论文标题
在FLRW时空的宇宙常数上
On the cosmological constant of flat FLRW spacetime
论文作者
论文摘要
我们考虑一个呈指数型扩展，平坦的，弗里德曼·莱米特尔 - 罗伯逊 - 沃克（FLRW）宇宙，里面充满了自由的施罗丁格领域。后者的概率流体用于模仿宇宙流体（Baryonic Plus暗物质），因此提供了相应的Friedmann-Lemaitre方程中的物质密度和压力项。我们首先在平坦的FLRW空间上获得Laplacian操作员的本征函数。将作为宇宙常数的量子运算符定义为在施罗辛格字段上起作用。然后，我们计算在拉普拉斯征征基础上代表宇宙常数的矩阵。为了估算所涉及的数量级，足以确定该操作员的期望值。最适合宇宙常数实验测量值的期望值使我们能够确定最能代表当前宇宙的物质内容（Baryonic和Dark）的Schroedinger场的量子状态。最后，代表宇宙常数的操作员逆（Modulo尺寸因子）提供了对宇宙的重力玻璃体熵的度量。我们根据拉普拉斯（Laplacian）特征函数计算其矩阵，并验证该熵操作员的期望值是否符合全息原理的上限集。
We consider an exponentially expanding, flat, Friedmann-Lemaitre-Robertson-Walker (FLRW) Universe filled with a free Schroedinger field. The probability fluid of the latter is used to mimic the cosmological fluid (baryonic plus dark matter), thus providing the matter density and pressure terms in the corresponding Friedmann-Lemaitre equations. We first obtain the eigenfunctions of the Laplacian operator on flat FLRW space. A quantum operator qualifying as a cosmological constant is defined to act on the Schroedinger field. We then compute the matrix representing the cosmological constant in the basis of Laplacian eigenfunctions. For an estimate of the orders of magnitude involved it suffices to determine the expectation values of this operator. The expectation value that best fits the experimentally measured value of the cosmological constant allows us to identify the quantum state of the Schroedinger field that best represents the matter contents (baryonic and dark) of the current Universe. Finally, the operator inverse (modulo dimensional factors) to the one representing the cosmological constant provides a measure of the gravitational Boltzmann entropy of the Universe. We compute its matrix in the basis of Laplacian eigenfunctions and verify that the expectation values of this entropy operator comply with the upper bound set by the holographic principle.
