An analytic approach to the late ISW effect in a Lambda dominated   universe
  The integrated Sachs-Wolfe (ISW) effect in a Lambda 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 C_l momenta and show the agreement of our results with earlier, numeric calculations. 
Viktor Czinner, M\'aty\'as Vas\'uth and \'Arp\'ad Luk\'acs