Is the cosmological constant an eigenvalue?

Abstract

We propose to reinterpret Einstein's field equations as a nonlinear eigenvalue problem, where the cosmological constant $\Lambda$ plays the role of the (smallest) eigenvalue. This interpretation is fully worked out for a simple model of scalar gravity. The essential ingredient for the feasibility of this approach is that the classical field equations be nonlinear, i.e., that the gravitational field is itself a source of gravity. The cosmological consequences and implications of this approach are developed and discussed.

References in corpus (22)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Cosmological Imprint of an Energy Component with General Equation of State
• The Cosmological Constant
• Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions
• The stability for the Cauchy problem for elliptic equations
• The R_h = ct Universe
• The Cosmic Horizon
• Marginal evidence for cosmic acceleration from Type Ia supernovae
• Introducing the Dirac-Milne universe
• N-body methods for relativistic cosmology
• The cosmological constant as an eigenvalue of f(R)-gravity Hamiltonian constraint
• On Recent Claims Concerning the R_h=ct Universe
• Cosmological structure formation with negative mass
• On the nature of dark energy: the lattice Universe
• The Consistent Newtonian Limit of Einstein's Gravity with a Cosmological Constant
• Gravity, antimatter and the Dirac-Milne universe
• Gravity and the spin-2 planar Schroedinger equation
• Consistently Implementing the Fields Self-Energy in Newtonian Gravity
• The cosmological constant as an eigenvalue of the Hamiltonian constraint in Horava-Lifshits theory
• Self-Consistent, Self-Coupled Scalar Gravity
• Structure formation in a Dirac-Milne universe: comparison with the standard cosmological model