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A Non-perturbative Hamiltonian Approach to the Cosmological Constant Problem

  • Syed Moeez HassanEmail author
Article
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Abstract

It was recently suggested that the cosmological constant problem as viewed in a non-perturbative framework is intimately connected to the choice of time and a physical Hamiltonian. We develop this idea further by calculating the non-perturbative vacuum energy density as a function of the cosmological constant with multiple choices of time. We also include a spatial curvature of the universe and generalize this calculation beyond cosmology at a classical level. We show that vacuum energy density depends on the choice of time, and in almost all time gauges, is a non-linear function of the cosmological constant. This non-linear relation is a calculation for the vacuum energy density given some arbitrary value of the cosmological constant. Hence, in this non-perturbative framework, certain conventional aspects of the cosmological constant problem do not arise. We also discuss why the conventional cosmological constant problem is not well-posed, and formulate and answer the question: “Does vacuum gravitate?”

Keywords

Cosmological constant problem Quantum Gravity Vacuum energy 

Notes

Acknowledgements

I am very thankful to Dr. Viqar Husain for numerous discussions, suggestions, motivation and useful comments on the manuscript without which this work would not have been possible. I also thank Masooma Ali, Dr. Jack Gegenberg, Dr. Sanjeev Seahra and Dr. Jon Ziprick for providing useful comments on various versions of the manuscript. I would also like to thank anonymous referees whose comments and questions led to significant improvements in the manuscript. I was supported by the Lewis Doctoral Fellowship.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of New BrunswickFrederictonCanada
  2. 2.Department of PhysicsSyed Babar Ali School of Science and Engineering, Lahore University of Management SciencesLahorePakistan

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