arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1503.03677gr-qchep-th
收藏

变光速理论中作为哈密顿约束本征值的宇宙学常数

The Cosmological Constant as an Eigenvalue of the Hamiltonian constraint in a Varying Speed of Light theory

Remo Garattini, Mariafelicia De Laurentis

摘要:

在光速变化理论的框架下,我们研究了Wheeler-DeWitt方程的本征值,它代表了与宇宙学常数有关的真空期望值。我们发现,在本征值和宇宙学常数确定的条件下,Friedmann-Lema\^itre-Robertson-Walker度规的Wheeler-DeWitt方程完全等价于Sturm-Liouville问题.显式计算的帮助下进行的变分过程与试探波泛函有关的第二类贝塞尔函数$K_{ν}\left( x\right) $。我们发现存在一个家庭的特征值相关联的规模的负功率。此外,我们表明,在通货膨胀的规模,这样的家庭的特征值不会出现。

英文摘要:

In the framework of a Varying Speed of Light theory, we study the eigenvalues associated with the Wheeler-DeWitt equation representing the vacuum expectation values associated with the cosmological constant. We find that the Wheeler-DeWitt equation for the Friedmann-Lema\^ıtre-Robertson-Walker metric is completely equivalent to a Sturm-Liouville problem provided that the related eigenvalue and the cosmological constant be identified. The explicit calculation is performed with the help of a variational procedure with trial wave functionals related to the Bessel function of the second kind $K_{ν}\left( x\right) $. We find the existence of a family of eigenvalues associated to a negative power of the scale. Furthermore, we show that at the inflationary scale such a family of eigenvalues does not appear.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑