1. bwdem – 06/04/2005doing cosmology with galaxy clusters Cosmology with galaxy clusters: testing the evolution of dark energy Raul Abramo – Instituto de Física – Universidade de São Paulo BWDE/M – Joinville Miller et al. 2005 Gemini

2. bwdem – 06/04/2005doing cosmology with galaxy clusters Summary Galaxy clusters are the largest virialized structures in the Universe. They are rich is gas (both hot and ionized as well as cold gas) as well as cold dark matter. The hot gas can be detected through the Sunyaev-Zeldovich effect, i.e., inverse compton scattering of the CMB photons off the hot intracluster electrons. This non-thermal effect leaves a characteristic imprint on the (originally) planckian spectrum. Hot gas can also be detected, at high concentrations, through its X-ray emission (brehmsstrahlung). The total (baryons + CDM) amount of matter in a cluster can be detected through weak (e.g. shear) and strong (e.g. Einstein ring) lensing. Cold gas can also be detected through the hydrogen absorption spectra if a background quasar is available. Clusters are great tools to study Cosmology! What about Dark Energy?

3. bwdem – 06/04/2005doing cosmology with galaxy clusters 1. How clusters help pinpoint Dark Energy: that “little extra mile” WMAP 2003 Allen et al. 2004

4. bwdem – 06/04/2005doing cosmology with galaxy clusters Constraints from future SZe surveys Carlstrom, Holder & Reese 2002

5. bwdem – 06/04/2005doing cosmology with galaxy clusters Constraints from cosmic shear Jain & Taylor 2004 Effective depth to measure w of a shear survey, compared to other observations Ferguson & Bridle 2005

6. bwdem – 06/04/2005doing cosmology with galaxy clusters 2. Cluster Polarization and DE The map of the CMB temperature fluctuations are essencially the portrait of a two-dimensional surface (the LSS) of radius R= r. [: conformal time; d= dt/a(t) ] In the presence of DE, the large-scale gravitational potential decays when DE starts to dominate. CMB photons propagating to us through space fall in and out of these time-changing potentials, gaining (or losing) energy. [Integrated Sachs-Wolfe effect – ISWe] (z>>1) (z<1) It is hard to actually use the ISWe to extract information about the equation of state, since we cannot know in principle what in the CMB is due to the SW (intrinsic, at the LSS) effect and what is due to the ISWe. We can use the Sunyaev-Zeldovich effect, which induces a polarization on the CMB photons that scatter off free electrons in galaxy clusters, to determine the ISWe. We can also use this polarization signal to make a tomography of the 3D spectrum of fluctuations! Kamionkowski & Loeb 1997, Cooray & Baumann 2002

7. bwdem – 06/04/2005doing cosmology with galaxy clusters CMB Bennett et al. ApJS 148:1 (2003)

8. bwdem – 06/04/2005doing cosmology with galaxy clusters What goes into the a lm that we measure today: 1. Sachs-Wolfe effect:

9. bwdem – 06/04/2005doing cosmology with galaxy clusters 2. ISWe: Crittenden & Turok 1997

10. bwdem – 06/04/2005doing cosmology with galaxy clusters Therefore, the total temperature fluctuations are: where:

11. bwdem – 06/04/2005doing cosmology with galaxy clusters Consider now a cluster at the direction  c and at redshift z c. What kind of CMB would an observer in that cluster observe? Spherical harmonic at cluster:

12. bwdem – 06/04/2005doing cosmology with galaxy clusters Hot ionized gas in clusters affects CMB photons through inverse Compton effect: How can we in fact measure the a lm ‘s or the C l ‘s in clusters?  Sunyaev-Zeldovich effect Sunyaev & Zeldovich 80,81 Sazonov & Sunyaev 99 The scattering also polarizes the CMB photons according to the quadrupole of the CMB temperature seen by the cluster. If we ignore the ISWe, the Q and U polarization modes for a cluster at position () are given by: x=h/kT, f(x) is a spectral correction (of order 1),  is the optical depth of the cluster, x and y are linear combinations (eigenvalues) of the components of the quadrupole (a 20, a 21, a 22 ) at the location of the cluster.

13. bwdem – 06/04/2005doing cosmology with galaxy clusters These clusters appear to us as “mini-quadrupoles” through the polarized CMB photons. However, in the presence of DE we know that the quadrupole evolved quite a lot, recently (z<~2) because of the ISWe. Therefore, with independent data (thermal SZe, X-ray) about the optical depth of a given cluster, the polarization of the CMB in the direction of clusters is a witness to the redshift-dependent quadrupole of the CMB. This means that, if the CMB quadrupole is constant, the degree and orientation of the SZe-induced polarization of clusters along a given line of sight does not vary with redshift (except for Cosmic Variance).

14. bwdem – 06/04/2005doing cosmology with galaxy clusters Computing the C l ’s for redshift bins and averaging over their positions will give: Effect is stronger for the quadrupole (l=2). If we measure the change of the quadrupole with time, we set limits over F l (k, c ) and the growth function, g(z). This is a strong test of DE.

15. bwdem – 06/04/2005doing cosmology with galaxy clusters The time variation for the low multipoles (l<10) is very sensitive to the decay of the gravitational potentials: We can estimate how this test determines the parameters  m and w through the function g’(z):

16. bwdem – 06/04/2005doing cosmology with galaxy clusters Baumann & Cooray 2004 Efficacy of the observations Assuming a survey of clusters down to 10 14 M O, with sensitivity for polarization of 0.1 K, over 10 4 deg 2 :

17. bwdem – 06/04/2005doing cosmology with galaxy clusters 2. Polarization tomography Let’s return to the expression for the harmonic components, and let me assume for simplicity that the ISWe is small, so only the SWe remains: where Notice that the harmonic components are essentially functions of the position of the cluster, and are quite similar to a Fourier transform. Let’s invert this: Where

18. bwdem – 06/04/2005doing cosmology with galaxy clusters Using the completeness of Bessel’s functions and doing some algebra we get: Summing over m=-l,...,l we obtain: Where

19. bwdem – 06/04/2005doing cosmology with galaxy clusters Therefore, if we can measure with some accuracy the quadrupole in galaxy clusters up to relatively high redshifts (z3), then we will be able to reconstruct the three-dimensional density field inside our LSS volume – and not only the two-dimensional spectrum on the LSS surface! For the quadrupole, the weight function which multiplies the spectrum is approximately peaked at cos  = ± 1. Therefore, up to an approximation which can be easily improved, we can reconstruct the 3-dimensional spectrum of fluctuations by measuring the harmonic components in space (through cluster polarization). The final result: