  Radiative diffusion damps acoustic modes at large comoving wavenumber (k)
before decoupling (``Silk damping''). In a simple WKB analysis, neglecting
moments of the temperature distribution beyond the quadrupole, damping appears
in the acoustic mode as a term of order ik^2/(taudot) where taudot is the
scattering rate per unit conformal time. Although the Jeans instability is
stabilized on scales smaller than the adiabatic Jeans length, I show that the
medium is linearly unstable to first order in (1/taudot) to a slow diffusive
mode. At large comoving wavenumber, the characteristic growth rate becomes
independent of spatial scale and constant: (t_{KH}a)^-1 ~ (128 pi G/9 kappa_T
c)(rho_m/rho_b), where "a" is the scale factor, rho_m and rho_b are the matter
and baryon energy density, respectively, and kappa_T is the Thomson opacity.
This is the characteristic timescale for a fluid parcel to radiate away its
thermal energy content at the Eddington limit, analogous to the Kelvin-Helmholz
(KH) time for a massive star or the Salpeter time for black hole growth.
Although this mode grows at all times prior to decoupling and on scales smaller
than the horizon, the growth time is long, about 100 times the age of the
universe at decoupling. Thus, it modifies the density and temperature
perturbations on small scales only at the percent level. The physics of this
mode is already accounted for in the popular codes CMBFAST and CAMB, but is
typically neglected in analytic studies of the growth of primordial
perturbations. This work clarifies the physics of this instability in the epoch
before decoupling, and emphasizes that the universe is formally unstable on
scales below the horizon, even in the limit of large taudot. Analogous
instabilities at yet earlier epochs are also mentioned. (Abridged)
