The cosmological constant as an eigenvalue of the Hamiltonian constraint in a varying speed of light theory

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• 作者：Remo Garattini and Mariafelicia De Laurentis
• 刊名：Fortschritte der Physik
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：65
• 期：1
• 全文大小：264K
• ISSN：1521-3978

文摘

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 kind ion-construct="true" class="math-equation-construct">ion-image="true" class="math-equation-image">ion-mathml="true" class="math-equation-mathml" style="display:none">iley.com/namespaces/wiley" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" xmlns:cr="urn://wiley-online-library/content/render" xmlns="http://www.w3.org/1998/Math/MathML">i>Ki>i>νi>(i>xi>). 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.