Abstract
It has been around fifty years since R. K. Sachs and A. M. Wolfe predicted the existence of anisotropy in the Cosmic Microwave Background (CMB) and ten years since the integrated Sachs Wolfe effect (ISW) was first detected observationally. The ISW effect provides us with a unique probe of the accelerating expansion of the Universe. The cross-correlation between the large-scale structure and CMB has been the most promising way to extract the ISW effect from the data. In this article, we review the physics of the ISW effect and summarize recent observational results and interpretations.
Highlights
Theory of the ISW effect In the Standard CosmologyWe derive the basic equations of the ISW effect based on the original paper [116]
Because the large r value constrained by the B-mode power spectrum, ClBB of the BICEP2 enhances the amplitude of the temperature fluctuation, ClTT on large scales, it is required to make some modifications of the model to keep the current observational constraints from the WMAP or the Planck unchanged: either the smaller value of running of scalar spectral index αs [8] or isocurvature component of the initial fluctuation is required [67] to suppress the large scale power of the Cosmic Microwave Background (CMB) temperature power spectrum
It is well known that the Sachs-Wolfe effect and the ISW effect are simultaneously derived from the cosmological perturbation theory
Summary
We derive the basic equations of the ISW effect based on the original paper [116]. We first write the line element in a spatially flat FRW metric, ds2 = gμν dxμdxν = a2(τ )gμν dxμdxν ,. Where a is the scale factor that depends solely on the conformal time τ and gμν and gμν are the metric and a conformally transformed metric, respectively. The metric perturbation can be decomposed into scalar, vector and tensor modes. H0i can be divided into the contributions from scalar and vector while hij can be divided into the contributions from scalar, vector, and tensor modes as, h00 = −2A(s). Where A, B, C and D are arbitrary functions and superscript with the parenthesis (s), (v) and (t) stand for the scalar, vector and tensor quantities respectively.
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