1 Observational constraints on dark energy Robert Crittenden Institute of Cosmology and Gravitation University of Portsmouth Workshop on High Energy Physics Phenomenology - Bhubaneswar January 10, 2006

2 SN: fainter than expected! Is this because the universe is accelerating or due to a systematic? Dust, lensing, evolution Confirmed by many varied observations What drives it? “Dark energy” What might this dark energy be and how can we learn about it?

3 What drives the acceleration? Cosmological constant Introduced by Einstein to make a static universe. Associated with a vacuum energy density, typically It could be the Planck mass, or the super-symmetry or electro-weak breaking mass scale, but it is BIG. Constant in space and time. Equation of state:

4 What drives the acceleration? Cosmological constant Quintessence models Motivated by models of inflation. Scalar field rolling down shallow potential well. Equation of state varies: Smooth on small scales by repulsion, but clusters on scales larger than dark energy sound horizon scale. Naturalness issues: Why now?

5 Myriad of Quintessence models The equation of state is dynamic and depends on the precise choice of potential. Fundamental physics has not determined the functional form of the potential, much less the specific parameters. Like inflation, no preferred model! Albrecht & Weller

6 What drives the acceleration? Cosmological constant Quintessence models Phantoms and ghosts Any equation of state, Can lead to ‘Big Rip’ divergences in finite times. Violates weak and dominant energy conditions, and has negative energy states. Classical and quantum instabilities. Very difficult to find a working physical model.

7 What drives the acceleration? Cosmological constant Quintessence models Phantoms and ghosts Tangled defect networks Tangled string or domain wall networks give very specific predictions but are effectively ruled out observationally:

8 What drives the acceleration? Cosmological constant Quintessence models Phantoms and ghosts Tangled defect networks Modification of gravity on large scales Many possible ideas: Branes, Brans-Dicke theories, MOND, backreaction of fluctuations?

9 What drives the acceleration? Cosmological constant Quintessence models Phantoms and ghosts Tangled defect networks Modification of gravity on large scales What can the observational data tell us about the dark energy properties: its density, evolution and clustering?

10 Expansion rate H(z)  We have no evidence that dark energy interacts other than gravitationally.  It is believed to be smooth on small scales.  Thus, virtually our only handle on its nature is through its effect on the large scale expansion history of the universe, described by the Hubble parameter, H(z), and things which depend on it.

11 Observable effects of dark energy 1. It contributes to the present energy density and thus to the Hubble expansion rate. 2. It contributed to the past expansion rate, so affects the distance and time measurements to high redshifts. 3. It affects the growth rate of dark matter perturbations in two ways: o A faster expansion rate in the past would have made it harder for objects to collapse. o On large scales, the dark matter reacts to the perturbations in the dark energy.

12 CMB and large scale surveys What can these tell us about dark energy? Virtually all of the information is in their two point correlations, with themselves and with each other.

13 Power spectra These spectra describe the statistical properties of the maps and their features contain a great deal of information about the universe.

14 Weighing the universe There must be enough matter to explain the present expansion rate: Dark energy density we’re trying to determine

15 Weighing the universe There must be enough matter to explain the present expansion rate: Dark matter density constraints (~25%): CMB Doppler peak heights Position of LSS turnover

16 Weighing the universe There must be enough matter to explain the present expansion rate: Dark matter density constraints (~20-25%): Baryon/dark matter ratio in x-ray clusters Large scale velocities, mass/light ratio

17 Weighing the universe There must be enough matter to explain the present expansion rate: Baryon density constraints (~4%): Light element abundances CMB Doppler peak ratios

18 Weighing the universe There must be enough matter to explain the present expansion rate: Photon density constraint (0.004 %): Observed CMB temperature

19 Weighing the universe There must be enough matter to explain the present expansion rate: Neutrino density constraints (< 1%): Small scale damping in LSS Overall neutrino mass limits

20 Weighing the universe There must be enough matter to explain the present expansion rate: Curvature of universe constraint (< 2%): Angular size of CMB structures

21 Weighing the universe There must be enough matter to explain the present expansion rate: Critical density constraint: Measurement of Hubble constant Biggest source of possible systematic errors

22 Weighing the universe There must be enough matter to explain the present expansion rate: Assuming value measured by Hubble Key Project, 70-75% of matter not observed. H 0 = km/s/Mpc

23 Evolution of the expansion rate H(z) Evolution of dark energy determined by its equation of state: While the dark energy density is larger than the other components, it can be constrained by measuring the evolution of H(z). Changing H(z) effects distances and times to high redshifts.

24 Evolution of the expansion rate Cosmic clocks Age of objects, now and at high redshifts: Weak constraints from globular cluster ages. Use luminous red galaxies as clocks if they evolve passively? Not all formed at the same time, so requires many high redshift galaxies to find the oldest.

25 Evolution of the expansion rate Cosmic clocks Co-moving volume If objects have constant co-moving density, then their number counts can constrain the expansion evolution Requires many high redshift galaxies and no density evolution. Constraints from strong gravitational lensing.

26 Evolution of the expansion rate Cosmic clocks Co-moving volume Angular distance relation Angular size of distant objects can tell you how far away they are: Requires large yardstick of known size.

27 The baryon yardstick Before electrons and protons combined, they were tightly coupled to photons and so the density fluctuations oscillated acoustically. The largest scales which had time to compress before recombination were imprinted on the CMB and LSS power spectra Given  and its angular size, we can find d A … if we know the curvature! FlatClosed

28 CMB as cosmic yardstick WMAP compilation Angular distance to last scattering surface Both the curvature and the dark energy can change the scale of the Doppler peaks. We used the position of the Doppler peaks to determine the curvature, assuming a cosmological constant. However, if we assume a flat universe, we can turn this around to find a constraint on the equation of state.

29 CMB angular distance Degeneracy needs to be broken by other data, like Hubble constant or SN data. Present data is consistent with w=-1, so we cannot change w too much, unless we compensate it by changing the curvature. Flat universe Recall DE slightly changes peak position Lewis & Bridle 03 MCMC results Small amount of curvature keeps peak position unchanged Single integrated constraint on w and present density from the shape of CMB spectrum: w < -0.8.

30 LSS as a cosmic yardstick Imprint of oscillations less clear in LSS spectrum unless high baryon density Detection much more difficult: o Survey geometry o Non-linear effects o Biasing Eisenstein et al. 98 Big pay-off: Potentially measure d A (z) at many redshifts!

31 Baryon oscillations detected! SDSS data SDSS and 2dF detect baryon oscillations at 3-4 sigma level. SDSS detection in LRG sample z ~ 0.35 Thus far, fairly weak constraints on equation of state. Future: many competing surveys KAOS - Kilo-Aperture Optical Spectrograph, SKA ~10 6 galaxies at z = , z =

32 Evolution of the expansion rate Cosmic clocks Co-moving volume Angular distance relation Alcock-Paczynski tests Compare dimensions of objects parallel and perpendicular to the line of sight and ensure that they are the same on average.

33 Evolution of the expansion rate Cosmic clocks Co-moving volume Angular distance relation Alcock-Paczynski tests Luminosity distance relation Use supernovae (or perhaps GRB’s) as standard candles and see how their brightness changes with their redshift.

34 Recent supernovae constraints ‘Gold’ data has best 150 SN and includes high redshift SN discovered with the Hubble telescope. Rules out ‘grey’ dust models. Residuals relative to an empty universe Riess et al. 2004

35 Recent supernovae constraints Limits on density and equation of state Riess et al. 2004

36 SNLS results New independent sample of 71 supernovae Astier et al. 2005

37 SNLS + baryon oscillations Combining data sets indicates close to cosmological constant with about 70% of the present density.

38 Growth rate of structure Accelerated expansion makes gravitational collapse more difficult Normalized to present, dark energy implies fluctuations were higher in the past This ignores d.e. clustering, reasonable on small scales.

39 Probes of  (z) Difficult to measure, even its present value (parameterized in  8 ) is subject to some debate ( ?). CMB amplitude provides early point of reference. Gravitational lensing (Jain talk.) Evolution of galaxy clustering, though tied up with bias! Controls the number of collapsed objects, like clusters.

40 Cluster abundances If the statistics are Gaussian, the number of collapsed objects above a given threshold depends exponentially on the variance of the field. Press-Schecter Thus, the growth factor controls the number of clusters at a given redshift.

41 Cluster abundances We can observe these in x-rays or the CMB via the Sunyaev-Zeldovich effect. XCS clusters from K. Romer Normalizing to the present, a dark energy dominated universe will have many more objects at high redshifts. Unfortunately, we don’t measure the masses directly, which can complicate the cosmological interpretation.

42 Probes of  (z) Difficult to measure, even its present value (parameterized in  8 ) is subject to some debate ( ?). CMB amplitude provides early point of reference. Gravitational lensing (Jain talk.) Evolution of galaxy clustering, though tied up with bias! Controls the number of collapsed objects, like clusters. Induces very recent CMB anisotropies!

43 Recent CMB anisotropies While most CMB fluctuations are created at last scattering, some can be generated at low redshifts gravitationally via the ISW (linear) and Rees-Sciama (non-linear) effects: The potential is constant for a matter dominated universe, but begins to evolve when the two dark energy effects modify the growth rate of the fluctuations. gravitational potential traced by galaxy density potential depth changes as cmb photons pass through

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

45 large scale correlations On small scales, positive and negative ISW effects will tend to cancel out. This leads to an enhancement of the large scale power spectrum The early and late power is fairly weakly correlated, so the power spectra add directly: ISW fluctuations tend to be on the very largest scales WMAP best fit scale invariant spectrum

Observing the ISW effect in the cmb map, additional anisotropies should increase large scale power Not observed in WMAP data In fact, decrease is seen why might this be? cosmic variance no ISW, still matter dominated accidental cancellation drop in large scale power simple adiabatic scenario wrong

47 Correlations with the galaxy distribution The gravitational potential determines where the galaxies are and where the ISW fluctuations are created! Thus the galaxies and the CMB should be correlated. 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?

48 cmb sky WMAP internal linear combination map (ilc) also Tegmark, de Oliveira-Costa & Hamilton map (no significant differences in resulting correlations) WMAP Galactic plane, centre removed most aggressive WMAP masking 68% of sky dominant source of noise to cross correlation is accidental correlations of cmb map with other maps S. Boughn, RC 2004

49 hard x-ray background HEAO-1 x-ray satellite Removed nearby sources: Cuts (leaving 33% of sky): Galactic plane, centre removed brightest point sources removed Fits: monopole, dipole detector time drift Galaxy local supercluster 3 degree resolution 3-17 keV’s Flown in 1970’s Virtually all visible structures cleaned out

x-ray cmb correlation compare observed correlation to that with Monte Carlo cmb maps with WMAP power spectrum correlation detected at sigma level, very close to that expected from ISW. dots: observed thin: Monte Carlos thick: ISW prediction (WMAP best fit model) errors highly correlated

51 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.)  FIRST radio galaxy survey (Boughn & student) Infrared galaxies:  2MASS near infrared survey (Afshordi et al.) Optical galaxies:  APM survey (Folsalba and Gaztanaga)  Sloan Digital Sky Survey (Scranton et al., FGC)  Band power analysis of SDSS data (N. Pamanabhan, et al.)

52 Dark energy clustering and  (z) The ISW probes the fluctuations on very large scales, where we cannot ignore the clustering of dark energy: If it is not a cosmological constant, the dark energy clusters on large scales, while remaining smooth on smaller scales. The dark energy sound horizon divides smooth and clustered regimes; quintessence type models have large sound speeds (c s ~ 1) and the transition occurs near the horizon scale, but it can be smaller. Failing to include the clustering makes a big difference in ISW predictions. If the sound speed is large, the ISW effect is one of the few ways we can see its affects.

53 dark energy sound speed The isw contribution with and without including clustering of dark energy (Weller & Lewis 03) The ISW signal can reflect the clustering of dark energy The ISW signal changes dramatically when dark matter clustering is included (Caldwell, Dave & Steinhardt; Bean & Dore; Hu & Scranton) Without clustering, dark energy increases the ISW effect, since the dark energy becomes important earlier However, the dark energy clustering helps aids the collapse of dark matter, which suppresses the ISW effect.

54 ISW summary  Independent confirmation of need for dark energy.  Many observations at 2-3  level in many frequencies, but these are not entirely independent -- same CMB sky!  All consistent with predictions for cosmological constant model, given uncertainties in source redshift distributions.  Ideally want surveys with full sky coverage and known source distribution in redshift out to z ~ 2-3 (depending on dark energy model.)  Fundamentally limited by `noise’ of CMB, 7-10  level.  Potentially only probe of dark energy sound speed.

55 Conclusions Probing the expansion history and growth of density perturbations illuminate different aspects of dark energy: its density, equation of state, and sound speed. Many independent indications that dark energy is 70-80% of critical density and w < Everything we have seen seems consistent with a cosmological constant. Improvements are expected on many fronts, particularly as large scale structure observations get bigger and better.

Future prospects Microwave background Future WMAP data Planck QUAD, other polarized CMB missions Large scale structure Sloan DSS Dark Energy Survey, SALT? Lyman alpha studies DEEP2 Astro-F KAOS, LSST, SKA Supernovae Nearby SN factory SNLS, Essence w-project SDSS SNAP/JDEM SZ clusters AMI Amiba OCRA Planck South Pole Telescope Weak lensing Megacam DarkCam (VISTA) PanSTARRS, LSST JDEM DUNE X-ray clusters XMM Cluster survey MACS REFLEX2 DUET

57 Avoiding dark energy Blanchard et al have investigated what is necessary to have a cosmological model without dark energy. Briefly, they must discard: Hubble constant measurements High redshift SN observations Baryon oscillation data ISW correlations Strong gravitational lensing data To fit the remaining data, they must Add a particular feature to the primordial spectrum Add a massive neutrino to suppress small scale power Any one of these is very reasonable, but it is difficult to justify all of them.

58 CMB frequency dependence X-ray and radio cross correlations for ILC and various WMAP bands There appears to be no strong frequency dependence

59 How good will it get? 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 Peires & Spergel 2000 For the favoured cosmological constant the best signal to noise one can expect is about 7.

could it be a foreground? insensitive to level of galactic cuts insensitive to point source cuts comparable signal in both hemispheres correlation on large angular scales in addition, the contribution to the correlation from individual pixels is consistent with what is expected for a weak correlation NOT dominated by a few pixels blue: product of two Gaussians red: product of two weakly correlated Gaussians

61 2MASS data Afshordi, Loh & Strauss Near infrared Full sky, but low redshift 2.5 sigma detection of ISW 3+ detection of SZ

62 radio galaxies NRAO VLA Sky Survey (NVSS) flux limited at 1.4 GHz 82% of the sky 1.8 million sources 50 per square degree nearby objects and Galaxy removed (leaving 56% of sky) declination dependent banding corrected redshift distribution somewhat uncertain correlated with x-rays!!!

63 radio cmb correlation dots: observed thin: Monte Carlos thick: ISW prediction (WMAP best fit value) errors highly correlated Radio galaxies are also correlated at sigma level, again consistent with ISW origin Not independent of x-ray signal, but agreement suggests its not due to systematic of maps Independent WMAP analysis confirmation (Nolta et al.)

64 SDSS data (Scranton et al.) Luminous red galaxies 3400 square degrees Significant (>90%) detections in all bands

65 Signal to Noise (S/N) 2 as a function of redshift and wavenumber (Afshordi 04) A good fraction of the signal comes from low redshifts, so a signal is possible with low redshift surveys

66 Bennett et al comparison Differences appear fairly consistent with COBE noise level, apart from near galaxy

67 COBE WMAP comparison Why wasn’t a correlation seen using the COBE map? This was previously used to put bounds on a cosmological constant COBE map was used to minimize detector noise, but still most of the pixel variance was noise Correlations seem to agree on large scales, but cosmic variance is large there. Cosmic variance is smallest at small separations, but noise is largest Were we just unlucky that the noise cancelled the correlations?

68 isw vs anisotropies from last scattering The quadrupole primarily arises from modes on the scale of the horizon The ISW anisotropies are created nearer to us, and are generated by smaller modes (larger wave number) Contribution to the quadrupole power as a function of wave number, the oscillations at high k alternatively constructively or destructively interfere, effectively cancelling out Highest correlations are for the quadrupole, but it is still very weak isw fluctuations are basically uncorrelated with those produced earlier