1. State of the (dark) universe report Uros Seljak Zurich/ICTP/Princeton Heidelberg, november 7, 2006

2. Outline 1)Methods to investigate dark energy and dark matter: SN, CMB, galaxy clustering, cluster counts, weak lensing, Lya forest 2)Current constraints: what have we learned so far, controversies 3) What can we expect in the future?

3. ContextContext 1.Conclusive evidence for acceleration of the Universe. Standard cosmological framework  dark energy (70% of mass-energy). 2.Possibility: Dark Energy constant in space & time (Einstein’s  ). 3.Possibility: Dark Energy varies with time (or redshift z or a  (  z )  ). 4.Impact of dark energy can be expressed in terms of “equation of state” w ( a )  p ( a ) /  ( a ) with w ( a )  for  5.Possibility: GR or standard cosmological model incorrect. 6.Whatever the possibility, exploration of the acceleration of the Universe will profoundly change our understanding of the composition and nature of the Universe.

4. Contents of the universe (from current observations) Baryons (4%) Dark matter (23%) Dark energy: 73% Massive neutrinos: 0.1% Spatial curvature: very close to 0

5. How to test dark energy/matter? 1)Classical tests: redshift- luminosity distance relation (SN1A etc), redshift- angular diameter distance, redshift- Hubble parameter relation

6. Classical cosmological tests (in a new form) Friedmann’s (Einstein’s) equation

7. How to test dark energy/matter? 1)Classical tests: redshift-distance relation (SN1A etc)… 2)Growth of structure: CMB, Ly-alpha, weak lensing, clusters, galaxy clustering

8. Growth of structure by gravity  Perturbations can be measured at different epochs: 1. CMB z=1000 2. 21cm z=10-20 (?) 3. Ly-alpha forest z=2-4 4. Weak lensing z=0.3-2 5. Galaxy clustering z=0-1 (3?) Sensitive to dark energy, neutrinos…

9. How to test dark energy/matter? 1)Classical tests: redshift-distance relation (SN1A etc)… 2)Growth of structure: CMB, Ly-alpha, weak lensing, clusters, galaxy clustering 3)Scale dependence of structure

10. CBIACBAR Lyman alpha forest Scale dependence of cosmological probes WMAP Complementary in scales and redshift SDSS

11. Sound Waves from the Early Universe Before recombination: –Universe is ionized. –Photons provide enormous pressure and restoring force. –Perturbations oscillate as acoustic waves. After recombination: –Universe is neutral. –Photons can travel freely past the baryons. –Phase of oscillation at t rec affects late-time amplitude.

12. This is how the Wilkinson Microwave Anisotropy Probe (WMAP) sees the CMB

13. Determining Basic Parameters Angular Diameter Distance w = -1.8,..,-0.2 When combined with measurement of matter density constrains data to a line in  m -w space

14. Determining Basic Parameters Matter Density  m h 2 = 0.16,..,0.33

15. Determining Basic Parameters Baryon Density  b h 2 = 0.015,0.017..0.031 also measured through D/H

16. Current 3 year WMAP analysis/data situation Current data favor the simplest scale invariant model

17. Galaxy and quasar survey 400,000 galaxies with redshifts

18. Sloan Digital Sky Survey (SDSS) Image Credit: Sloan Digital Sky Survey 2.5 m aperture 5 colors ugriz 6 CCDs per color, 2048x2048, 0.396”/pixel Integration time ~ 50 sec per color Typical seeing ~ 1.5” Limiting mag r~23 current 7000 deg 2 of imaging data, 40 million galaxies 400,000 spectra (r<17.77 main sample, 19.1 QSO,LRG)

19. Galaxy power spectrum: shape analysis Galaxy clustering traces dark matter on large scales Current results: redshift space power spectrum analysis based on 200,000 galaxies (Tegmark etal, Pope etal), comparable to 2dF (Cole etal) Padmanabhan etal: LRG power spectrum analysis, 10 times larger volume, 2 million galaxies Amplitude not useful (bias unknown) Nonlinear scales

20. Are galaxy surveys consistent with each other? Some claims that SDSS main sample gives more than 2 sigma larger value of  SDSS LRG photo 2dF SDSS main spectro Bottom line: no evidence for discrepancy, new analyses improve upon SDSS main Fixing h=0.7

21. Acoustic Oscillations in the Matter Power Spectrum Peaks are weak; suppressed by a factor of the baryon fraction. Higher harmonics suffer from diffusion damping. Requires large surveys to detect! Linear regime matter power spectrum

22. A Standard Ruler The acoustic oscillation scale depends on the matter-to- radiation ratio (  m h 2 ) and the baryon-to-photon ratio (  b h 2 ). The CMB anisotropies measure these and fix the oscillation scale. In a redshift survey, we can measure this along and across the line of sight. Yields H(z) and D A (z)! Observer  r = (c/H)  z  r = D A 

23. Baryonic wiggles Best evidence: SDSS LRG spectroscopic sample (Eisenstein etal 2005), about 3.5 sigma evidence SDSS LRG photometric sample (Padmanabhan, Schlegel, US etal 2005): 2.5 sigma evidence

24. To perturb or not to perturb dark energy Should one include perturbations in dark energy? For w=-1 no perturbations For w>-1 perturbations in a single scalar field model with canonical kinetic energy, speed of sound c Non-canonical fields may give speed of sound <<c For w<-1 (phantom model) one can formally adopt the same, but the model has instabilities For w crossing from -1 it has been argued that the perturbations diverge: however, no self-consistent model based on Lagrangian exists There is a self-consistent ghost condensate model that gives w<-1 (Creminelli etal 2006) and predicts no perturbations in DE sector

25. Weak Gravitational Lensing Distortion of background images by foreground matter UnlensedLensed

26. Weak Lensing: Large-scale shear Convergence Power Spectrum 1000 sq. deg. to R ~ 27 Huterer

27. Gravitational Lensing –Advantage: directly measures mass –Disadvantages Technically more difficult Only measures projected mass- distribution Intrinsic alignments? Tereno et al. 2004 Refregier et al. 2002

28. Possible sources of systematic error PSF induced errors: rounding (need to calibrate), ellipticity (use stars) Shear selection bias: rounder objects can be preferentially selected Noise induced bias: conversion from intensity to shear nonlinear Intrinsic correlations STEP2 project bottom line: current acccuracy at 5% level, plenty of work to do to reach 1% level, not clear 0.1% even possible

29. Shear-intrinsic (GI) correlation Same field shearing is also tidally distorting, opposite sign What was is now, possibly an order of magnitude increase Cross-correlations between redshift bins does not eliminate it B-mode test useless (parity conservation) Vanishes in quadratic models Hirata and US 2004 Lensing shear Tidal stretch

30. Intrinsic correlations in SDSS 300,000 spectroscopic galaxies No evidence for II correlations Clear evidence for GI correlations on all scales up to 60Mpc/h Gg lensing not sensitive to GI Mandelbaum, Hirata, Ishak, US etal 2005

31. Up to 30% for shallow survey at z=0.5 10% for deep survey at z=1: current surveys underestimate   More important for cross-redshift bins Implications for future surveys Mandelbaum etal 2005, Hirata and US 2004

32. Galaxy clustering: power spectrum shape Galaxy clustering traces dark matter on large scales Current results: redshift space power spectrum analysis based on 200,000 galaxies (Tegmark etal, Pope etal, 2dF (Cole etal) Padmanabhan etal: LRG photometric power spectrum analysis, 10 times larger volume, 2 million galaxies LRG spectro analysis: Tegmark etal, Eisenstein etal, Percival etal Amplitude not useful (bias) Nonlinear scales

33. Galaxy bias determination Galaxies are biased tracers of dark matter; the bias is believed to be scale independent on large scales (k<0.1-0.2/Mpc) If we can determine the bias we can use galaxy power spectrum to determine amplitude of dark matter spectrum  8 High accuracy determination of  8 is important for dark energy constraints Weak lensing is the most direct method

34. galaxy-galaxy lensing dark matter around galaxies induces tangential distortion of background galaxies: extremely small, 0.1%  Useful to have redshifts of foreground galaxies: SDSS Express signal in terms of projected surface density and transverse r  Signal as a function of galaxy luminosity, type…

35. Galaxy-galaxy lensing measures galaxy-dark matter correlations Goal: lensing determines halo masses (in fact, full mass distribution, since galaxy of a given L can be in halos of different mass) Halo mass increases with galaxy luminosity SDSS gg: 300,000 foreground galaxies, 20 million background, S/N=30, the strongest weak lensing signal to date testing ground for future surveys such as LSST,SNAP Seljak etal 2004

36. dark matter corr function On large scales galaxies trace dark matter G-g lensing in combination with autocorrelation analysis gives projected dark matter corr. function Mandelbaum, US etal, in prep

37. WMAP-LSS cross-correlation: ISW Detection of a signal indicates time changing gravitational potential: evidence of dark energy if the universe IS flat. Many existing analyses (Boughn and Crittenden, Nolta etal, Afshordi etal, Scranton etal, Padmanabhan etal) Results controversial, often non-reproducible and evidence is weak Future detections could be up to 6(10?) sigma, not clear if this probe can play any role in cosmological parameter determination

38. WMAP-SDSS cross-correlation: ISW N. Padmanabhan, C. Hirata, US etal 2005 4000 degree overlap Unlike previous analyses we combine with auto-correlation bias determination (well known redshifts)

39. 2.5 sigma detection Consistent with other probes

40. Counting Clusters of Galaxies Sunyaev Zel’dovich effect X-ray emission from cluster gas Weak Lensing Simulations: growth factor

41. Cosmic complementarity: Supernovae, CMB, and Clusters

42. Ly-alpha forest as a tracer of dark matter Basic model: neutral hydrogen (HI) is determined by ionization balance between recombination of e and p and HI ionization from UV photons (in denser regions collisional ionization also plays a role), this gives Recombination coefficient depends on gas temperature Neutral hydrogen traces overall gas distribution, which traces dark matter on large scales, with additional pressure effects on small scales (parametrized with filtering scale k F ) Fully specified within the model, no bias issues

43. SDSS Lya power spectrum analysis McDonald, US etal 2005 Combined statistical power is better than 1% in amplitude, comparable to WMAP 2<z<4 in 11 bins  2 ≈ 129 for 104 d.o.f. A single model fits the data over a wide range of redshift and scale Ly-alpha helps by reducing degeneracies between dark energy and other parameters that Lya determines well (amplitude, slope…) Direct search for dark energy at 2<z<4 reveals no evidence for it

44. The amplitude controversy Some probes, Ly-alpha, weak lensing, SZ clusters prefer high amplitude (sigma_8>0.85) Other probes, WMAP, X-ray cluster abundance, group abundance… prefer low amplitude (sigma_8<0.75) Statistical significance of discrepancy is 2.5?- sigma or less For the moment assume this is a statistical fluctuation among different probes and not a sign of a systematic error in one or more probes

45. Putting it all together US etal 04, 06  Dark matter fluctuations on 0.1-10Mpc scale: amplitude, slope, running of the slope  Growth of fluctuations between 2<z<4 from Lya  Lya very powerful when combined with CMB or galaxy clustering for inflation (slope, running of the slope), not directly measuring dark energy unless DE is significant for z>2  still important because it is breaking degeneracies with other parameters and because it is determining amplitude at z=3.

46. Dark energy constraints: complementarity of tracers US, Slosar, McDonald 2006

47. DE constraints: degeneracies and dimension of parameter space

48. Time evolution of equation of state w Individual parameters very degenerate

49. Time evolution of equation of state w remarkably close to - 1 Best constraints at pivot z=0.2-0.3, robust against adding more terms error at pivot the same as for constant w Perturbations switched off

50. What if GR is wrong? Friedman equation (measured through distance) and growth rate equation are probing different parts of the theory For any distance measurement, there exists a w(z) that will fit it. However, the theory can not fit growth rate of structure Upcoming measurements can distinguish Dvali et al. DGP from GR (Ishak, Spergel, Upadye 2005) (But DGP is already ruled out)

51. A look at neutrinos Neutrino mass is of great importance in particle physics (are masses degenerate? Is mass hierarchy inverted?): large next generation experiments proposed (KATRIN…) Neutrino free streaming inhibits growth of structure on scales smaller than free streaming distance If neutrinos have mass they are dynamically important and suppress dark matter as well, 50% suppression for 1eV mass For m=0.1-1eV free-streaming scale is >10Mpc Neutrinos are quasi-relativistic at z=1000: CMB is also important, opposite sign m=0.15x3, 0.3x3, 0.6x3, 0.9x1 eV

56. New limits on neutrino mass WMAP3+SDSS Lya+SDSS+2dF+SN 6p: Together with SK and solar limits: Lifting the degeneracy of neutrino mass

58. Neutrino as dark matter Initial conditions set by inflation (or something similar) Neutrino free streaming erases structure on scales smaller than free streaming distance For neutrino to be dark matter it must have short free streaming length: low temperature or high mass We can put lower limit on mass given T model One possibility to postulate a sterile neutrino that is created through mixing from active neutrinos. This is natural in a 3 right handed neutrinos setting, two are used to generate mass for LH, 3rd can be dark matter. To act like CDM need high mass, >keV. To suppress its abundance need small mixing angle,  0.001, never thermalized

59. Sterile neutrino as dark matter A sterile neutrino in keV range could be the dark matter and could also explain baryogenesis, pulsar kicks, seems very natural as we need sterile neutrinos anyways (Dodelson and Widrow, Asaka, Shaposhnikov, Kusenko, Dolgov and Hansen…) However, a massive neutrino decays and in keV range its radiative decays can be searched for in X-rays. If the same mixing process is responsible for sterile neutrino generation and decay then the physics is understood (almost, most of the production happens at 100MeV scale and is close or above QCD phase transition) Strongest limits come from X-ray background and COMA/Virgo cluster X-rays and our own galaxy, absence of signal gives m<3.5- 8keV (Abazajian 2005, Boyarsky etal 2005)

60. Sterile neutrino as dark matter To proceed we need to specify the model: assume no generation of sterile neutrinos above GeV, no lepton asymmetry enhancements, only production through mixing First approximation: production independent of momentum calculations in Abazajian (2005) give more accurate momentum distribution: 10% weaker mass constraints relative to previous calculations which assume momentum distribution is the same as active The limits for this model can be easily modified to other models (mirror, thermal, entropy injection from massive steriles etc)

63. Results and implications Combined with the 6keV (COMA), 8-9keV (Virgo, X-ray background) upper limit from radiative decays THIS model is excluded How do the constraints change with possible entropy injection that dilutes sterile neutrinos relative to CMB photons/active neutrinos? T is decreased relative to CMB, neutrinos are colder Dilution requires larger mixing angle for same matter density, so decay rate higher, which makes X-ray constraints tighter This does not open up the window To solve the model need to generate neutrinos with additional interactions at high energies above GeV

64. Future Dark Energy Prospects Prospects Based on dark energy task force

65. Members Andy Albrecht, Davis Gary Bernstein, Penn Bob Cahn, LBNL Wendy Freedman, OCIW Jackie Hewitt, MIT Wayne Hu, Chicago John Huth, Harvard Mark Kamionkowski, Caltech Rocky Kolb, Fermilab/Chicago Lloyd Knox, Davis John Mather, GSFC Suzanne Staggs, Princeton Nick Suntzeff, NOAO Future as seen by the dark side of the universe task force

66. Goals and Methodology 1.The goal of dark-energy science is to determine the very nature of the dark energy that causes the Universe to accelerate and seems to comprise most of the mass-energy of the Universe. 2.Toward this goal, our observational program must: a.Determine as well as possible whether the accelerated expansion is consistent with being due to a cosmological constant. b.If it is not due to a constant, probe the underlying dynamics by measuring as well as possible the time evolution of dark energy, for example by measuring w ( a ); our parameterization is w ( a )  w   w a (  a ). c.Search for a possible failure of GR through comparison of cosmic expansion with growth of structure. 3.Goals of dark-energy observational program through measurement of expansion history of Universe [ d L ( z ), d A ( z ), V ( z )], and through measurement of growth rate of structure. All described by w ( a ). If failure of GR, possible difference in w ( a ) inferred from different types of data.

67. Goals and Methodology 4.To quantify progress in measuring properties of dark energy we define dark energy figure-of-merit from combination of uncertainties in w  and w a. 5.Use of statistical (Fisher-matrix) techniques incorporating CMB and H  information to predict future performance. 6.Our considerations follow developments in Stages: I.What is known now (12/31/05). II.Anticipated state upon completion of ongoing projects. III.Near-term, medium-cost, currently proposed projects. IV.Large-Survey Telescope (LST) and/or Square Kilometer Array (SKA), and/or Joint Dark Energy (Space) Mission (JDEM). 7.Dark-energy science has far-reaching implications for other fields of physics  discoveries in other fields may point the way to understanding nature of dark energy (e.g., evidence for modification of GR).

68. Fifteen Findings 1.Four observational techniques dominate future proposals: a.Baryon Acoustic Oscillations (BAO) large-scale surveys measure features in distribution of galaxies. BAO: d A ( z ) and H ( z ). b.Cluster (CL) surveys measure spatial distribution of galaxy clusters. CL: d A ( z ), H ( z ), growth of structure. c.Supernovae (SN) surveys measure flux and redshift of Type Ia SNe. SN: d L ( z ). d.Weak Lensing (WL) surveys measure distortion of background images due to garavitational lensing. WL: d A ( z ), growth of structure. 2.Different techniques have different strengths and weaknesses and sensitive in different ways to dark energy and other cosmo. parameters. 3.Each of the four techniques can be pursued by multiple observational approaches (radio, visible, NIR, x-ray observations), and a single experiment can study dark energy with multiple techniques. Not all missions necessarily cover all techniques; in principle different combinations of projects can accomplish the same overall goals.

69. Four techniques at different levels of maturity: a.BAO only recently established. Less affected by astrophysical uncertainties than other techniques. b.CL least developed. Eventual accuracy very difficult to predict. Application to the study of dark energy would have to be built upon a strong case that systematics due to non-linear astrophysical processes are under control. c.SN presently most powerful and best proven technique. If photo-z’s are used, the power of the supernova technique depends critically on accuracy achieved for photo-z’s. If spectroscopically measured redshifts are used, the power as reflected in the figure-of-merit is much better known, with the outcome depending on the ultimate systematic uncertainties. d.WL also emerging technique. Eventual accuracy will be limited by systematic errors that are difficult to predict. If the systematic errors are at or below the level proposed by the proponents, it is likely to be the most powerful individual technique and also the most powerful component in a multi-technique program.TechniquesTechniques

70. Systematics, Systematics, Systematics Statistical+Systematics Statistical A sample WL fiducial model

71. 5.A program that includes multiple techniques at Stage IV can provide an order-of-magnitude increase in our figure-of-merit. This would be a major advance in our understanding of dark energy. 6.No single technique is sufficiently powerful and well established that it is guaranteed to address the order-of-magnitude increase in our figure-of- merit alone. Combinations of the principal techniques have substantially more statistical power, much more ability to discriminate among dark energy models, and more robustness to systematic errors than any single technique. Also, the case for multiple techniques is supported by the critical need for confirmation of results from any single method. Fifteen Findings

72. ww wawa   w ( a )  w  + w a (  a ) The ability to exclude  is better than it appears There is some z where limits on  w are better than limits on  w  Call this z p ( p = pivot) corresponding to  w p w z  wpwp zpzp w  ww

73. wpwp wawa   Our figure of merit:  ( w p )   ( w a ) w ( a )  w  + w a (  a )

74. The Power of Two (or Three, or Four) Technique A  ( w p )   ( w a )  Technique Z  ( w p )   ( w a )  Combined  ( w p )   ( w a ) 

75. 7.Results on structure growth, obtainable from weak lensing or cluster observations, are essential program components in order to check for a possible failure of general relativity. Fifteen Findings

76. 8.In our modeling we assume constraints on H  from current data and constraints on other cosmological parameters expected to come from measurement of CMB temperature and polarization anisotropies. a.These data, though insensitive to w ( a ) on their own, contribute to our knowledge of w ( a ) when combined with any of the dark energy techniques we have considered. b.Different techniques most sensitive to different cosmo. parameters. c.Increased precision in a particular cosmological parameter may benefit one or more techniques. Increased precision in a single technique is valuable for the important procedure of comparing dark energy results from different techniques. d.Since different techniques have different dependences on cosmological parameters, increased precision in a particular cosmological parameter tends to not improve the figure-of-merit from a multi-technique program significantly. Indeed, a multi-technique program would itself provide powerful new constraints on cosmological parameters. Fifteen Findings

77. 9.In our modeling we do not assume a spatially flat Universe. Setting the spatial curvature of the Universe to zero greatly helps the SN technique, but has little impact on the other techniques. When combining techniques, setting the spatial curvature of the Universe to zero makes little difference because the curvature is one of the parameters well determined by a multi-technique approach. 10.Experiments with very large number of objects will rely on photometrically determined redshifts. The ultimate precision that can be attained for photo-z’s is likely to determine the power of such measurements. Fifteen Findings

78. Our inability to forecast reliably systematic error levels is the biggest impediment to judging the future capabilities of the techniques. We need a.BAO– Theoretical investigations of how far into the non-linear regime the data can be modeled with sufficient reliability and further understanding of galaxy bias on the galaxy power spectrum. b.CL– Combined lensing and Sunyaev-Zeldovich and/or X-ray observations of large numbers of galaxy clusters to constrain the relationship between galaxy cluster mass and observables. c.SN– Detailed spectroscopic and photometric observations of about 500 nearby supernovae to study the variety of peak explosion magnitudes and any associated observational signatures of effects of evolution, metallicity, or reddening, as well as improvements in the system of photometric calibrations. d.WL– Spectroscopic observations and narrow-band imaging of tens to hundreds of thousands of galaxies out to high redshifts and faint magnitudes in order to calibrate the photometric redshift technique and understand its limitations. It is also necessary to establish how well corrections can be made for the intrinsic shapes and alignments of galaxies, removal of the effects of optics (and from the ground) the atmosphere and to characterize the anisotropies in the point-spread function.SystematicsSystematics

79. Four types of next-generation projects have been considered: a.an optical Large Survey Telescope (LST), using one or more of the four techniques b.an optical/NIR JDEM satellite, using one or more of four techniques c.an x-ray JDEM satellite, which would study dark energy by the cluster technique d.a Square Kilometer Array, which could probe dark energy by weak lensing and/or the BAO technique through a hemisphere-scale survey of 21-cm emission Each of these projects is in the $0.3-1B range, but dark energy is not the only (in some cases not even the primary) science that would be done by these projects. 13.Each of these projects considered (LST, JDEM, and SKA) offers compelling potential for advancing our knowledge of dark energy as part of a multi-technique program. The technical capabilities needed to execute LST and JDEM are largely in hand. Future Probes

80. The Stage IV experiments have different risk profiles: a.SKA would likely have very low systematic errors, but needs technical advances to reduce its cost. The performance of SKA would depend on the number of galaxies it could detect, which is uncertain. b.Optical/NIR JDEM can mitigate systematics because it will likely obtain a wider spectrum of diagnostic data for SN, CL, and WL than possible from ground, incurring the usual risks of a space mission. c.LST would have higher systematic-error risk, but can in many respects match the statistical power of JDEM if systematic errors, especially those due to photo-z measurements, are small. An LST Stage IV program can be effective only if photo-z uncertainties on very large samples of galaxies can be made smaller than what has been achieved to date. A mix of techniques is essential for a fully effective Stage IV program. No unique mix of techniques is optimal (aside from doing them all), but the absence of weak lensing would be the most damaging provided this technique proves as effective as projections suggest. Combining all information can lead to a factor of 3 improvement on w, w’ each.FindingsFindings

81. Conclusions Dark energy remarkably similar to cosmological constant, w=-1.04+/- 0.06, no evidence for w evolution or modified gravity Best constraints achieved by combining multiple techniques: this is also needed to test robustness of the results against systematics. Dark matter best described as cold and collisionless: no evidence for warm dark matter (sterile neutrinos) Neutrinos not yet detected cosmologically, but getting really close to limits from mixing experiments: unlikely to be degenerate and inverted hieararchy is mildly disfavored (at one sigma…) Future prospects: many planned space and ground based missions, this will lead to a factor of several improvements in dark energy parameters like w, w’.