  Elastic models of the glass transition relate the relaxation dynamics and the
elastic properties of structural glasses. They are based on the assumption that
the relaxation dynamics occurs through activated events in the energy landscape
whose energy scale is set by the elasticity of the material. Here we
investigate whether such elastic models describe the relaxation dynamics of
systems of particles interacting via a purely repulsive harmonic potential,
focusing on a volume fraction and temperature range that is characterized by
entropy--driven water--like density anomalies. We do find clear correlations
between relaxation time and diffusivity on the one hand, and plateau shear
modulus and Debye--Waller factor on the other, thus supporting the validity of
elastic models of the glass transition. However, we also show that the plateau
shear modulus is not related to the features of the underlying energy landscape
of the system, at variance with recent results for power--law potentials. This
challenges the common potential energy landscape interpretation of elastic
models.
