Download - 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 Portsmouth

Workshop on High Energy Physics Phenomenology - Bhubaneswar

January 10, 2006

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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?

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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:

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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?

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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

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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.

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Cosmological constant Quintessence models Phantoms and ghosts Tangled defect networksTangled string or domain wall networks give very specific predictions but are effectively ruled out observationally:

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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?

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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?

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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.

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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.

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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.

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Power spectra

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

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Weighing the universe

There must be enough matter to explain the present expansion rate:

Dark energy density we’re trying to determine

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Dark matter density constraints (~25%):

• CMB Doppler peak heights

• Position of LSS turnover

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Dark matter density constraints (~20-25%):

• Baryon/dark matter ratio in x-ray clusters

• Large scale velocities, mass/light ratio

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Baryon density constraints (~4%):

• Light element abundances

• CMB Doppler peak ratios

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Photon density constraint (0.004 %):

• Observed CMB temperature

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Neutrino density constraints (< 1%):

• Small scale damping in LSS

• Overall neutrino mass limits

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Curvature of universe constraint (< 2%):

• Angular size of CMB structures

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Critical density constraint:

• Measurement of Hubble constant

• Biggest source of possible systematic errors

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Assuming value measured by Hubble Key Project, 70-75% of matter not observed.

H0 = 72+-8 km/s/Mpc

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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.

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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.

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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.

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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.

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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 dA …

if we know the curvature!

Flat Closed

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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.

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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.

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LSS as a cosmic yardstick

Imprint of oscillations less clear in LSS spectrum unless high baryon density

Detection much more difficult:

o Survey geometryo Non-linear effects

o Biasing Eisenstein et al. 98Big pay-off:

Potentially measure dA(z) at many redshifts!

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Baryon oscillations detected!

SDSS dataSDSS 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

~106 galaxies at z = 0.5-1.3, z = 2.5-3.5

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

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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.

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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.

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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

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Recent supernovae constraints

Limits on density and equation of state

Riess et al. 2004

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

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SNLS + baryon oscillations

Combining data sets indicates close to cosmological constant with about 70% of the present density.

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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.

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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.

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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.

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Cluster abundancesWe 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.

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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!

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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

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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.

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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

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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?

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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

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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 correlationcompare observed correlation to that with Monte Carlo cmb maps with WMAP power spectrum

correlation detected at 2.5-3 sigma level, very close to that expected from ISW.

dots: observed

thin: Monte Carlos

thick: ISW prediction (WMAP best fit model)

errors highly correlated

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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.)

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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.

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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.

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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.

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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 < -0.8. 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 prospectsMicrowave background

Future WMAP dataPlanckQUAD, other polarized CMB missions

Large scale structureSloan DSSDark Energy Survey, SALT?Lyman alpha studiesDEEP2Astro-FKAOS, LSST, SKA

SupernovaeNearby SN factorySNLS, Essence w-projectSDSSSNAP/JDEM

SZ clustersAMIAmibaOCRAPlanckSouth Pole Telescope

Weak lensingMegacamDarkCam (VISTA)PanSTARRS, LSSTJDEMDUNE

X-ray clustersXMM Cluster surveyMACSREFLEX2DUET

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Avoiding dark energyBlanchard 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 dataTo fit the remaining data, they must Add a particular feature to the primordial spectrum Add a massive neutrino to suppress small scale powerAny one of these is very reasonable, but it is difficult to justify all of them.

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CMB frequency dependence

X-ray and radio cross correlations for ILC and various WMAP bands

There appears to be no strong frequency dependence

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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

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2MASS data

Afshordi, Loh & Strauss

Near infrared

Full sky, but low redshift

2.5 sigma detection of ISW

3+ detection of SZ

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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!!!

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radio cmb correlation

dots: observed

thin: Monte Carlos

thick: ISW prediction (WMAP best fit value)

errors highly correlated

Radio galaxies are also correlated at 2.0-2.5 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.)

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SDSS data (Scranton et al.)

Luminous red galaxies

3400 square degrees

Significant (>90%) detections in all bands

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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

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Bennett et al comparison

Differences appear fairly consistent with COBE noise level, apart from near galaxy

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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 53 + 90 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?

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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

08.0/ 222 ≈× earlyiswCCC

Highest correlations are for the quadrupole, but it is still very weak

isw fluctuations are basically uncorrelated with those produced earlier

Download - 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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