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The late-time integrated Sachs Wolfe effect

This version was saved 15 years, 7 months ago View current version     Page history
Saved by Anais Rassat
on August 27, 2008 at 2:51:01 pm
 

 

 

Outline 

 


 


 


 

Introduction

 

The Integrated Sachs-Wolfe (ISW) effect is due to the decays of graviational potential wells.  It can be split into two parts: the early ISW and the late-time ISW effects.   This page focusses on the latter.

 

While the early ISW effect occurs shortly after fecombination during the radiation era, the late-time ISW effect occurs much later, and is due to the gravitational potentials of Large Scale Structure (LSS).  It can also be a result of the potential of Dark Energy if one considers it is a fluid with perturbations.

 

The Origin of the late-time ISW effect

 

The gravitational potential of the LSS will distort space-time so that a photon travelling through it will be subject to a graviational blueshift on entry of the potential well, and redshift on exit. If the potential does not change during the travel time of the photon, then the net effect of the gravitational redshift will be null: the photon will emerge unaffected by LSS. This is always the case on linear scales in an Einstein-de Sitter Universe. 

 

If, however, these large scale potential wells vary with time, as they would in the presence of dark energy or curvature, the photon will emerge from the LSS gravitational field, either red- or blue-shifted depending on whether the potentials grow or decay respectively. This is illustrated in the image above. Photons travel (from the left of the image) towards the observer (right) through LSS potential wells. The photons at the top of the image travel through large scale structure in an Einstein-de Sitter universe and emerge from the LSS potential well with the same redshift as on entry. The photons at the bottom of the illustration travel through the LSS in an accelerating universe in which large scale potential wells decay and exit bluer than on entry.

 

For photons travelling from the surface of last scattering (CMB), the varying gravitational potential of LSS will create secondary temperature anisotropies which will add power to the temperature-temperature angular power spectrum Formula. The power added on large scales is:

 

Formula

 

where T is the temperature of the CMB, η is the conformal time, defined by  Formulaand Formula and Formula are the conformal times today and at the surface of last scattering respectively;

Formula is the unit vector along the line of sight; Formula is the gravitational potential at position

x and at conformal time Formula, and Formula.

 

Cross-Correlation of Galaxy and Temperature Anisotropy Fields

 

 

Redshift Evolution of the ISW Signal

 

 

Cosmological Parameter Dependence

 

Galaxy Bias

 

Dark Energy vs. Curvature

 

Lambda vs. Dark Energy

 

 

Effect of Cosmic Magnification

 

Effect of Non-Trivial Topologies

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