jigsaw-07 @ tifr, feb 19 th 2007 observational probes of dark energy subha majumdar tata institute...

JIGSAW-07 @ TIFR , Feb 19th 2007

Observational Probesof

Dark Energy

Subha MajumdarTata Institute of Fundamental Research

Mumbai


Multiple Observations show that Dark + Visible matter is NOT enough. There is ‘SOMETHING ELSE’Within standard cosmological framework, this must be due to substance that behaves as if it has negative pressure. [Eqn of state w(a) = w0 + w1(1-a) ] This has been termed DARK ENERGY.

Is there Dark Energy?


What do current data tell us about DE?

Wang & Mukherjee 2006

Consistent with However, doesn’tconstrain w(a)

Spergel etal 2006


So what are the (theoretical) So what are the (theoretical) possibilties?possibilties?So what are the (theoretical) So what are the (theoretical) possibilties?possibilties?

Possibility 1: Universe permeated by energy density, constant in time

and uniform in space (Einstein’s ).

Possibility 2: DE some kind of ‘unknown’ dynamical fluid. Its eqn of state

varies with time (or redshift z or a (z)).

Impact of DE (or different theories) can be expressed

in terms of different “evolution of equation of state” w(a) p(a) / (a) with w(a) for

Possibility 3: GR or standard cosmological model incorrect.

Current observations cannot distinguish between Options 1,2 or 3 !!Lecture

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Lecture

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What are the “Observational” possibilities? Dark Energy and Cosmology..

• DE alters the evolution of the Hubble Expansion H(z) through the Friedman eqn.

-This then modifies the distance to an object

( SNe, galaxy correlations)

• It alters the evolution of g(z), the growth function of structures, through the perturbation eqn.

-large scale structures are sensitive to both g(z) and H(z)


How does DE come into play in observations: (A Hasty Primer)

Expansion history H(z) : written in terms of energy density of each component

In GR, scale factor a(t) describes growthof Universe. We know the time evolutionof a(t) H(a)

This holds for each component


Standard measures : Distance (or co-ordinate) to source at z

r(z) can be connected to observables

Standard Candle : apparentflux to standard flux

Standard Ruler: apparentangular size to real physicalsize

Standard density:


Growth of structures...Static Universe – exponential growth of structures!Expanding Universe – struggle between gravitational collapse and expansion. (DE more recent expansion)

reln between expansionand growth factor g(z)

CMB fixes amplitude of matter fluctuations at z~1100. Thisis seen at low redshift coupled to g(z).

Within GR, the above diffn reln provides ‘one-to-one’ relnbetween two observables : D(z) & g(z). Any inconsistencywould mean either GR is failing at largest scales.


Effect of DE on D(z) and g(z)


And the probes are: And the probes are:

Supernovaemeasure flux and redshift of Type Ia SNe.

Baryon Acoustic Oscillations measure features in distribution of galaxies.

Clustersmeasure spatial distribution of galaxy clusters.

Weak Lensingmeasure distortion of background images due to gravitational

lensing.

Plus : CMB peaks, ISW effect, GRB’s as standard sirens, Lookback time, Alcock-Paczynski test.


Probe 1

SUPERNOVAE(standard candles)


Supernovae as Standard Candles..• Standard candles – Their intrinsic luminosity known.

• Their apparent luminosity can be measured.

• The ratio of the two can provide the luminosity-distance (dL) of the supernova

• The red shift z can be measured independently from spectroscopy

• Finally, one can obtain dL (z) or equivalently the magnitude(z) and draw a Hubble diagram presence of DE makes distant SNe appear fainter.


Evidence for DE. Well tested method.

Main concern: progenitors‘may’ evolve systematically withredshift.


Supernova systematics...For SNe to be good cosmological standard candles

1) need for “standard” candle: need to have 1% control1) need for “standard” candle: need to have 1% controlover luminosity evolution over luminosity evolution careful spectroscopy careful spectroscopy

2) Other corrections like gravitational lensinggravitational lensing, dust etc.dust etc.

This will require thousands of SNe with at least hundreds of SNe Ia at z>1z>1.

Difficult to do spectroscopy on all of them. So will have select SNe Type Ia from imaging surveys (look at similar galaxies at diff z’s)


Probe 2

Baryon Accoustic Oscillations

(BAO standard rulers)


Connecting CMB to Matter...The same physical processes affect both the CMB and the matter power spectrum.

M White 2005

From galaxy catalog, it is possible to extract the matter power spectrum.

structures grow


Prior to recombination, there is tight coupling between matter & radiation.this imprints a characteristic oscillation scale on the power spec (gravitational compression balanced by radiation pressure)The acoustic waves are frozen at recombination.

The characteristic scale is given by distance sound could travel beforerecombination (the CMB peaks).gives a preferred scale at the matter distribution.

The matter perturbations grow to give large scale structure (distribution ofgalaxies). the scale is imprinted in the ‘correlation function’ of these galaxies.

Combined with CMB data, we get the “standard rulers”(Eisenstein & Hu 1998, Blake & Glazebrook 2003)

The ratio along transverse direction gives dA(z) and in radial gives H(z)

Recap: where does BAO come from?


BAO has been detected:

Eisenstein et al. (2005)SDSSCole et al. (2005) 2DFGRS


Example of how well we aim to detect BAO...


BAO cons and pros...• To exploit full potential of BAO, must resolve radial direction

necessary to get spectroscopic redshifts. If only photometric redshifts, then one has to cover 20 X area! (Blake & Bridle, 2005)

• To get correlation need wide survey. To get more peaks, need deep survey. So expensive in terms of observing time.

• Need to understand galaxy formation and evolution. Need for simulations at % level to see if BAO is fully there at non-linear scales (overcoming bias, redshift space distortion). (White 2005).

Improvement of theoretical/simulation predictions to 1% level.

• Since H(z) is derivative of dA(z) measuring both gives internal consistency check

• Also measuring both, breaks degeneracy between DE & curvature.


Comment: BAO is also possible with clusters or Lyman alpha P(k)

Example from simulation (Angulo etal 2005)


Probe 3

Cluster Surveys(redshift counts but BAO is

also possible)


Clusters in simulations/theory?

• A large peak in the dark matter density

• Mass defined (for example) as total mass within R200, where mean overdensity is 200 times the critical density => M200

Springel et al. 2001

R200


Ensemble of clusters from Simulations:

Universality when written in terms M

Press-Schecter form, theoretical(since 1976)

Seth-Tormen: ellipsoidal collapse & Nbody

Jenkins etal, bestfit to simulationsAlso Warren etal, Lukic etal latest.


DE affects cluster redshift distribution...

lim

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zMdndMzd

zHc

dzd

dn

• Increasing w keeping WE fixed has following effects:

– It decreases volume.

It decreases growth rate of density perturbations.

Detect clusters + z


Chandra Image of Zw38

How are ‘real’ clusters ?

Large peak in matter density– Dark matter clump (~80%

of mass)– Many luminous galaxies

(~2%: 10% of baryons)• BCG and red sequence

• Additional galaxies

• Diffuse light

– Hot gas (~18%: 90% of baryons)

• Emits X-rays

• Causes SZ decrement in microwave background

Carlstrom et al. 2002


Cluster systematics – Where your boon is your bane!

Mass function exponentially sensitive to mass

Observables translates to masses through simple observed/theoretical scaling relation

Error in translation can ruin use of clusters as DE probes. Way to go: Need thousands of clusters to calibrate out uncertainties or nuisance

parameters 1) Self-Calibration (SM & Mohr 2004, Hu 2004)

Many methods have now been suggested. Recently demonstrated with RCS clusters.

2) Have unbiased mass followup calibration (SM & Mohr 2003, Hoekstra 2007)

In general cosmology and gastrophysics degeneracies


Systematics in cluster probes of DE...

cosmologicalastrophysical

uncertain evolution M-Flux


Need for extra information..

CMB is neededHigh-z obs needed, training set


Probe 4

Weak Lensing Surveys


Foreground mass will lense background light...

Abell 2218: A Galaxy Cluster Lens, Andrew Fruchter et al. (HST)


Weak Gravitational Lensing

Distortion of background images by foreground matter

Unlensed LensedCredit: SNAP WL group


• Method : statistical study of distortion patter induced in the shape of bkg galaxies and the change in their surface density/magnification, due to foreground large scale structure.

• The signal is sensitive to geometry of the Universe, growth of structure and source distribution.

• Already Done: measure 2-D projection of the lensing signal or shear maps (ex- Hoekstra etal 2005).

• In Future : Weak Lensing Tomography: compare observed cosmic shear correlations using photometric redshifts of lensed galaxies with theoretical/numerical predictions to measure g(z) [Wittman et al. 2000, Hu 2002] . Also, WL Cross-Correlation Cosmography measure the relative shear signals of galaxies at different distances for the same foreground mass distribution: gives distance ratios that can be used to obtain H(z) [Jain & Taylor 2003]

How to constrain ‘w’ ?


Systematics ...– Advantage: directly measures mass (no assumption of mass-to-light

relation). Also relatively easy to simulate (only DM sims)

– Disadvantages• Technically more difficult : to achieve precise statistical accuracy,

systematics must be controlled at the % level!

1) for measuring shapes, low “seeing” needed ( < 0.9 arc sec)

2) weak lensing distortions are needed to be measured at 1% level at arc min scales to 0.1% level at degree scales. accurate knowledge of instrument distortion.

3) Great photo –z calibration needed ( roughly 1% in random error and systematic bias) of million plus galaxies To do this training set of 104 galaxy spectroscopy needed.

• Depends crucially on background galaxy distribution modeling

4) Need to tackle instrinsic alignment of the the bkg galaxies.

5) In theory, need to accurately model non-linearities and baryonic physics at 1-2% levelTereno et al. 2004


DE-’s degeneracies...

Hannestad, Tu, Wong 2006

Present

Future

Spergel etal 2006


Future Dark Energy Surveys :• Essence (2002-2007): 200 SNe Ia, 0.2 < z < 0.7, 3 bands, t ~ 2d • Supernova Legacy Survey (2003-2008): 2000 SNe Ia to z=1• ESO VISTA (2005?-?): few hundred SNe, z < 0.5 • CFHT Legacy (2003-2008): 2000 SNe Ia, 100’s high z SNe, 3 bands, t ~ 15d• Pan-STARRS (2006-?): all sky WL, 100’s SNe y, z < 0.3, 6 bands, t = 10d

• HETDEX (?): 200 sq deg BAO, 1.8 < z < 3.• WFMOS on Subaru (?): 2000 sq deg BAO, 0.5<z<1.3 and 2.5<z<3.5• ALPACA (?): 50,000 SNe Ia per yr to z=0.8, t = 1d , 800 sq deg WL & BAO with

photo-z’s• Dark Energy Survey (?): cluster at 0.1<z<1.3, 5000 sq deg WL, 2000 SNe at

0.3<z<0.8

• LSST (2013-): 106 SNe Ia y, z < 0.8, 6 bands, t = 4d; 20,000 sq deg WL & BAO with photo-z’s.

• JDEM (2015?): several competing mission concepts

• SPT (2007), 4000 deg, CL , z< 1.3, 3+ bands• RCS2, 2007, 10000 deg, optical, • APEX, ACT, AMI, SZA, eROSITA, Planck etc

MANY


From present ‘w’ contraints to future :


Conclusions...• Most ambitious observational programme. Many astrophysical

probes of DE, four major (SNe, BAO, Clusters, Weak Lensing)

• Improvement in constraints by factor of 3-4 possible in next few years. An order of magnitude improvement expected in 10 yrs time with really big surveys Prove/disprove CDM!

• Combining different probes break degeneracy and can differentiate between DE & GR effects.

• However, to get such statistical precision, we need to control systematics to 1% level in almost all the cases.

Most importantly, it’ll give theorists the impetus to come with more innovative (a.k.a crazy) ideas about DE. One of these maybe even right and explain what Dark Energy really is!

jigsaw-07 @ tifr, feb 19 th 2007 observational probes of dark energy subha majumdar tata institute...

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