1 / 9

Understanding the Tensor CMB Polarisation Power Spectrum

Understanding the Tensor CMB Polarisation Power Spectrum . Jonathan Pritchard with Marc Kamionkowski Caltech. Overview. Have been attempting to develop analytic expressions for the tensor CMB power spectrum.

kerryn
Download Presentation

Understanding the Tensor CMB Polarisation Power Spectrum

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. TASC 2004 Understanding the Tensor CMB Polarisation Power Spectrum Jonathan Pritchard with Marc Kamionkowski Caltech

  2. Overview TASC 2004 • Have been attempting to develop analytic expressions for the tensor CMB power spectrum. • Analytic expressions aid intuition and give insight into results of numerical calculations. • Today will discuss only polarisation power spectrum. • B-mode polarisation current target of observational effort. Tensor power spectra

  3. CMB Polarisation Introduction TASC 2004 • Primordial plasma cools leading to recombination. e + p -> H • Photon mean free path increases. • CMB originates at the surface of last scattering (SLS). • Inflationary tensor perturbations to metric = stocastic gravitational wave background. • Time evolving gravitational potential generates temperature perturbations via Integrated Sachs-Wolfe (ISW) effect. • Thomson scattering of anisotropic temperature distribution generates polarisation. • Resulting polarisation spectrum decomposed into E (grad) and B (curl) modes.

  4. Structure of the problem TASC 2004 • Decompose T and polarisation perturbations using Legendre polynomials,e.g., • Solving equations for radiation transport then gives polarisation multipoles Visibility Function Source Evolution Geometric Projection

  5. Geometric Projection TASC 2004 • 3D Fourier modes projected onto 2D angular scales. • Aliasing: Single Fourier mode contributes to many angles. Peak at • Projection terms involve spherical Bessel functions, oscillate and are messy to calculate. • Approximate Bessel functions using Debye’s asymptotic formula. • Average over oscillation to get polynomial envelope.

  6. Growth of Anisotropy TASC 2004 • Before recombination radiation and baryons are tightly coupled and the photon mean free path is small. • Increasing photon m.f.p. allows growth of anisotropy. • Resulting multipole depends on the strength of sourcing term and the time its had to grow. • Little power on large scales where gravitational wave varies little across width of SLS.

  7. Gravitational Wave Evolution TASC 2004 • Gravitational waves evolve according to damped wave equation • After horizon entry g.w. amplitude redshifts as • Expansion rate depends on radiation/matter content. • Scaling relation for amplitude • Use l=k (lookback) to get scaling for polarisation power spectrum . • Redshifting of g.w. leads to decrease in power on scales smaller than the horizon scale at recombination.

  8. Phase damping TASC 2004 • On small scales the tensor mode varies rapidly over the width of the SLS. • Coherent scattering of photons from regions of different phase leads to cancellation. • Exponential damping of multipoles • Suppression of power on small scales.

  9. Conclusions TASC 2004 • Combining all the physics mentioned can derive semi-analytic expressions for the power spectra. • Without phase damping recover appropriate scaling relations. • With phase damping see rapid drop in power on small scales. • Projection approximations only valid l<600. • Wiggles contain information about evolution of gravitational waves in the early universe.

More Related