A variational analysis of Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds

Abstract

We establish new existence and non-existence results for positive solutions of the Einstein-scalar field Lichnerowicz equation on compact manifolds. This equation arises from the Hamiltonian constraint equation for the Einstein-scalar field system in general relativity. Our analysis introduces variational techniques, in the form of the mountain pass lemma, to the analysis of the Hamiltonian constraint equation, which has been previously studied by other methods.

15 pages

References in corpus (4)

• Dark Matter and Dark Energy
• Intermediate inflation and the slow-roll approximation
• Accelerated cosmological expansion due to a scalar field whose potential has a positive lower bound
• The constraint equations for the Einstein-scalar field system on compact manifolds

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• The Constraint Equations in the Presence of a Scalar Field - the Case of the Conformal Method with Volumetric Drift
• Lichnerowicz-type equations with sign-changing nonlinearities on complete manifolds with boundary
• Einstein flow with matter sources: stability and convergence
• Rotating Bowen-York initial data with a positive cosmological constant