Abstract
We consider a modification of the Brans–Dicke gravitational Action Integral inspired by the existence of a minimum length uncertainty for the scalar field. In particular, the kinetic part of the Brans–Dicke scalar field is modified such that the equation of motion for the scalar field is modified according to the quadratic Generalized Uncertainty Principle (GUP). For the background geometry, we assume the homogeneous and isotropic Friedmann–Lemaître–Robertson–Walker metric. We investigate the dynamics and the cosmological evolution of the dynamical variables of the theory, and we compare the results with the unmodified Brans–Dicke theory. It follows that in consideration because of the additional degrees of freedom in the energy-momentum tensor the dynamical variables describe various aspects of the cosmological history. This is one of the first studies on the effects of GUP in a Machian gravitational theory.
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This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This is a theoretical work, so, no observational data-sets are associated with this work.]
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Acknowledgements
This work is based on the research supported in part by the National Research Foundation of South Africa (Grant Number 131604). Additionally, the research of Genly Leon is funded by Vicerrectoría de Investigación y Desarrollo Tecnológico (Vridt) at Universidad Católica del Norte. He also thanks Vridt support through Concurso De Pasantías De Investigación Año 2022, Resolución Vridt N0040/2022 and through Resolución Vridt N 054/2022. The authors thank the support of Núcleo de Investigación Geometría Diferencial y Aplicaciones, Resolución Vridt N\(\circ \)096/2022.
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Paliathanasis, A., Leon, G. Modified Brans–Dicke cosmology with minimum length uncertainty. Gen Relativ Gravit 55, 12 (2023). https://doi.org/10.1007/s10714-022-03059-3
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DOI: https://doi.org/10.1007/s10714-022-03059-3