1 Observational constraints on dark energy Robert Crittenden Institute of Cosmology and Gravitation University of Portsmouth Workshop on High Energy Physics.

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  • Observational constraints on dark energy Robert Crittenden Institute of Cosmology and GravitationUniversity of PortsmouthWorkshop on High Energy Physics Phenomenology - Bhubaneswar January 10, 2006

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

  • 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:

  • What drives the acceleration?Cosmological constantQuintessence 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?

  • Myriad of Quintessence modelsThe 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

  • What drives the acceleration?Cosmological constantQuintessence modelsPhantoms 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.

  • What drives the acceleration?Cosmological constantQuintessence modelsPhantoms and ghostsTangled defect networksTangled string or domain wall networks give very specific predictions but are effectively ruled out observationally:

  • What drives the acceleration?Cosmological constantQuintessence modelsPhantoms and ghostsTangled defect networksModification of gravity on large scalesMany possible ideas:Branes, Brans-Dicke theories, MOND, backreaction of fluctuations?

  • What drives the acceleration?Cosmological constantQuintessence modelsPhantoms and ghostsTangled defect networksModification of gravity on large scalesWhat can the observational data tell us about the dark energy properties: its density, evolution and clustering?

  • 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.

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

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

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

  • Weighing the universeThere must be enough matter to explain the present expansion rate:Dark energy density were trying to determine

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

  • Weighing the universeThere 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

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

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

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

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

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

  • Weighing the universeThere must be enough matter to explain the present expansion rate:Assuming value measured by Hubble Key Project, 70-75% of matter not observed.H0 = 72+-8 km/s/Mpc

  • 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.

  • Evolution of the expansion rateCosmic clocksAge 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.

  • Evolution of the expansion rateCosmic clocksCo-moving volumeIf 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.

  • Evolution of the expansion rateCosmic clocksCo-moving volumeAngular distance relationAngular size of distant objects can tell you how far away they are: Requires large yardstick of known size.

  • 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 spectraGiven and its angular size, we can find dA if we know the curvature!FlatClosed

  • CMB as cosmic yardstickWMAP compilationAngular distance to last scattering surfaceBoth 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.

  • CMB angular distanceDegeneracy 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 positionLewis & Bridle 03 MCMC resultsSmall amount of curvature keeps peak position unchangedSingle integrated constraint on w and present density from the shape of CMB spectrum: w < -0.8.

  • LSS as a cosmic yardstickImprint of oscillations less clear in LSS spectrum unless high baryon densityDetection much more difficult:Survey geometryNon-linear effectsBiasing

    Eisenstein et al. 98Big pay-off:Potentially measure dA(z) at many redshifts!

  • Baryon oscillations detected!SDSS dataSDSS and 2dF detect baryon oscillations at 3-4 sigma level. SDSS detection in LRG sample z ~ 0.35Thus far, fairly weak constraints on equation of state.Future: many competing surveysKAOS - Kilo-Aperture Optical Spectrograph, SKA~106 galaxies at z = 0.5-1.3, z = 2.5-3.5

  • Evolution of the expansion rateCosmic clocksCo-moving volumeAngular distance relationAlcock-Paczynski testsCompare dimensions of objects parallel and perpendicular to the line of sight and ensure that they are the same on average.

  • Evolution of the expansion rateCosmic clocksCo-moving volumeAngular distance relationAlcock-Paczynski testsLuminosity distance relationUse supernovae (or perhaps GRBs) as standard candles and see how their brightness changes with their redshift.

  • Recent supernovae constraintsGold 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 universeRiess et al. 2004

  • Recent supernovae constraintsLimits on density and equation of state Riess et al. 2004

  • SNLS resultsNew independent sample of 71 supernovae Astier et al. 2005

  • SNLS + baryon oscillationsCombining data sets indicates close to cosmological constant with about 70% of the present density.

  • Growth rate of structureAccelerated expansion makes gravitational collapse more difficultNormalized to present, dark energy implies fluctuations were higher in the pastThis ignores d.e. clustering, reasonable on small scales.

  • Probes of (z)

    Difficult to measure, even its present value (parameterized in 8) is subject to some debate (0.6 - 1.0?).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.

  • Cluster abundancesIf 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.

  • Cluster abundancesWe can observe these in x-rays or the CMB via the Sunyaev-Zeldovich effect. XCS clusters from K. RomerNormalizing to the present, a dark energy dominated universe will have many more objects at high redshifts. Unfortunately, we dont measure the masses directly, which can complicate the cosmological interpretation.

  • Probes of (z)

    Difficult to measure, even its present value (parameterized in 8) is subject to some debate (0.6 - 1.0?).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!

  • 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 densitypotential depth changes as cmb photons pass through

  • Two uncorrelated CMB mapsISW map, z< 4 Mostly large scale featuresEarly map, z~1000 Structure on many scalesThe 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.

  • large scale correlationsOn 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 scalesWMAP 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 seenwhy might this be? cosmic variance no ISW, still matter dominated accidental cancellation drop in large scale power simple adiabatic scenario wrong

  • Correlations with the galaxy distributionThe 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?

  • cmb skyWMAP internal linear combination map (ilc)also Tegmark, de Oliveira-Costa & Hamilton map(no significant differences in resulting correlations)

    WMAPGalactic plane, centre removedmost aggressive WMAP masking68% of skydominant source of noise to cross correlation is accidental correlations of cmb map with other mapsS. Boughn, RC 2004

  • hard x-ray backgroundHEAO-1 x-ray satelliteRemoved nearby sources:Cuts (leaving 33% of sky): Galactic plane, centre removed brightest point sources removedFits: monopole, dipole detector time drift Galaxy local supercluster3 degree resolution3-17 keVsFlown in 1970sVirtually all visible structures cleaned out

  • x-ray cmb correlationcompare observed correlation to that with Monte Carlo cmb maps with WMAP power spectrumcorrelation detected at 2.5-3 sigma level, very close to that expected from ISW. dots: observed thin: Monte Carlosthick: ISW prediction (WMAP best fit model)errors highly correlated

  • Correlations seen in many frequencies! X-ray backgroundRadio 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.)

  • 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 (cs ~ 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.

  • dark energy sound speedThe isw contribution with and without including clustering of dark energy (Weller & Lewis 03)The ISW signal can reflect the clustering of dark energyThe 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.

  • 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 redsh...