Exact Solutions to Einstein’s Field Equations, (Cambridge
- H. Stephani, D. Kramer, M.A.H. MacCallum, C. Hoenselaers, E. Herlt
The integrated Sachs-Wolfe (ISW) effect in a Λ dominated universe can be an important factor in the evolution of cosmic microwave background fluctuations. With the inclusion of cosmological constant we present the complete analytic solution of the covariant linear perturbations of the Einstein equations in the Newtonian gauge, in the case of a spatially flat (K = 0), Friedman-Robertson-Walker (FRW) universe, filled with pressureless ideal fluid. We use the analytic time dependence of the perturbation potentials to derive the anisotropy power spectrum of the late ISW effect. We choose the scale invariant Harrison-Zeldovich spectrum for obtaining the Cl momenta and show the agreement of our results with earlier, numeric calculations.