  We use recently published redshift space distortion measurements of the
cosmological growth rate, f sigma_8(z), to examine whether the linear evolution
of perturbations in the R_h=ct cosmology is consistent with the observed
development of large scale structure. We find that these observations favour
R_h=ct over the version of LCDM optimized with the joint analysis of Planck and
linear growth rate data, particularly in the redshift range 0 < z < 1, where a
significant curvature in the functional form of f sigma_8(z) predicted by the
standard model---but not by R_h=ct---is absent in the data. When LCDM is
optimized using solely the growth rate measurements, however, the two models
fit the observations equally well though, in this case, the low-redshift
measurements find a lower value for the fluctuation amplitude than is expected
in Planck LCDM. Our results strongly affirm the need for more precise
measurements of f sigma_8(z) at all redshifts, but especially at z < 1.
