Covariant and gauge-invariant formulation of the Sachs-Wolfe effect

We derive a formula relating the large-scale temperature anisotropy of the cosmic microwave background radiation with the cosmological perturbations responsible for them using the local covariant and gauge-invariant formalism developed by Ellis and Bruni. Comparisons of our covariant expression with previously derived Sachs-Wolfe formulas are given. Expanding our covariant variables in terms of Bardeen quantities, we derive a generalization of a result due to Panek.