CMB anisotropy induced by tachyonic perturbations of dark energy

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.