Is the cosmological constant an eigenvalue?

TL;DR

This paper reinterprets Einstein's equations as a nonlinear eigenvalue problem, suggesting the cosmological constant as an eigenvalue, with implications for understanding gravity and cosmology.

Contribution

It introduces a novel eigenvalue perspective on Einstein's equations, specifically linking the cosmological constant to an eigenvalue in a nonlinear framework.

Findings

Cosmological constant as an eigenvalue in scalar gravity model

Feasibility relies on nonlinearity of classical field equations

Implications for cosmology and gravitational theory

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.