State of the (dark) universe report Uros Seljak Zurich/ICTP/Princeton Heidelberg, november 7, 2006 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? Context 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 L). 3. Possibility: Dark Energy varies with time (or redshift z or a = (1+z)-1). 4. Impact of dark energy can be expressed in terms of “equation of state” w(a) = p(a) / r(a) with w(a) = -1 for L. 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. How to test dark energy/matter? 1) Classical tests: redshift- luminosity distance relation (SN1A etc), redshift- angular diameter distance, redshift- Hubble parameter relation Classical cosmological tests (in a new form) Friedmann’s (Einstein’s) equation 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 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… 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 Scale dependence of cosmological probes WMAP z 1088 CBI ACBAR Lyman alpha forest z 0 z 3 SDSS Complementary in scales and redshift Sound Waves from the Early Universe Before recombination: – Universe is ionized. After recombination: – Photons provide enormous – Universe is neutral. pressure and restoring force. – Photons can travel freely past – Perturbations oscillate as the baryons. acoustic waves. – Phase of oscillation at trec affects late-time amplitude. Same Initial Maximal Effect Amplitude Phase Time Minimal Effect Recombination This is how the Wilkinson Microwave Anisotropy Probe (WMAP) sees the CMB Determining Basic Parameters Angular Diameter Distance w = -1.8,..,-0.2 When combined with measurement of matter density constrains data to a line in Wm-w space Determining Basic Parameters Matter Density Wmh2 = 0.16,..,0.33 Determining Basic Parameters Baryon Density Wbh2 = 0.015,0.017..0.031 also measured through D/H Current 3 year WMAP analysis/data situation Current data favor the simplest scale invariant model 400,000 galaxies with redshifts Galaxy and quasar survey Sloan Digital Sky Survey (SDSS • 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 deg2 of imaging data, 40 million galaxies • 400,000 spectra (r<17.77 main sample, 19.1 QSO,LRG) Image Credit: Sloan Digital Sky Survey Galaxy power spectrum: shape analysis Galaxy clustering traces dark matter on large scales Nonlinear 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) Are galaxy surveys consistent with each other? Some claims that SDSS main sample gives more than 2 sigma larger value of W Fixing h=0.7 SDSS LRG photo 2dF SDSS main spectro Bottom line: no evidence for discrepancy, new analyses improve upon SDSS main 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 A Standard Ruler • The acoustic oscillation scale depends on the matter-to- radiation ratio (Wmh2) and the baryon-to-photon ratio (Wbh2). • The CMB anisotropies measure these and fix the oscillation scale. dr = DAdq dr = (c/H)dz • In a redshift survey, we can measure this along and across the line of sight. • Yields H(z) and DA(z)! Observer 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 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 to >-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 Weak Gravitational Lensing Distortion of background images by foreground matter Unlensed Lensed Weak Lensing: Large-scale shear Convergence Power Spectrum 1000 sq. deg. to R ~ 27 Huterer Gravitational Lensing Refregier et al. 2002 – Advantage: directly measures mass – Disadvantages • Technically more difficult • Only measures projected mass- distribution • Intrinsic alignments? Tereno et al. 2004 Shear-intrinsic (GI) correlation Hirata and US 2004 • 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 Lensing shear Tidal stretch Intrinsic correlations in SDSS Mandelbaum, Hirata, Ishak, US etal 2005 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 Implications for future surveys Mandelbaum etal 2005, Hirata and US 2004 Up to 30% for shallow survey at z=0.5 10% for deep survey at z=1: current surveys underestimate s8 More important for cross-redshift bins Galaxy bias determination Pgg (k ) b (k ) = 2 Pdm (k ) •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 s 8 •High accuracy determination of s is 8 important for dark energy constraints •Weak lensing is the most direct method 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… 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 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 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 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) •2.5 sigma detection QuickTime™ an d a TIFF (LZW) decomp resso r are need ed to see this picture. QuickTime™ an d a TIFF (LZW) decomp resso r are need ed to see this picture. Consistent with other probes 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 r HI r gas 2 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 kF) Fully specified within the model, no bias issues 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 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 Putting it all together Dark matter fluctuations on US etal 04, 06 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 QuickTime™ and a TIFF (Uncompressed) decompre ssor are neede d to see this picture. 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. Dark energy constraints: complementarity of tracers US, Slosar, McDonald 2006 DE constraints: degeneracies and dimension of parameter space Time evolution of equation of state w Individual parameters very degenerate 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 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) • look at Agreat importance in neutrinos Neutrino mass is of 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 New limits on neutrino mass • WMAP3+SDSS Lya+SDSS+2dF+SN 6p: • Together with SK and solar limits: • Lifting the degeneracy of neutrino mass 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, Q<0.001, never thermalized 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) 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 Future as seen by the dark side • Membersof the universe task force 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 Techniques 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. Systematics 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. Future Probes 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. Findings 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. 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’.
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