Unimodular theory of gravity and the cosmological constant
Y. Jack Ng, H. van Dam
Source abstract
The unimodular theory of gravity with a constrained determinant gμν is equivalent to general relativity with an arbitrary cosmological constant Λ. Within this framework Λ appears as an integration constant unrelated to any parameters in the Lagrangian. In a quantum theory the state vector of the universe is thus expected to be a superposition of states with different values of Λ. Following Hawking’s argument one concludes that the fully renormalized Λ=0 completely dominates other contributions to the integral over Λ in the vacuum functional. In this scenario of the unimodular theory of gravity the cosmological constant problem is solved. Furthermore, this formulation naturally provides an external (cosmic) time for time ordering of measurements so that the quantum version of the unimodular theory can have a normal ‘‘Schrödinger’’ form of time development, giving a simpler interpretation to the equation of the universe.
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