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The cosmological constant as an eigenvalue of the Hamiltonian constraint in a varying speed of light theory
Author(s) -
Garattini Remo,
Laurentis Mariafelicia
Publication year - 2017
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.201600108
Subject(s) - cosmological constant , eigenvalues and eigenvectors , physics , constant (computer programming) , mathematical physics , hamiltonian (control theory) , constraint (computer aided design) , classical mechanics , mathematics , quantum mechanics , geometry , mathematical optimization , computer science , programming language
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‐Lemaître‐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 kindK ν ( x ) . After having verified that in ordinary General Relativity no eigenvalue appears, we find that in a Varying Speed of Light theory this is not the case. Nevertheless, instead of a single eigenvalue, we discover the existence of a family of eigenvalues associated to a negative power of the scale. A brief comment on what happens at the inflationary scale is also included.