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

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.

No reviews yet.

No comments yet.