# ISW effect

The ISW e ect is caused by the change in energy of CMB photons as they traverse the linear changing of gravitational potentials (Cai et al., 2009) (Cai et al., 2010). If gravitational potential nonlinearly evolves then the ISW e ect becomes nonlinear e ect which has alternative name as the Ree-Sciama (RS) e ect. When CMB photons travel through an over dense region, such as galaxy cluster, will gain more energy falling into the potential well than it later loses climbing out of the evolved shallower potential well. Consequently, overdense regions correspond to hot regions in a linear ISW map. In contrast, as voids are underdense regions they appear cold in linear ISW map. If the geometry of the universe is spatially at as described by FLRW metric tensor then the ISW e ect only occurs if and only if dark energy exist. So, the ISW effect is a suitable tool to study dark energy dynamics.

Fig 5. Appearance of ISW e ect on CMB map which is observed by Planck. Left panel shows the result from stacking of 50 supercluster, the middle is the results from stacking of 50 voids and right panel shows the di erence between both result. It is clearly that the ISW e ects due to the cluster appear hot in CMB map while voids give the cold region. The picture is taken from Planck Collaboration et al. (2014).