# A Non-perturbative Hamiltonian Approach to the Cosmological Constant Problem

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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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