Making the most of the ISW effect

1. Making the most of the ISW effect Robert Crittenden Work with S. Boughn, T. Giannantonio, L. Pogosian, N. Turok, R. Nichol, P.S. Corasaniti, C. Stephan-Otto

2. Outline What is the ISW effect? Detecting the ISW • Example - X-ray background- WMAP • Present limits • Future measurements Getting rid of the noise? Optimal statistics Conclusions

3. Two independent CMB maps The CMB fluctuations we see are a combination of two largely uncorrelated pieces, one induced at low redshifts by a late time transition in the total equation of state. Early map, z~1000 Structure on many scales Late ISW map, z< 4 Mostly large scale features

4. Dark energy signature The ISW effect is gravitational, much like gravitational lensing, but instead of probing the gravitational potential directly, it measures its time dependence along the line of sight. potential depth changes as cmb photons pass through gravitational potential traced by galaxy density The gravitational potential is actually constant in a matter dominated universe on large scales. However, when the equation of state changes, so does the potential, and temperature anisotropies are created.

5. What can the ISW do for us? Independent evidence for dark energy • Matter dominated universe in trouble Direct probe of the evolution of structures • Do the gravitational potentials grow or decay? • Constrain modified gravity models? Sensitive on the largest scales (horizon) • Measure dark energy clustering (Bean & Dore, Weller & Lewis, Hu & Scranton)

6. Modified gravity Modified gravity theories might have very different predictions for ISW even with the same background expansion! DGP braneworld picture might give opposite sign, so could already be ruled out by ISW (Sawicki & Carroll 05.) Extra dimensional changes typically affect largest scales the most. Lue, Scoccimarro, Starkman 03 See talks by Song, Zhang

7. How do we detect ISW map? The typical scale is the horizon size, because smaller structures tend to cancel out. On linear scales positive and negative effects equally likely. Difficult to measure directly: • Same frequency dependence. • Small change to spectrum. • Biggest just where cosmic variance is largest. But we can see it if we look for correlations of the CMB with nearby (z < 2) matter! RC & N. Turok 96 SDSS: H. Peiris & D. Spergel 2000

8. Cross correlation spectrum The gravitational potential determines where the galaxies form and where the ISW fluctuations are created! Thus the galaxies and the CMB should be correlated, though its not a direct template. Most of the cross correlation arises on large or intermediate angular scales (>1degree). The CMB is well determined on these scales by WMAP, but we need large galaxy surveys. Can we observe this? Yes, but its difficult!

9. Fundamental problem While we see the CMB very well, the usual signal becomes a contaminant when looking for the recently created signal. Effectively we are intrinsically noise dominated and the only solution is to go for bigger area. But we are fundamentally limited by having a single sky. Noise! Signal ISW map, z< 4 Early map, z~1000

10. Example: hard X-ray background • XRB dominated by AGN at z ~ 1. • Remove possible contaminants from both: • Galactic plane, center • Brightest point sources • Fit monopole, dipole • Detector time drifts • Local supercluster Hard X-ray background - HEAO-1 CMB sky - WMAP

11. Cross correlations observed! What is the significance? • Dominated not by measurement errors, but by possible accidental alignments. • This is modeled by correlating the XRB with random CMB maps with the same spectrum. • This gives the covariance matrix for the various bins. Result: 3 detection dots: observed thin: Monte Carlos thick: ISW prediction given best cosmology and dN/dz errors highly correlated S. Boughn & RC, 2004

12. Could it be a foreground? Possible contaminations: • Galactic sources • Clustered extra-galactic sources emitting in microwave • Sunyaev-Zeldovich effect Tests: • insensitive to level of galactic cuts • insensitive to point source cuts • comparable signal in both hemispheres • correlation on large angular scales • independent of CMB frequency channel

13. CMB frequency independence Cross correlations for ILC and various WMAP frequency bands lie on top of each other. Not the strong dependence expected for sources emitting in the microwave. Radio-WMAP XRB-WMAP

14. A few contaminated pixels? The contribution to the correlation from individual pixels pairs is consistent with what is expected for a weak correlation. Correlation is independent of threshold, thus NOT dominated by a few pixels blue: product of two Gaussians red: product of two weakly correlated Gaussians

15. Correlations seen in many frequencies! • X-ray background • Radio galaxies: • NVSS confirmed by Nolta et al (WMAP collaboration) • Wavelet analysis shows even higher significance (Vielva et al. McEwan et al.) • FIRST radio galaxy survey (Boughn) Infrared galaxies: • 2MASS near infrared survey (Afshordi et al.) Optical galaxies: • APM survey (Folsalba & Gaztanaga) • Sloan Digital Sky Survey (Scranton et al., FGC, Cabre et al.) • Band power analysis of SDSS data (N. Pamanabhan, et al.)

16. Detections of ISW • Correlations at many frequencies, many redshifts. • All consistent, with cosmological constant, if a bit higher thanexpected. This has made them easier to detect! • Relatively weak detections, and there is covariance between different observations! • Large horizontal error bars. 2mass APM SDSS New! X-ray/NVSS

17. What does it say about DE? Thus far constraints are fairly weak from ISW alone. • Consistent with cosmological constant model. • Can rule out models with much larger or negative correlations. • Very weak constraints on DE sound speed. Corasantini, Giannantonio, Melchiorri 05 Gaztanaga, Manera, Multamaki 04

18. Parameter constraints A more careful job is needed! Quantify uncertainties: • Bias - usually estimated from ACF consistently. How much does it evolve over the samples? Non-linear or wavelength dependent? • Foregrounds - incorporate them into errors. • dN/dz - how much are the uncertainties? Understand errors: • To use full angular correlations, we need full covariances for all cross correlations. • Monte Carlo’s needed with full cross correlations between various surveys.

19. How good will it get? For the favoured cosmological constant the best signal to noise one can expect is about 7-10. This requires significant sky coverage, surveys with large numbers of galaxies and some understanding of the bias. The contribution to (S/N)2 as a function of multipole moment. This is proportional to the number of modes, or the fraction of sky covered, though this does depend on the geometry somewhat. RC, N. Turok 96 Afshordi 2004

20. Future forecasts Ideal experiment : • Full sky, to overcome ‘noise’ • 3-D survey, to weight in redshift (photo-z ok) • z ~ 2-3, to see where DE starts • 107 -108 galaxies, to beat Poisson noise Unfortunately, z=1000 ‘noise’ limits the signal to the 7-10 level, even under the best conditions. Realistic plans: • Short term - DES, Astro-F (AKARI) • Long term - LSST, LOFAR/SKA Pogosian et al 2005 astro-ph/ 0506396 See talk by Pogosian

21. Getting rid of the ‘noise’ Is there any way to eliminate the noise from the intrinsic CMB fluctuations? Suggestion from L. Page: use polarization! The CMB is polarized, and this occurs before ISW arises, either at recombination or very soon after reionization! Can we use this to subtract off the noise? To some extent, yes!

22. Estimating the polarized temperature map Suppose we had a good full sky polarization map (EE) and a theory for the cross correlation (TE). We could use this to estimate a temperature map (e.g. Jaffe ‘03) that was 100% correlated with the polarization. Subtracting this from the observed map would reduce the noise somewhat, improving the ISW detection! Only a small effect at the multipoles relevant for the ISW, but could improve S/N by 20%.

23. Wavelet detections • Recent wavelet analyses (Vielva et al., McEwen et al) have apparently claimed better significance of detections than analyses using correlation functions. • NVSS-WMAP: • CCFs give 2-2.5 ISW detections. • Wavelets give 3.3-3.9  correlation detections. • Despite better detection, parameter constraints comparable?! What’s going on? Claims: • Wavelets localize regions that correlate most strongly. • Better optimized for a single statistic than CCF(0).

24. Wavelet method Wavelet analysis: Modulate both maps with wavelet filter (e.g. SMH). Take the product of two new maps (effectively CCF(0).) Compare this to expected variance. Repeat for different sizes, shapes, orientations; largest is reported as detection significance. Use all wavelets and covariances for parameter constraints. The quoted wavelet detection significances are biased! It does not try to match what is seen from what is theoretically expected. They actually present the probability of measuring precisely what they saw. The more wavelets they try, the better the more significant the detections will appear.

25. Wavelets vs correlation functions Assuming the maps are Gaussian, the CCF or the power spectrum should be sufficient; they should contain all the information in the correlations. It is true that wavelets do better for a single statistic, but CCF measurements look for particular angular dependence, combining different bins with full covariance. In both cases, Gaussianity of quadratic statistics is assumed. The true full covariance distribution should be calculated to get true significance. Wavelets could be improved by using information about the expected ISW signal, and the optimal ‘wavelet’ is simple to calculate, but it is not compact.

26. Conclusions ISW effect is a useful cosmological probe, capable of telling us useful information about nature of dark energy. It has been detected in a number of frequencies and a range of redshifts, providing independent confirmation of dark energy. There is still much to do: • Fully understanding uncertainties and covariances to do best parameter estimation. • Using full shape of probability distributions. • Finding new data sets. • Reducing ‘noise’ with polarization information.