  We study effects of possible tachyonic perturbations of dark energy on the
CMB temperature anisotropy. Motivated by some models of phantom energy, we
consider both Lorentz-invariant and Lorentz-violating dispersion relations for
tachyonic perturbations. We show that in the Lorentz-violating case, the shape
of the CMB anisotropy spectrum generated by the tachyonic perturbations is very
different from that due to adiabatic scalar perturbations and, if sizeable, it
would be straightforwardly distinguished from the latter. The tachyonic
contribution improves slightly the agreement between the theory and data;
however, this improvement is not statistically significant, so our analysis
results in limits on the time scale of the tachyonic instability. In the
Lorentz-invariant case, tachyonic contribution is a rapidly decaying function
of the multipole number $l$, so that the entire observed dipole can be
generated without conflicting the data at higher multipoles. On the
conservative side, our comparison with the data places limit on the absolute
value of the (imaginary) tachyon mass in the Lorentz-invariant case.
