  We introduce a new quasi-isometry invariant, called the divergence spectrum,
to study finitely generated groups. We compare the concept of divergence
spectrum with the other classical notions of divergence and we examine the
divergence spectra of relatively hyperbolic groups. We show the existence of an
infinite collection of right-angled Coxeter groups which all have exponential
divergence but they all have different divergence spectra. We also study Morse
boundaries of relatively hyperbolic groups and examine their connection with
Bowditch boundaries.
