On the scalar sector of the covariant graviton two-point function in de Sitter spacetime

We examine the scalar sector of the covariant graviton two-point function in de Sitter spacetime. This sector consists of the pure-trace part and another part described by a scalar field. We show that it does not contribute to two-point functions of gauge-invariant quantities. We also demonstrate that the long-distance growth present in some gauges is absent in this sector for a wide range of gauge parameters.