Observational Evidence of Dark Energy and the Integrated Sachs-Wolfe Effect

1. Observational Evidence of Dark Energyand the Integrated Sachs-Wolfe Effect Debashish Burman and Ryan Kirker School of Astronomy and Physics University of Minnesota Minneapolis, MN 55455 December 12, 2006

2. A History of Expansion [www.nasa.gov]

3. Fundamentals Opposing Effects on Universe’s acceleration Relating the universe’s acceleration or deceleration to the equation of state … And in terms of compositional densities …

4. Negative Pressure • An accelerated expansion of the universe requires w less than –1/3 • Result is a gravitationally repulsive “negative pressure” • Similar to Inflaton in behavior • Possible Explanations • Cosmological constant driven (w = –1) • Uniform sea of quantum zero-point energy, property of vacuum • Elementary quantum field theory predicts a constant 120 orders of magnitude too large • Most likely culprit • Quintessence • Dynamic, time evolving, spatially dependent equation of state • No observation evidence to date

5. In the Beginning - SN Ia • Supernova Cosmology Project • High z, SN1a events • Assume flat universe • Determination of cosmological parameters from magnitudes of explosions [Knop et al (2003)] SN Ia as standard candles – Perlmutter, 03

6. Cosmological Parameters • Parameters assume flat universe • Probability of dark energy existence based on certainty calculations greater than 99% [Knop et al (2003)]

7. Dark Energy Domination • The larger the value of lambda, the earlier the onset of its domination Dave Miller @ U Chicago

8. Additional SN1a Data [Riess et al. (2004)]

9. Perlmutter, 03 SNAP Supernova/Acceleration Probe • Space-based telescope • 1 square-degree FoV; 1 GPixel imaging; 2m mirror • 2000 supernovae per year • Range: z = 1.7 Deliverables: • ΩM, ΩΛ, ΩK: within 1%, including systematic errors • wΛ within 4%

10. Evolution of the CMB map

11. CMB Anisotropies • WMAP satellite results reveal temperature fluctuations on the order of 10-5 degrees • Fluctuations provide constraints on cosmological parameters • Power spectrum provides evidence for large scale structure

12. Cosmic Microwave Background • Prior to z ~ 1000 photons and electrons tightly coupled • Universe cools, neutral hydrogen forms • CMB photons decouple from electrons and stream outwards • Differences in temperature on last scattering surface are reflected in anisotropies in CMB • Photons red-shifted as universe expands

13. The Universe is Flat [Courtesy of L. Williams]

14. Cosmological Parameters • CMB proves geometry of universe is flat • Independent calculation of dark energy density • Independent calculation of matter density [Spergel et al.(2003)]

15. Integrated Sachs-Wolfe • Time varying gravitational potentials • Early and late ISW Wayne Hu

16. Late Integrated Sachs-Wolfe Wayne Hu

17. CMB Power Spectrum [Spergel et al. ’03]

18. LSS Surveys 3D mapping of the Universe with galaxy redshift surveys SDSS

19. Correlations

20. CMB and Galactic Surveys • Large-scale galactic surveys provide opportunity to test late ISW effect • If CMB photons are effected by time-variant potential wells there should be cross-correlation between temperature anisotropies found in the CMB and dark-matter fluctuations traced by galaxies at near redshifts • Typical Cross-correlation for angular separation:

21. CMB and the APM Galactic Survey • Correlation with APM Galaxy Survey [Fosalba & Gaztanaga 2004] • Cross-Correlation Function: • wi’s are weighting factors • Used to minimize variance when pixel noise is not uniform • This study follows WMAP team, uses uniform weights • 1- error determined by a jack-knife covariance matrix • APM survey broken into 10 (M) separate regions of equal area • Covariance calculated 10 (M) times removing a different region each time • Method also used by WMAP team

22. Visual Correlation • Correlation visible on larger scales • Anti-correlation visible on smaller scales

23. Boxes give 68% confidence level Cross correlation strongest at higher angular scales (  = 4 - 10 ) Anti-correlation seen on small angular scales Due to SZ effect Predicted by model (long-dashed) All but one bin has zero correlation within error Measurement vs. Prediction

24. A Discussion of Error • Jack-knife errors checked against Monte-Carlo (MC) simulations • Errors from a single MC simulation agree well with the JK errors • However, observational JK errors only correlate at higher angular scales

25. CMB and Galactic Surveys • Correlation with SDSS [Scranton et al, 2003] • Cross-Correlation Function: • χ2Analysis utilizes two different covariance functions to check for statistical significance Random CMB maps Jack-knife estimator

26. Correlation is in the Eye of the Beholder • Theoretical Model • ΛCDM cosmology: • Suggests non-zero cross-correlation, especially from 2-6 degrees • Observations • Consistent non-zero signal that is achromatic in Q,V, and W maps • At close redshifts, correlation function is zero within the error bars

27. Significance? • χ2 values produced by both covariance functions • Individual measurements are significant at the > 90% • False Discovery Rate technique used to disregard null hypothesis with a confidence > 95%

28. Spergel et al 2006 Constraints on w

29. Conclusions • There are a lot of observational data on dark energy, but poor physical understanding • CMB, despite its early origins, provides confirmation via the late ISW effect • SN-Ia data provide increasingly tight bounds over a range of redshifts; let’s hope that SNAP continues to be funded • LSS – cross-correlating is hard • Systematic errors • Galaxy bias • More extensive catalogs needed as well as deeper field surveys • Equation of state Perlmutter, 03