
论文作者
论文摘要
我们比较了在非模块性重力和一般相对论中过渡功能的路径积分。在单模型的重力中，宇宙常数是在边界处指定的状态的特性，而在一般相对论中，宇宙常数是动作的参数。具有非动力背景时空体积元件的单模型重力具有一个时间变量，该变量在规范上与宇宙常数共轭。波函数取决于时间并满足schrödinger方程。相反，在Henneaux和Teitelboim提出的具有3型量规场的单模型重力的协变版本中，波函数是时间独立的，并且满足了Wheeler-Dewitt方程，就像一般相对论一样。仅在半经典近似中，在超空曲面上集成的3型仪表场才成为“宇宙时间”。在单模型的重力中，观察到的宇宙常数的较小必须被解释为初始状态的特性。
We compare the path integral for transition functions in unimodular gravity and in general relativity. In unimodular gravity the cosmological constant is a property of states that are specified at the boundaries whereas in general relativity the cosmological constant is a parameter of the action. Unimodular gravity with a nondynamical background spacetime volume element has a time variable that is canonically conjugate to the cosmological constant. Wave functions depend on time and satisfy a Schrödinger equation. On the contrary, in the covariant version of unimodular gravity with a 3-form gauge field, proposed by Henneaux and Teitelboim, wave functions are time independent and satisfy a Wheeler-DeWitt equation, as in general relativity. The 3-form gauge field integrated over spacelike hypersurfaces becomes a "cosmic time" only in the semiclassical approximation. In unimodular gravity the smallness of the observed cosmological constant has to be explained as a property of the initial state.
