The conjecture that the essential spectrum is a half-line under a Ricci lower bound

Let $M$ be a complete noncompact Riemannian manifold with Ricci curvature bounded below. Denote by the $L^2$ essential spectrum of the Laplacian on functions the spectral set associated with the Laplace operator acting on $L^2$ functions. Essential-spectrum half-line conjecture. The $L^2$ essential spectrum of the Laplacian on functions is a connected subset of the real line. Equivalently, it has the form

$$[a,\infty),$$

where $a$ is a nonnegative real number.

The conjecture concerns whether a lower Ricci-curvature bound forces the essential spectrum to have no gaps. It is presented by the authors as the most important open problem in the direction studied by the paper, and no resolution is given here.