Book contents
- Frontmatter
- Contents
- Preface
- 1 The homogeneous and isotropic universe
- 2 Perturbation theory
- 3 Initial conditions
- 4 CMB anisotropies
- 5 CMB polarization and the total angular momentum approach
- 6 Cosmological parameter estimation
- 7 Lensing and the CMB
- 8 The CMB spectrum
- Appendix 1 Fundamental constants, units and relations
- Appendix 2 General relativity
- Appendix 3 Perturbations
- Appendix 4 Special functions
- Appendix 5 Entropy production and heat flux
- Appendix 6 Mixtures
- Appendix 7 Statistical utensils
- Appendix 8 Approximation for the tensor Cℓ spectrum
- Appendix 9 Boltzmann equation in a universe with curvature
- Appendix 10 The solutions of some exercises
- References
- Index
7 - Lensing and the CMB
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- 1 The homogeneous and isotropic universe
- 2 Perturbation theory
- 3 Initial conditions
- 4 CMB anisotropies
- 5 CMB polarization and the total angular momentum approach
- 6 Cosmological parameter estimation
- 7 Lensing and the CMB
- 8 The CMB spectrum
- Appendix 1 Fundamental constants, units and relations
- Appendix 2 General relativity
- Appendix 3 Perturbations
- Appendix 4 Special functions
- Appendix 5 Entropy production and heat flux
- Appendix 6 Mixtures
- Appendix 7 Statistical utensils
- Appendix 8 Approximation for the tensor Cℓ spectrum
- Appendix 9 Boltzmann equation in a universe with curvature
- Appendix 10 The solutions of some exercises
- References
- Index
Summary
In this chapter we discuss the most important second-order effect on CMB anisotropies and polarization. Patches of higher or lower CMB temperature are modified and polarization patterns are distorted when they propagate through an inhomogeneous gravitational field. The content of this chapter is strongly inspired by the excellent review by Lewis & Challinor (2006) on the subject.
An introduction to lensing
On their path from the last scattering surface into our antennas, the CMB photons are deflected by the perturbed gravitational field. If the CMB were perfectly isotropic, the net effect of this deflection would vanish, since, by the conservation of photon number, as many photons would be deflected out of a small solid angle as into it. On the other hand, if there is no perturbation in the gravitational field, the latter is perfectly isotropic and the effect also vanishes. Hence, gravitational lensing of the CMB is a second-order effect and we have not discussed it within linear perturbation theory.
To estimate the effect let us consider the CMB temperature in a point n in the sky, T(n). If the direction n is deflected by a small angle α, we receive the temperature T(n) from the direction n′ = n + α. Note that, since α is a vector normal to n also n′ is a unit vector to first order in α.
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- Chapter
- Information
- The Cosmic Microwave Background , pp. 278 - 303Publisher: Cambridge University PressPrint publication year: 2008