How do GWs generate B-modes in the CMB polarization pattern?

[Brinx]

I have been searching through some of the literature, as well as this forum - but I have not found a clear explanation on how exactly the B-modes in the CMB polarization pattern are caused by gravitational waves. I have seen Wayne Hu's pages ( see for instance http://background.uchicago.edu/~whu/intermediate/Polarization/polar5.html ) and the Berkeley cosmology pages ( http://cosmology.berkeley.edu/~yuki/CMBpol/CMBpol.htm ). I do think I understand the mechanism behind the generation of E-modes from density variations, vorticity and gravitational waves, but the B-modes and their 'handedness' are confusing. How would local quadrupolar patterns of effective temperature generate polarizations that have a 45-degree angle with respect to them?

I have attached a diagram I made of what happens in the case of density variations, from which (irrotational) E-modes are generated. Is there a similar picture for B-modes?

 

[AndyW]

Thank you for your question and for sharing your diagrams. The B-modes in the cosmic microwave background (CMB) polarization pattern are indeed caused by gravitational waves, specifically primordial gravitational waves from the early universe.

To understand how B-modes are generated, it is important to first understand the concept of tensor perturbations. In cosmology, perturbations are small deviations from the uniformity of the universe. They can arise from density variations, vorticity, and gravitational waves. Tensor perturbations, also known as gravitational waves, are a type of perturbation that causes the fabric of spacetime to stretch and compress in different directions.

In the case of density variations, as shown in your diagram, the perturbations are scalar perturbations and they generate E-modes in the CMB polarization pattern. However, gravitational waves generate tensor perturbations, which can produce both E-modes and B-modes in the CMB polarization pattern.

The key difference between E-modes and B-modes is their polarization direction. E-modes have a polarization direction that is parallel or perpendicular to the direction of the density perturbations, while B-modes have a polarization direction that is at a 45-degree angle to the direction of the gravitational waves.

This can be better understood by visualizing the effect of gravitational waves on the CMB photons. As the gravitational waves pass through the universe, they cause the photons to move in a circular or elliptical pattern. This circular or elliptical motion results in a polarization direction that is at a 45-degree angle to the direction of the gravitational waves, creating the B-modes in the CMB polarization pattern.

To summarize, B-modes in the CMB polarization pattern are caused by tensor perturbations or gravitational waves from the early universe. These gravitational waves produce a 45-degree angle polarization direction, which is distinct from the parallel or perpendicular polarization direction of E-modes generated by scalar perturbations.

I hope this explanation helps clarify the mechanism behind the generation of B-modes in the CMB polarization pattern. If you have any further questions, please do not hesitate to ask. Thank you for your interest in this fascinating subject.