Observational Probes of Dark Energy

Observational Probes of Dark Energy Subha Majumdar Tata Institute of Fundamental Research Mumbai

Is there Dark Energy? 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.

What do current data tell us about DE? Consistent with L However, doesn’t constrain w(a) Spergel etal 2006 Wang & Mukherjee 2006

So what are the (theoretical) possibilties? • Possibility 1: Universe permeated by energy density, constant in time and uniform in space (Einstein’s L). • Possibility 2: DE some kind of ‘unknown’ dynamical fluid. Its eqn of state varies with time (or redshift z or a =(1+z)-1). • Impact of DE (or different theories) can be expressed in terms of different “evolution of equation of state” • w(a)= p(a) / r(a)with w(a)= -1forL. • Possibility 3: GR or standard cosmological model incorrect. • Current observations cannot distinguish between Options 1,2 or 3 !! Lectures by Prof Wetterich

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) In GR, scale factor a(t) describes growth of Universe. We know the time evolution of a(t)  H(a)  This holds for each component Expansion history H(z) : written in terms of energy density of each component

Standard measures : Distance (or co-ordinate) to source at z r(z) can be connected to observables Standard Candle : apparent flux to standard flux Standard Ruler: apparent angular size to real physical size 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 expansion and growth factor g(z) • CMB fixes amplitude of matter fluctuations at z~1100. This • is seen at low redshift coupled to g(z). • Within GR, the above diffn reln provides ‘one-to-one’ reln • between two observables : D(z) & g(z). Any inconsistency • would mean either GR is failing at largest scales.

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

And the probes are: • Supernovae • measure flux and redshift of Type Ia SNe. • Baryon Acoustic Oscillations • measure features in distribution of galaxies. • Clusters • measure spatial distribution of galaxy clusters. • Weak Lensing • measure 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 with redshift.

Supernova systematics... For SNe to be good cosmological standard candles  1) need for “standard” candle: need to have 1% control over luminosity evolution  careful spectroscopy 2) Other corrections like gravitational lensing, dust etc. This will require thousands of SNe with at least hundreds of SNe Ia at z>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 structures grow From galaxy catalog, it is possible to extract the matter power spectrum. White (2005)

Recap: where does BAO come from? • 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 before recombination (the CMB peaks). gives a preferred scale at the matter distribution. The matter perturbations grow to give large scale structure (distribution of galaxies).  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 givesdA(z)and in radial gives H(z)

Eisenstein et al. (2005) SDSS 2DFGRS Cole et al. (2005) BAO has been detected:

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)

R200 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

Ensemble of clusters from Simulations: Universality when written in terms sM Press-Schecter form, theoretical (since 1976) Seth-Tormen: ellipsoidal collapse & Nbody Jenkins etal, bestfit to simulations Also Warren etal, Lukic etal latest.

Increasing w keeping WE fixed has following effects: It decreases volume. DE affects cluster redshift distribution... It decreases growth rate of density perturbations. Detect clusters + z

How are ‘real’ clusters ? Chandra Image of Zw38 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... g uncertain evolution M-Flux cosmological astrophysical

Need for extra information.. High-z obs needed, training set CMB is needed

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 Lensed Credit: SNAP WL group

How to constrain ‘w’ ? • 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]

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% level Tereno et al. 2004

DE-n’s degeneracies... Future Present Spergel etal 2006 Hannestad, Tu, Wong 2006

Future Dark Energy Surveys : • Essence (2002-2007): 200 SNe Ia, 0.2 < z < 0.7, 3 bands, Dt ~ 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, Dt ~ 15d • Pan-STARRS (2006-?): all sky WL, 100’s SNe y-1, z < 0.3, 6 bands, Dt = 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, Dt = 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-1, z < 0.8, 6 bands, Dt = 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 LCDM! • 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!

Observational Probes of Dark Energy