Classical Variational Theory of the Cosmological Constant and Its Consistency with Quantum Prescription

• Main Authors: Claudio Cremaschini, Massimo Tessarotto
• Format: Article
• Language: English
• Published: MDPI AG 2020-04-01
• Series: Symmetry
• Subjects: general relativity; variational principles; hamilton equations; cosmological constant; quantum gravity
• Online Access: https://www.mdpi.com/2073-8994/12/4/633

The manifestly-covariant Hamiltonian structure of classical General Relativity is shown to be associated with a path-integral synchronous Hamilton variational principle for the Einstein field equations. A realization of the same variational principle in both unconstrained and constrained forms is provided. As a consequence, the cosmological constant is found to be identified with a Lagrange multiplier associated with the normalization constraint for the extremal metric tensor. In particular, it is proved that the same Lagrange multiplier identifies a 4-scalar gauge function generally dependent on an invariant proper-time parameter <i>s</i>. Such a result is shown to be consistent with the prediction of the cosmological constant based on the theory of manifestly-covariant quantum gravity.