  First principles linear response calculations are used to investigate the
lattice dynamics of what is thought to be the third most abundant phase in the
lower mantle, CaSiO_3 perovskite. The commonly assumed cubic structure (Pm3m)
is found to be dynamically unstable at all pressures, exhibiting unstable modes
along the Brillouin zone edge from the M-point to the R-point. Based on these
results, we predict that the ground state structure of CaSiO_3 perovskite is a
distorted phase with lower than cubic symmetry. We predict that a phase
transition occurs in CaSiO_3 perovskite within the earth's lower mantle from
the low temperature distorted phase to the cubic phase at high temperature. The
predicted phase transition provides a possible explanation of some of the
seismological observations of reflective features within the lower mantle.
