Cosmic microwave background temperature fluctuations and gravitational waves

Temperature fluctuations in the cosmic microwave background radiation may include an important contribution from gravitational waves (tensor metric perturbations). We show here how one can calculate analytically these fluctuations on all angular scales. In our treatment, we include the effect of the radiation-dominated period and the finite thickness of the last scattering surface. The adiabatic damping of gravitational waves inside the horizon leads to a strong decrease in amplitude at scales smaller than the size of the horizon at recombination.