Method to Incorporate Black Hole Effects on the Power Spectrum in 3+1 Schwarzschild-de Sitter Spacetime

The presence of primordial black holes during the inflationary epoch could introduce deviations from the standard power spectrum, which might lead to observable signatures in the cosmic microwave background. A method to compute the power spectrum in Schwarzschild-de Sitter spacetime is given. This spacetime is an exact solution to the vacuum Einstein equations in the presence of a positive cosmological constant consisting of an eternal black hole immersed in an exponentially expanding universe. As usual, the power spectrum is computed using a massless minimally coupled scalar field. In order to incorporate black hole evaporation effects, the Unruh state is considered.