Pos(DSU 2012)016 Ce

PoS(DSU 2012)016 http://pos.sissa.it/ ce. nknown energy component, or history, and the growth history clustering, and weak lensing are as dark energy probes, and discuss lahoma, 440 W Brooks St., he universe is unknown, and referred es of dark energy. Due to page limit, tes the measurements that are optimal , ive Commons Attribution-NonCommercial-ShareAlike Licen ∗ [email protected] The cause for the observed acceleration in the expansion of t to as “dark energy” for convenience. Dark energy could be an u a modiﬁcation of Einstein’s general relativity. This dicta in unveiling the nature of dark energy: thegenerally cosmic considered the expansion most powerful observational prob of cosmic large scale structure. Type Ia supernovae,I galaxy will only examine Type Ia supernovae and galaxy clustering the recent results and future prospects. Speaker. ∗ Copyright owned by the author(s) under the terms of the Creat c Norman, OK 73019 E-mail: Yun Wang Homer L. Dodge Department of Physics & Astronomy, Univ. of Ok Probing the Nature of Cosmic Acceleration VIII International Workshop on the DarkJune Side 10-15, of 2012 the Universe Rio de Janeiro, Brazil

PoS(DSU 2012)016 , ) z ( H [7]. A ) z Yun Wang ( X is the cosmic ρ ) t ( , [3, 4]). Refs.[5, a e.g. 1, is usually used as − ) t , where ( a ect measurements of ravity, a / / ˙ . WL provides measurements a k lensing (WL) are generally is one of the most important 1 ) z ing and constraining alternative ( ≡ ) measurement using the Hubble Space g )= 0 f time. The expansion history of the z a given astrophysical object. Fig.1 H dt nergy density function / inues to be consistent with data, but nergy. SNe Ia provide a measurement a f theoretical models. an unknown energy component (dark , measured from current observational current data [7]. Data used: Cosmic microwave are not sufficient for differentiating two a y but non-vanishing cosmological con- our ignorance of the true nature of dark ln d onstant ( ons [8]; 472 Type Ia supernovae (SNe Ia) (compiled S) [9], the Hubble Space Telescope (HST) [10], as well via a derivative) [12]. It is important to utilize unction of redshift measured from the same data. ) = ( ) Sloan Digital Sky Survey (SDSS) Luminous Red Galaxies t z ( ( 2 g H f , as well as ˙ ) z ( H (related to ) z (a) (b) ( G is cosmic time. The cosmological redshift, t , [2]), and the modification of general relativity (modified g Left panel: Expansion history of the universe measured from derived from luminosity distances of SNe Ia. GC provides dir and the growth factor e.g. ) ) , as well as the growth rate of cosmic large scale structure, z z ) ( ( Solving the mystery of the observed cosmic acceleration [1] The evidence for cosmic acceleration has strengthened over Type Ia supernovae (SNe Ia), galaxy clustering (GC), and wea z ( H H A D challenges in cosmology today. Current observationallikely data explanations for theenergy, observed cosmic acceleration: Telescope (HST) [16]. Right panel: Dark energy density as a f 1. Introduction by [9], including data from theas nearby Supernova SNe Legacy Ia Survey [36]); (SNL galaxy clustering measurements from background anisotropy (CMB) data from WMAP 7 year observati (LRGs) [11], 69 Gamma Ray Bursts [14], and the latest Hubble c of data [7]. Fig.1 (right panel) shows the corresponding dark e 6] contains reviews with more complete lists of references o universe is described by the Hubble parameter, Figure 1: Probing the Nature of Cosmic Acceleration scale factor, and the indicator for cosmic time,(left because panel) it shows can the be Hubble measured parameter for considered the most powerful observational probesof of dark e cosmological constant (and no modificationthe of uncertainties are gravity) large cont (seeenergy, Fig.1, and right the panel). theoretical Given difficultiesstant of using explaining known physics, a we tin explanations. need to be open minded in explor PoS(DSU 2012)016 ) k y 1. z ( )= X = t (2.2) (2.1) [20]. , and from , ) w X with ) ) x z z ( a ( 2 Ω 0 ) ( becomes 1 Yun Wang g H − ( H ] as a free f + ) ) / 1 δ z k z ( k ( ( a Ω X − and H w ρ + ) = + z m is related to k ( 0 are the ratios of the Ω ) w Ω H z X , does not change sign ( 2 Ω ) X / z )= 1 ρ ( a , and X ) ( and ) z ρ on large scales, X ( e yielded the strongest direct G m w cosmological parameters (see X π , Ω X 8 vely, and conclude with a brief energy and modified gravity, for ary method to probe dark energy ( ate is likely different in these models surement of Ω / 0 requires that ) )] 2 0 xample)[24]. If the present cosmic ′ z portant to make model-independent + z ( ]. Note that ta and independent measurements of H = 2 ( y observational projects. ′ g alaxies, or radio galaxies [15] provide mplest general guidelines for probing ) osmic acceleration [19]. sion history of the universe, 3 f cognize that we need to measure two z z X . Furthermore, GC and WL constrain z rk energy. t quired to achieve a robust test of gravity. w + = [or the expansion history + 1 0 c + ) 1 z ( ρ 1 ( k [ . Modified gravity models can give identical ) 3 X Ω z ′ ρ ( z g + d f 3 3 z ) implicitly assumes that 0 z Z ) z is the Hubble constant. + ( has advantages over measuring dark energy equation of ) 1 X ) 0 ( z exp m ( = X Ω is more closely related to observables, hence is more tightl z = ρ ( ) ) ) z H z = 0 ( ( ( X ) X = X z 0 ρ ρ ( 0 ρ H H H . ) ≡ 0 ) ( z X ( ρ E / ) z This precludes whole classes of dark energy models in which ( X ρ as a free function; ≡ is specified, the evolution of matter density perturbations ) ) ) z z z ( ( ( X X E as a dark energy model by design, but the growth rate w Clusters of galaxies provide an independent and complement Dark energy is often parameterized by a linear equation of st Due to the page limit, I will focus on SNe Ia and GC, as these hav Because of the existence of two possible explanations, dark ) are required to break the degeneracy between dark energy and z ( 0 H state denoting the curvature constant. Consistency of Eq.(2.2) a the growth rate of cosmic large scale structure, in cosmic time. function of cosmic time. Measuring as follows [21]: different aspects in the modification of gravity; both are re [13]. Other methods, e.g., using gamma-rayadditional bursts, cross-checks old on red g dark energyH constraints. CMB da Probing the Nature of Cosmic Acceleration all three methods, as they have different systematic errors observational data will allow us to probe the true nature of c compared to dark energy models. The precise and accurate mea where e.g. [17, 7]), hence are important as well in constraining da constraints on dark energy todark date. energy, I then will SNe first Iasummary discuss of and the current GC si status as and future dark prospects energy of probes dark energ respecti 2. Probing dark energy and testing gravity the observed cosmic acceleration,functions it of is cosmic time critical from for observational data: us the to expan re Hence parametrizing dark energy with w Because of our ignorance of theconstraints nature by of measuring dark the energy, dark it is energy im density negative in the future (“Bigacceleration Crunch” is models, caused see by [23] dark for energy, an e matter and dark energy density to the critical density constrained for the same number of redshift bins used [21, 22 Once PoS(DSU 2012)016 s [30] (2.3) (2.4) (3.1) ) z ( Yun Wang H (decline in , where the ) z 15 1 ( , r m ) [19]. ) x ∆ z ) ( z δ ( + g / f 1 ) t , x ( ) ) = ( 1 z , ( ( 0 0 L δ . This is the reason SNe Ia are , d H y model [4, 27], which can be ⊙ = )] / = method for probing dark energy, z mic acceleration is caused by a ) 1 M 0 respectively. ( 1 z ( D Γ e when using SNe Ia as cosmolog- D > 3 2 niques used so far are based on one H as been discovered [1]. This method ) 1.4 / k separate, which is true for the vast majority rametrized either as dshift, z 1 | . Ω k rve width is associated with the amount + a SN Ia peak luminosity (Hubble diagram )= ples of studies of observational signatures sic scatter in SN Ia peak luminosity. The Ω 1 z ln | ( ( [ is given by d m E z / 0, and Ω 1 veys can be used to probe dark energy [29]. -band maximum, see [31]), or a stretch factor e. If dark energy and dark matter are coupled (a more sinn istent with observation. 2 3 ls. They showed that these models produce oscillations or D B 2 = idence for the separation of dark energy and dark matter by / 4 k 1 − are unified (unified dark matter models), Eq.(2.3) would need ln ) − Ω , d | . The right panel of Fig.12 shows a DGP model that τ k ) 2 ( ′ ′ 0, ≡ ′ 1 z , and can provide a robust measurement of Ω ( | 3 ) dz D < z 1 E ) ( k − z 0 z g ( f 0 Ω Z E cH 2 A SN Ia is a thermonuclear explosion that completely destroy for )= ) )= )+ z x z ( . The linear growth rate τ ( ( ) ( r Γ t ′′ 1 0 D H ( , sinh x d from the observer to redshift , / ) ) d z x as a dark energy model, but gives significantly different ( ( r ) z ( sin H )= x is determined by solving the following equation for ( ) x ( δ The validity of the DGP modelGalaxy has peculiar been velocities studied from by large-scale [28]. supernova sur Note that we have assumed that dark energy and dark matter are In the simplest alternatives to dark energy, the present cos Type Ia as standard candles. The use of Type Ia supernovae (SNe Ia) is the best established ) 2 3 1 t ( 1 a carbon/oxygen white dwarf near the Chandrasekher limit of Probing the Nature of Cosmic Acceleration D magnitudes for a SN Ia in the first 15 days after exponential blowup of the dark matter power spectrum incons of dark energy modelscomplicated that possibility), have or if been dark studied energyto and in be dark matter modified the accordingly. literatur Ref.[25] foundruling the out first a strong broad ev class of so-called unified dark matter mode so uniform in peak luminosity.ical The standard first candles challenge is to properly overcom usual incorporating calibration the of intrin SNe Ia reducesdispersion) the to intrinsic about scatter in 0.16 magobservable [31, parameter, the 32]. lightcurve The width, which calibration can tech be pa (which linearly scales the time axis, see [33]). The lightcu where primes denote where sinn comoving distance gives identical described by a modified Friedmann equation of modified gravity models. A worked example is the DGP gravit modification to general relativity. Ref.[26] contains exam through the measured luminosity distance as a function of re since this is the methodis through which independent cosmic of acceleration the h clustering of matter 3. Type Ia supernovae as dark energy probe PoS(DSU 2012)016 is a ) M Yun Wang (where ) , and a flat universe. M w , corrections have been made m no Ω , 20 from the Calan/Tololo sample w . , weak lensing amplification structure can be modeled by en the carbon burning makes ( 0 4 ≤ s very different from the typical 1000 3000 10000 max t [38] ng of intrinsic SN Ia color variation urs of V Redshift in CMB frame (km/sec) SN Ia data can be minimized through − ectra [35] that can further improve the for dark energy, t [42]. The extinction by dust can be etonation [34]. There may be additional The main systematic effects of SNe Ia as n in the peak luminosity of SNe Ia. nfrared (NIR) observations of SNe, since ample of the homogeneity of SNe Ia [36]. max J H K B nsing amplification based on the measured tect by its reddening and could mimic the effect of cted for dust extinction; relation measurements can be used in combination with of the cosmic acceleration in 1998 [1]. The solid lines

18 18 18 16 16 16 14 12 10 14 12 10 14 12 10

provide a viable method to eliminate possible gray dust ly by the Cosmic Far Infrared Background [40], with no Extinction-corrected apparent magnitude at maximum at magnitude apparent Extinction-corrected 0) fall on these lines. Right panel: Hubble diagrams of SNe 5 = σ Left panel: Hubble diagrams showing 26 SNe Ia with 3 3.5 4 4.5 5 20 18 16 14 20 18 16 14 The weak lensing amplification of SNe Ia by cosmic large scale Recent data show that the apparent dust extinction of SNe Ia i Systematic effects of SNe Ia as dark energy probe. Gray dust, consisting of large dust grains, is difficult to de Ni produced in the SN Ia explosion, which in turn depends on wh 4 56 dust extinction decreases with wavelength. matter power spectrum [43]. The effect of weak lensing on the extinction law due to Milky Way dust,with possibly dust due to extinction, the or mixi corrected variations using in multi-band imaging the data, properties especially near of i dus a universal probability distribution function for weak-le flux-averaging [44]. Figs.3 shows the 2D marginalized conto by cosmic large scale structure [39], and possible evolutio Ia in the NIR bands. Note that these SNe Ia have only been corre for lightcurve width. [46] of a dark energy probe are: extinction by normal [37] or gray dus calibration of SNe Ia. Fig.2 (left panel) shows a historic ex physical parameters associated with SN Ia lightcurves or sp the transition from turbulent deflagration to a supersonic d Figure 2: Probing the Nature of Cosmic Acceleration contamination in SN Ia data [41]. other lensing data to infer the level of dust extinction, and dark energy [38]. Grayevidence dust found can in favor be of constrained gray quantitative dust so far. Supernova flux cor nuisance parameter), assuming a constant equation of state indicate Hubble’s law; perfect standard candles (with [36]. This sample provided half of the data for the discovery PoS(DSU 2012)016 ic nd Yun Wang enitor population drift, since , flux-averaging leads to smaller d by the theoretical modeling of stics, we can subtype SNe Ia and ignificantly larger uncertainties in ifferent (a much younger universe) lar in both lightcurves and spectra, anel of Fig.2 shows the Hubble di- increases the concordance of SNe Ia ed at the first lightcurve maximum) as ive transfer calculations (Kasen 2006 rors of SNe are included [7]. Clearly, nitor population drift [45]. for SNe data (with and without flux-averaging) er standard candles at NIR wavelengths ) dark energy and cosmological parameters 5 24.1 . 0 w =0 k , Ω −0.5 0 24 for SNe data compiled by [9] (with and without flux- and 95% confidence levels. [7] w ( ) 6 M 0 −1 and , 23.9 w M m ) a Ω , w , and GRB data (same data as in Fig.1). The contours are at 68% a , NIR observations of SNe Ia provide additional strong ad- w 23.8 0 0 +GRB+GC(CW2)+ ( 0 −1.5 H w SNe flux−averaged SNe not flux−averaged flux−averaged; stat+sys not flux−averaged; stat+sys not flux−averaged; stat only ( the usual lightcurve width correction. The smaller intrins SNe only 23.7 CMB+H −2 −1 −2 −1 −2

−0.4 −0.6 −0.8 −1.2 −1.4 −1.6 −1.8 −2.2

−0.5 −1.5 −2.5 0.5

w w without 0 0.5 0.4 −0.5 SNe only 0.3 0 m w Ω −1 0.2 The 2D marginalized contours of The 2D marginalized contours of +GRB+GC(CW2)+ flux−averaged; stat+sys not flux−averaged; stat+sys not flux−averaged; stat only 0 −1.5 0.1 =0 SNe flux−averaged SNe not flux−averaged k Ω CMB+H The evolution in SN Ia peak luminosity could arise due to prog Optimized observations of SNe Ia. 0 0 2 1 −2

−2 −1

−6 −1 −2 −3 −4 −5

−1.5 −2.5 a −0.5

w w combined with galaxy clustering (CW2), CMB, 95% confidence levels. [7] Note that the inclusionestimated of parameters, systematic compared errors to of whenflux-averaging SNe (thick only solid leads statistical lines) er leads to to s larger errors on if only SN Ia data are used. However, when other data are added errors on dark energy (seewith Figs.4-5) other because data. flux-averaging the most distant SNe Ia comethan from that a stellar of environment the verycompare d nearby SNe SNe Ia Ia. at highthus However, redshift overcoming with and the sufficient possible low stati systematic redshift effect that due are to simi proge vantages beyond being relatively dust-free. SNecompared Ia to are the bett optical wavelengthsagram [46, of 47, SNe 48]. Ia The in right the p NIR, dispersion of SN Ia peakSN luminosity Ia in lightcurves the using NIR[49]). time-dependent can Fig.6 multi-group be shows radiat the explaine dispersion in peak magnitude (measur averaging), assuming a flat universe. The contours are at 68% Figure 4: Figure 3: Probing the Nature of Cosmic Acceleration PoS(DSU 2012)016 nd [49]. ⊙ Yun Wang M ost strongly correlated with 5972 strength and luminosity e indicators. The correlation λ or flux ratios that correlate with elations that decrease the scatter n found in the observational data copic features and luminosity can uding NIR spectra, see [50]), since sed the Nearby Supernova Factory observational data. Hachinger et al. for SNe data (with and without flux-averaging) ve maximum) as a function of wavelength band en Si II ) k 2 Ω Ni masses between 0.4 and 0.9 0.3 , m 56 SNe Ω SNe m , 0.67 Ω 1 flux−averaged not flux−averaged 0 X flux−averaged not flux−averaged 0.25 . (Kasen 2006 [49]). 1 +GRB+GC(CW2)+ +GRB+GC(CW2)+ 5972 line may be a very promising spectroscopic 0 0 7 X ⊙ , λ M CMB+H 67 CMB+H 0.2 . 0 0 8 6 4 2 0 0 −2 −4

1.0 0.05

X ,

, and GRB data (same data as in Fig.1). The contours are at 68% a −0.05

k 0

33 Ω . H 0 X ( 0.3 SNe 1.2 SNe m 1 0.33 flux−averaged not flux−averaged Ω X flux−averaged not flux−averaged 0.25 +GRB+GC(CW2)+ +GRB+GC(CW2)+ 0 0 0.8 CMB+H CMB+H 0.2 0.6 8 6 4 2 0 1

−2 −4

1.4 1.2 0.8 0.6

1.0

0.33 X X Ni masses between 0.4 and 0.9 56 0.05 SNe 1.2 SNe k 1 0.33 Ω flux−averaged not flux−averaged 0 X flux−averaged not flux−averaged Dispersion in peak magnitude (measured at the ﬁrst lightcur The 2D marginalized contours of +GRB+GC(CW2)+ +GRB+GC(CW2)+ 0 0 0.8 CMB+H CMB+H It is important to obtain high quality spectra of SNe Ia (incl 0.6 2 0 0 8 6 4 2 1

−2 −4

−0.05

0.5 2.5 1.5

1.0

0.67 X X combined with galaxy clustering (CW2), CMB, 95% confidence levels. [7] Figure 6: Figure 5: Probing the Nature of Cosmic Acceleration the spectra of SNeof Ia SNe have been Ia shown inbetween to the provide SN Hubble calibration Ia diagram, r spectroscopic and(see, features make e.g., and SNe [51]). Ia luminosity better hasspectrophotomery More distanc of bee recently, 58 Bailey SNe et IaSN al. to Ia perform luminosity. (2009) an unbiased [52]SN They search u Ia found f absolute that magnitudes. thebe The 642/443 understood correlation nm through of comparing flux SN theoretical ratio(2008) Ia modeling [53] is spectros with found m that the strength of the Si II a function of wavelength band for SN Ia models with for SN Ia models with luminosity indicator for SNe Ia, withresulting the from the correlation effect betwe of ionization balance. PoS(DSU 2012)016 Yun Wang n [56, 57]. Fig.8 (which includes BAO in the radial direction, ) ) rtions and the bias factor k z ( ( P H to obtain the largest possible At the last scattering of CMB SS LRGs [58]. er at least one year [55]. Given power spectrum have the charac- ives lar power spectrum) and the mat- ion contained in galaxy clustering B anisotropy data (see, e.g., [8]). uch shallower survey in the reconstruction econstruct the dark energy density asure the cosmic expansion history bserver [54]. This is achieved by an litude than the CMB acoustic peaks, r spectrum has evolved significantly precisely, see Fig.7) [54]. growth history of cosmic large scale ) urvey is superior to a much shallower he drag epoch (which occurred shortly id became frozen, and imprinted their z . Assuming linear bias, the combination ( alaxy power spectrum). Because baryons H 8 as a free function of cosmic time [54]. ) (the angular diameter distance) in the transverse directio z ( ) z X ρ + 1 ( / ) z through independent measurements of redshift-space disto ( ) r z can be measured directly and used to test gravity [59]. ( ) g z f The comparison of an ultra deep supernova survey [55] with a m )= ( z m ( 8 as a free function of cosmic time (i.e., to measure A through BAO only or the shape of the galaxy power spectrum σ ) The key to the efficient use of SNe Ia for probing dark energy is Baryon acoustic oscillations (BAO) as a standard ruler. BAO represents only a fraction of the cosmological informat D ) ) z z z ( ( ( X g f of the dark energy density ρ Figure 7: Probing the Nature of Cosmic Acceleration unbiased sample of SNe Ia atultra the deep greatest survey distances of from the thethe o same same areas observational in resources, the ansurvey. ultra sky deep every A supernova few s sufficiently days deep ov supernova survey is required to r between the distribution of galaxies and that of matter [19] as features) measured from thestructure galaxy distribution, and the 4. Galaxy clustering as dark energy probe photons, the acoustic oscillationssignatures in on the both photon-baryon the CMB flu (theter acoustic peaks distribution in (the the baryon CMB acoustic angu oscillations in the g since last scattering of photons, BAO areand much are smaller washed in out amp on smallteristic scales. scale determined BAO in by the the observed comovingafter galaxy sound horizon recombination), at t which isComparing precisely the measured observed by BAO scales the with CM the expected values g comprise only a small fraction of matter, and the matter powe and shows the first detection of the BAO peak from a sample ofdata. the SD A flux-limited galaxy redshiftH survey can allow us to me PoS(DSU 2012)016 (the from ) ) d z z ( ( s Yun Wang A r D and using 0062 (4.2) . Mpc (4.1) ) ) 0 z z 0584), have tighter ( 60 58 ( . ± + − A 0 H D − e LasDamas SDSS LRG Mpc is used for a conser- = 1518 1048 . 1 and r 0 − ) h z )= ( the SDSS Data Release 7 [11]. )= o-point correlation function (2D 35 H isible in Fig.9) leads to tight and . g (2012) [11], based on a Markov 120 35 und that the derived measurements 0 . rrent limitations in the modeling of btained − ng irections. The measurable preferen- 0 = tematic effects. This is as expected, a and the mock in the range of scales ( xy correlation function on quasi-linear fficient of z A 40 n the transverse direction respectively; ( D A ed since they are independent degrees of . Since most of the constraining power in sured from the SDSS data, clearly showing a peak = / ) D ) s d 35 z . ( 0 s , ( r 1 A − 9 D / , ) d Mpc z 1 correspond to the preferential redshift separation along ( s − ) r 35 . 530km/s Mpc [58]. kms 0 and 1 The first simultaneous measurements of ( 8 9 ± − . . ) A 4 4 h d z + − D ( 1 / s 100 . ) r d ) ∼ 13020 82 z ( s 35 . r )= 0 )= d ( z 35 ( H . and s 0 r ) ) d = z 35 ( z . s ( r 0 ( ) H H 35 . The spherically-averaged galaxy correlation function mea 0 ( H Current GC Measurements. corresponding to the BAO scale at Figure 8: Probing the Nature of Cosmic Acceleration the line of sight,these and in the turn preferential arise from angular thetial separation BAO redshift in i and the angular radial separations and should transverse be d uncorrelat robust constraints on freedom. The presence of the BAO (although only marginally v galaxy clustering data was made very recentlyChain by Monte Chuang Carlo & (MCMC) Wan analysis2PCF) of they the measured two-dimensional from tw theFig.9 flux-limited sample shows of the LRGs 2D from mock 2PCF catalog measured for from comparison. The the similarityused SDSS between (indicated LRGs the by dat and the shaded asystematic disk) singl effects, is only apparent. the Due quasi-linear to scale the range cu of vative estimate in this analysis. Chuang & Wang (2012) [11] o this analysis comes from fitting the overall shape of the gala sound horizon at the drag epoch) inof the MCMC analysis, they fo without assuming a dark energy model or a flat universe. Scali constraints and are more robustsince with respect to possible sys are nearly uncorrelated (with a normalized correlation coe PoS(DSU 2012)016 ), 8 sed σ , h Mpc ) in 1 , − Yun Wang S h n , 2 120 measurements h b − ) , and GRB data. 0 Ω 40 35 H . ), the constraints on = 0 s 44 (solid black contours), eys in establishing the . 0 contours are denoted with = 0 = z measurement (both from < Ref.[7] showed that there ( d any other cosmological measurement by Blake et ξ ) rvey obtained by Blake et z A 6 . D < 0 35 . / measurement by Beutler et al. d nts. ) 0 for Fig.10 (right panel). When 16 0. The d . , z s are galaxy clustering measure- = 106 ( . fixed values of ( s z 0 r 005 ( . Fig.11 shows the 2D marginalized . easurements simultaneously without d t generation galaxy redshift surveys, 0 V , from GC data, see [61]. D ) CF) measured from SDSS DR7 LRGs (left panel) and 01 z ft range 0 / . ( ) 0 ) A d , d z D z ( ( s 025 s . r r and 0 ) coustic oscillation scale. The observed 2D 2PCF has been ters close to the best fit values in the likelihood analysis , ates the scale range considered ( ) = 1 z measurements by Percival et al. (2010) [65] from . ( 10 35 0 . , 35 Mpc for illustration in these figures only; smoothing is not u H . 0 from galaxy clustering data. 35 5 1 . 0 . 0 ) − 0 d = z d h ( = z A priors were imposed that would affect the combined con- ( ξ D and H no 2 . 0 and d ) z ( H for different GC measurements combined with CMB, ) k Ω , These results have significant implications for future surv m 5 Ω , w ( The two-dimensional two-point correlation function (2D 2P For the Chuang & Wang (2012) [11] GC measurements (CW2 and CW1 Possible systematic differences in different GC measureme For the most recent results on the measurement of The constraints in Eq.(4.2) can be used to combine with CMB an Fig.10 shows the first results from the WiggleZ Dark Energy Su 5 SDSS DR7 LRG and main galaxy samples and 2dFGRS, and the (2011) from 6dF GRS [69]. al. (2011) from the WiggleZ survey [68] combined with the SDSS DR7 LRGs), as well as the by Chuang & Wang (2012) [11] with their The first row of Fig.11 compares the and the background cosmological modeldramatically is larger assumed data to sets be becomeit known will available be from possible the to nex imposing extract strong both priors distance (see, and e.g., [64]). growth rate m may be systematic differences incontours different of GC measurements Figure 9: Probing the Nature of Cosmic Acceleration straints [11, 60]. dotted lines for clarity. [11] scales, and not fromments fitting (rather the than BAO BAO only peaks, measurements). these measurement data sets to constrain dark energy, as al. (2011ab) [62, 63]. Note that Fig.10 (left panel) assumes feasibility of measuring both and a LasDamas SDSS LRG mock catalog (right panel) in a redshi this study. The thick dashedsmoothed blue by circle a denotes Gaussian the filter baryon with rms a variance of 2 in our likelihood analysis. The contour levels are (dashed red contours). In both figures, the shaded disk indic compared to a theoretical correlation function with parame PoS(DSU 2012)016 h )= 35 . 0 measure- Yun Wang = , to 2D data 35 z . ( 0 35 . V d 0 d D / ) d z rom [65]), while the 1, the ( s r − ≡ = GRS measurements (CB+) w 35 oth the Percival et al. (2010) . CW 0 d 0036. The lower measured value f Fig.11. This is as expected, as . hifts z= 0.44, 0.6 and 0.73 in the galaxy 0 s. ± 1. aged data (CW1), i.e., − tically: measurements by Percival et al. (2010) = , as indicated by comparing the thin solid 1097 35 CW2 CW1 WP CB+ . . GC ) 0 0 0.3 0.3 w separately. Clearly, most of the constraining d Energy Survey. [62] Right panel: Measurements of 35 GC WP2(WP) WP1(z=.35) WP1(z=.2) . m m 35 . 0 Ω Ω )= 0 by Chuang & Wang (2012) [11] and Percival et +GRB+ +GRB+ 0.25 0.25 and 0 0 d for different galaxy clustering measurements combined wit = measurement favors 35 11 2 . 35 ) . z . 2 k 0 0 . ( 0 CMB+H CMB+H 0.2 0.2 0 d Ω A and d 0 0 , d = 2 D m 0.06 0.04 0.02 0.05 .

−0.05 −0.02 −0.04 / 0

k ( Ω

) Ω Ω d , V d w z ( D ( / s ) r CW2 CW1 WP CB+ GC d 0.3 0.3 z ( GC WP2(WP) WP1(z=.35) WP1(z=.2) s m m and r Ω Ω . While the ) +GRB+ +GRB+ 0.25 0.25 0 0 d 35 ≡ . z 0 ( 35 d s . CMB+H CMB+H 0.2 0.2 r WP 0 ) d −1 −2 −1 −2

−0.5 −1.5 −0.5 −1.5

w w 35 . 0 1. The measurements of − = 0.05 z < ( 0.05 CW2 CW1 WP CB+ comes from GC 1 (similar results were found by [67] using GC measurements f GC WP2(WP) WP1(z=.35) WP1(z=.2) H w k k Left panel: Measurements of the baryon acoustic peak at reds 0034, while 0 − Ω Ω The 2D marginalized contours of . w from the WiggleZ Dark Energy Survey data. [63] 0 +GRB+ 0 +GRB+ ) 0 0 z < , and GRB data. The contours are at 68% and 95% conﬁdence level ( ± 0 m w H 8 CMB+H CMB+H The second row in Fig.11 compares the σ ) −2 −2 −1 −1 −0.05 −0.05

z −1.5 −0.5 −0.5 −1.5

are tightened signiﬁcantly by going from spherically-aver

1161 ( w w . g f Figure 11: Figure 10: correlation function of the ﬁnal data set of the WiggleZ Dark Probing the Nature of Cosmic Acceleration w CMB, 0 (CW2), i.e., Chuang & Wang (2012) [11] GC measurements favor al. (2010) [65] are similar in precision, but differ systema contours (CW1) to thick solid contours (CW2) in the ﬁrst row o more information from GC is includedGC in measurements CW2 (WP) compared to and CW1. thefavor B combined WiggleZ survey and 6dF ment favors power on [65] (WP2), with their measurements of + 1 k ( D δ

PoS(DSU 2012)016 . cyc + 2 )+ b x / ( 2 b δ ft-space b studying [18, 19]. + Yun Wang ) b = z / and the growth ( xquisite pre- g ) g ) δ f 2 z ( axy redshift survey k E , (a) (b) 0 1 . When combined 1. Note that these H and k w ( − ) J z ) = ( z < ) ( 2 H w H k catalogs compared with a ( g P both ) 1 as follows [73]: favors k (which describes how light traces ) arger data sets become available; ( Chuang & Wang (2012) used the x g ) 35 ( arly, the 2D theoretical model used z . P WP 0 ( quasi-linear) scales. δ Fig.9); this is due to the reduction of tion function (2D 2PCF) measured from 160 1 using the galaxy power spectrum of d b 3 he measured 2D 2PCF even though no ) − rom GC. However, Montesano, Sanchez, sed galaxy power spectrum. It is not sur- π . We can assume that the galaxy density = 2 w = ( , compared to a theoretical model with the input parame- 1, while i line types and contour levels are the same as in Fig.9 [11]. 1 e cosmic expansion history − k g 12 = δ 2 w k g δ 1 k 2. [19] g , which in turn implies a more negative < δ favors ) h z 35 35 < . . CW 0 [70] and the bias parameter 5 0 ). The future data correspond to a magnitude-limited NIR gal . d ) b z ( = / g ) can be measured directly from galaxy redshift survey data by f z z ( can be obtained through independent measurements of redshi ( β g H ) f z The data contours in Fig.12 (left panel) gives a sense of the e ( g = f β is related to the matter density perturbation , and GRB data, g 0 δ H The galaxy bispectrum is Left panel: The average two-dimensional two-point correla . 2 10,000 square degrees and 0 implies a smaller / > ) x 35 . ( Future Prospects. A flux-limited galaxy redshift survey can allow us to measure WP 0 2 d δ 2 & Phleps (2012) [66] obtained results consistent with two measurements used different methodsgalaxy to correlation analyze function, GC while Percival data: etprising al. that (2010) they lead u to different distance measurements f the SDSS DR7 LRGs. cision the galaxy 2D 2PCFit can be shows measured the when averaged significantly 2D l theoretical model 2PCF [11]. measured The from contour 160smoothing levels LasDamas is are apparent used mock in (in t contrastshot to noise the achieved noisy by current averaging data, overby see 160 [11] mock provides catalogs. a reasonable Cle fit to data on intermediate (and The measurement of distortion parameter with CMB, the observed redshift-space correlation functionperturbation [71, 72] of rate of cosmic large scale structure covering LasDamas SDSS LRGfull mock catalogs (solidters black contours) of the LasDamas simulations (dashedRight red panel: contours). Current The and expected future measurements of th Figure 12: Probing the Nature of Cosmic Acceleration mass) [18]. The parameter b PoS(DSU 2012)016 k ame ) in ically 3 k , Yun Wang 2 k , 1 k half of the right by ( dF data. Independent axy redshift survey covering , compared with current data tinction between dark energy when bias, nonlinear effects, ) z , Dan Kasen, and Kevin Krisci- ( tween luminous matter and mat- , and WL) should be used, each ng, planned, or proposed. Ongo- g ETDEX), and Sloan Digital Sky ift survey provides measurement for a modified gravity model (the f & Rapid Response System (Pan- ) ected future projects include Large nd Square Kilometre Array (SKA) 74] developed the method for mea- z Proposed future projects include the ( nature of dark energy within the next (see the solid and dashed lines in the ]. It is an exciting time in cosmology. per. This work was supported in part g Visible and Infrared Survey Telescope e Volume simulation. For a detailed boosted and f ) g the dark energy mystery will not be systematic effects inherent in the data. that nonlinear effects can be accurately z ) t data can not differentiate between dark ( z , 1999, ApJ, 517, 565 ( H H tions [56]. Cosmological N-body simulations et al. 13 2 can constrain < z 25 (solid line), as well as a dark energy model that gives the s . < are very limited at present [71, 75]; this will change dramat 0 5 ) . z = ( 0 m b Ω and (dashed line). The cosmological constant model from the top ) z 0 m , 1998, AJ, 116, 1009; Perlmutter S ( Ω is a function that depends on the shape of the triangle formed β J et al. from the galaxy bispectrum, which was applied by [75] to the 2 ) where z accurate to a few percent; this will allow an unambiguous dis , ( ) b ) 3 z for the same k ( The right panel of Fig.12 shows how well a flux-limited NIR gal I am grateful to Chris Blake, Daniel Eisenstein, Mario Hamuy There are a large number of dark energy surveys that are ongoi The systematic effects of BAO as a standard ruler are: bias be ) g f z + ( 10,000 square degrees and 0 2 [1] Riess AG > in the near future. H panel in Fig.12 is also shownenergy (dotted and line). modified Clearly, curren gravity. Aof very wide and deep galaxy redsh [19]. The bottom half of the right panel in Fig.12 shows the DGP gravity model) with models and modified gravity models that give identical measurements of Probing the Nature of Cosmic Acceleration k space, but only depends very weaklysuring on cosmology [74]. Ref.[ ing projects include Carnegie Supernova Project (CSP), ESO for Astronomy (VISTA) Surveys, PanoramicSTARRS), Survey Hobby-Eberly Telescope Telescope Dark Energy ExperimentSurvey (H (SDSS) III, and the Dark EnergySynoptic Survey Survey (DES) Telescope [79]. (LSST) Sel [80], andWide-Field Euclid Infrared [64, Survey 81]. Telescope (WFIRST), BigBOSS,[82]. a It is criticalthe to statistics remember of that the the data challengeA obtained, to combination but solvin of the all three tightoptimized most control by promising of having its methods systematics (SNe minimized Ia,We by can GC design expect [83 to make ground-breaking discoveries aboutdecade the or two. unas for permission to useby their DOE figures grant in DE-FG02-04ER41305. this proceeding pa References and redshift distortions arediscussion, properly see included [6]. in the Hubbl 5. Summary: Current Status and Future Prospects ter distributions, nonlinear effects, and redshiftare distor required to quantify these effectstaken [76]. into Ref.[77] account. shows Ref.[78] shows that the BAO signal is bottom half of the right panel of Fig.12). PoS(DSU 2012)016 , (Eds.: Yun Wang , 1582 80 , 1 (2002); V. K. , 063512 (1999); C. 540 60 ., & Kamionkowski, M., reese, Phys.Lett. B632, 449 (2006) 604; P. J. E Peebles and B. Ratra, ApJ iv:0706.1565 (2007); Frieman, J., iv:1102.2251 ) 2, 006 (2004) ntz, arXiv:1103.4829 9.1121 23517 (2012); arXiv1109.3172 Three hundred years of gravitation ), 1753; Ruiz-Lapuente, P., Class. Xiv:1201.2434 . Rev. D 69, 123524 (2004) , et al., Phys. Rep. 493, 1 (2010); Li, M., et 10, 213 cs, 05, 021 (2008). Nucl.Part.Sci., 58, 99 (2008); D. Munshi, et ; Verde, L.; & Jimenez, R. 2005, PRD, 71, , 668 (1988); J. A. Frieman, C. T. Hill, A. Stebbin, 14 , 208 (2000) , 483 (1998). B302 485 508 , PLB , 107301 (2004). 70 , 797 (1987); A. Linde, in , 1766 (1998); L. Parker and A. Raval, PRD 81 B287 , 98 (2007). , 199 (2001); K. Freese and M. Lewis, Phys.Lett.B , Wiley-VCH (2010) 659 , in press (2008) 502 , 2077 (1995); R. Caldwell, R. Dave, and P. J. Steinhardt, PRL 75 , 2011, ApJ, 730, 119 , ApJ Nature , Nucl.Phys. , et al. et al. Dark Energy et al. et al. , L17 (1988); C. Wetterich, Nucl.Phys. Deffayet, Phys.Lett.B Hawking, S.W. and Israel, W., Cambridge Univ.325 Press, 1987), (1998); L. Wang and P. J. Steinhardt, ApJ Quantum. Grav., 24 (2007), 91; Ratra, B., Vogeley, M. S., arX Turner, M., Huterer, D., ARAA, 46,arXiv:0903.0866; 385 Uzan, (2008); J.-P., Caldwell, arXiv:0908.2243; R. Y.-F. Cai R al., 2011, arXiv1103.5870; D.H. Weinberg, et al. (2012), ar and I. Waga, PRL Onemli and R. P. Woodard, PRD al., Physics Reports, 462, 67 (2008); A. Heavens, arXiv:110 123001; Daly, R. A., et al., 2009, ApJ, 691, 1058 [6] Wang, Y., [3] V. Sahni and S. Habib, PRL [8] Komatsu, E., et al. 2011, Astrophys.J.Suppl., 192,[9] 18 Conley, A., et al., 2011, Astrophys.J.Suppl., 192, 1 [7] Wang, Y.; Chuang, C.-H.; Mukherjee, P., Phys. Rev. D 85, 0 [2] K. Freese [5] Copeland, E. J., Sami, M., Tsujikawa, S., IJMPD, 15 (2006 [4] G. Dvali, G. Gabadadze, M. Porrati, [10] A. G. Riess Probing the Nature of Cosmic Acceleration [11] Chuang, C.-H.; and Wang, Y., MNRAS, 426, 226 (2012); arX [12] For recent reviews, see H. Hoekstra, & B.Jain, Ann.Rev. [13] For a recent review, see S. W.[14] Allen, A. E. Wang, Y., Evrard, 2008, A. PRD, B. 78, Ma 123532 [15] See, e.g., Schaefer, B. E., 2007, ApJ, 660, 16; Simon, J. [19] Wang, Y., Journal of Cosmology and Astroparticle Physi [20] Chevallier, M., & Polarski, D. 2001, Int. J. Mod. Phys. D [16] Riess, A. G, [21] Wang, Y.; and Garnavich, P., ApJ, 552, 445[22] (2001) M. Tegmark, Phys. Rev. D66, 103507 (2002);[23] Y. Wang, & Y. K. Wang; J.M. F Kratochvil; A. Linde; M.[24] Shmakova, JCAP, 1 Y. Wang, & M. Tegmark, Phys. Rev. Lett.,[25] 92, 241302 H.B. (2004 Sandvik; M. Tegmark; M. Zaldarriaga; I. Waga, Phys [17] Wang, Y.; and Mukherjee, P., PRD, 76, 103533[18] (2007) Guzzo L PoS(DSU 2012)016 ,1 423 Yun Wang ApJ, 475, L81 (1997); D.E. Holz, J, 606, 654 (2004). Lett. 99, 141302 (2007) ); J. A. Frieman, Comments Astrophys., .-P. Uzan, Gen. Relat. Grav. 39, 307 727 995) 71 (2003), astro-ph/0209514 01); edings (2006), astro-ph/0606691 bmitted (2007) , A. R. PRD, 83, 043004 (2011) h/0109070 anch, et al., PASP, 118, 560 (2006); Y. Wang, 5 (1989) L81 (2004) , 124015 (2004); A. Lue, Physics Report 69 15 , 064003 (2007); K. Koyama, arXiv:0709.2399 75 , 084007; ( 2006) 74 , PRD , L105 ( 1993); 413 (2006). and N. Hall, MNRAS, 389, 489 (2008). 18, 323 (1997); J. Wambsganss, R.ApJ, Cen, 506, G. L1 Xu, (1998); & Y. J.P. Wang, Ostriker, ApJ, 525, 651 (1999) A. F. Heavens, T.D. Kitching, L. Verde, astro-ph/0703191; J (2007) P. Zhang; M. Liguori;R. Bean; S. Dodelson, Phys.Rev. H. F. Stabenau and B. Jain, [29] Bhattacharya, S.; Kosowsky, A.; Newman, J. A.; Zentner [30] Y. Wang, & M. Tegmark, Phys. Rev.[31] D 71, 103513 M. (2005) M. Phillips, ApJ [32] A.G. Riess, W.H. Press, & R.P. Kirshner, ApJ, 438, L17 (1 [33] G. Goldhaber, et al, ApJ, 558,[34] 359 (2001) Wheeler, J. C., AAPT/AJP Resource Letter,[35] Am. J. See, Phys., e.g., S. Bongard, et al., ApJ, 647, 513 (2006); D. Br [28] Y.-S. Song, I. Sawicki, and W. Hu, PRD, [38] A.N. Aguirre, ApJ, 525, 583 (1999) [39] R. Kantowski, T. Vaughan, & D. Branch, ApJ, 447, 35 (1995 [36] M. Hamuy, et al., AJ, 112,[37] 2398 (1996) J.A. Cardelli; G.C. Clayton; & J.S. Mathis, ApJ, 345, 24 [45] D. Branch; S. Perlmutter; E. Baron;[46] & P. Nugent, K. Krisciunas; astro-p M.M. Phillips; N.B. Suntzeff, ApJ, 602, [48] W. Michael et Wood-Vasey, al., arXiv:0711.2068, ApJ su [51] Garnavich, P. M., et al. 2004,[52] ApJ, 613, 1120 Bailey, S. et al. 2009, arXiv:0905.0340 [53] Hachinger, S., et al. 2008, MNRAS,[54] 389, 1087 Y. Wang, & G. Lovelace, ApJ Letter, 562, L115 (2001) [40] A.N. Aguirre, and Z. Haiman, ApJ,[41] 532, 28 P. (2000) Zhang, and P.S. Corasaniti, ApJ, 657,[42] 71 (2007) Conley, A., et al. 2007, ApJ,[43] 664, L13 Y. Wang; D.E. Holz; & D. Munshi,[44] ApJ, 572, Y. Wang, L15 ApJ, (2002) 536, 531 (2000); Y. Wang; & P. Mukherjee, Ap [47] M. M. Phillips; P. Garnavich; Y. Wang; et al., SPIE proce [49] Kasen, D., 2006, ApJ, 649, 939 [50] Marion, G. H., et al. 2006, ApJ, 645, 1392; 2009, AJ, 138, [27] A. Lue, R. Scoccimarro, and G. D. Starkman, PRD Probing the Nature of Cosmic Acceleration [26] J-P. Uzan, and F. Bernardeau, Phys. Rev. D64, 083004 (20 PoS(DSU 2012)016 , Yun Wang . , 573 (2007); J. da Angela , 891 (2006); Y. Wang, ApJ 381 449 P., MNRAS, 423, 1474 (2012); ;K. Heitmann, et al., ApJ, 705, 156 v:1209.0210 05); White, M. 2005, Astropart.Phys. 24, , MNRAS and R. Scoccimarro, arXiv:0704.2783; R. 21, 2656 & Eisenstein, D. J., 2003, ApJ, 598, 720 , astro-ph/0507043 (2005); E. Cheng http://www.lsst.org/ http://pan-starrs.ifa.hawaii.edu/public/ http://www.skatelescope.org/ , 1; , 7 (2007) , 651 ( 1997) ress et al. .-D., et al., JCAP 07 (2011) 011 H., & Wang, Y., arXiv:1205.5573; Xu, X., et .,362, L25-L29; Seo, H., & Eisenstein, D. J., et al. 462 290 , and , , / http://www.darkenergysurvey.org/ , 16 A&A , 626529 (2006). MNRAS , 334 (2005); G. Huetsi, A&A 24 , 447 ( 1993) Euclid Definition Study Report Vol. 6265 413 , , 78 (2003) , astro-ph/0702543. (2007). http://www.sdss.org/ , , 560 (2005); , 432 (2002) ApJ 346 , 123507 (2006); N. P. Ross http://www.vista.ac.uk/index.html , , n5;1560 (2004); A. Crotts et al. , 633 335 74 , 1 (1987) , v36 227 , ApJ , MNRAS , Proc. of SPIE , PRD , MNRAS , , BAAS et al. et al. et al. et al. MNRAS et al. et al. , astro-ph/0612401. http://www.euclid-emc.org/ http://wfirst.gsfc.nasa.gov/, http://bigboss.lbl.gov http://www.ociw.edu/csp/ , 1 (2006); R. Angulo 647 arXiv1008.4822 al. (2012), arXiv:1206.6732; Chuang, C.H., & Wang, Y., arXi et al. http://www.as.utexas.edu/hetdex/ and Y. Wang 2005, ApJ, 633, 575; V. Springel, et al., Nature, 435, 629 (20 334 E. Smith, R. Scoccimarro, and R. K. Sheth, astro-ph/0703620 (2009); ApJ, 715, 104 (2010) [57] See, e.g., M. White, Astropart. Phys. Probing the Nature of Cosmic Acceleration [55] Y. Wang, ApJ, 531, 676 (2000),[56] astro-ph/9806185 Blake, C., & Glazebrook, K, 2003, ApJ, 594, 665; Seo, H., [58] D. Eisenstein [59] Song, Y.-S.; Percival, W. J., 2009,[60] JCAP, 10, 004 Chuang, Chia-Hsun; Wang, Yun; Hemantha, Maddumage Don [71] E. Hawkins [62] Blake, C., et al., 2011,[63] MNRAS, 418, 1707 Blake, C., et al., 2011,[64] MNRAS, 415, 2876 Laureijs, R., et al., arXiv1110.3193, [65] Percival, W.J., et al. 2010, MNRAS,[66] 401, 2148 Montesano, F.; Sanchez, A. G.; Phleps,[67] S. 2012, Escamilla-Rivera, MNRAS, C.; 4 et al., 2011,[68] JCAP, 09, 003; Blake, Li, C., X et al. 2011,[69] MNRAS, 415, 2892 Beutler, F., et al., 2011, arXiv:1106.3366,MNRAS,[70] in N. p Kaiser, [61] Reid, B.A., et al. (2012), arXiv:1203.6641;Chuang, C. [72] M. Tegmark [73] J. N. Fry and E. Gaztanaga, [75] L. Verde [74] S. Matarrese, L. Verde, and A. F. Heavens, [81] See [82] See [83] Y. Wang [80] See LSST Science Collaborations, 2009, arXiv0912.020 [76] Angulo, R., et al. 2005, Mon.Not.Roy.Astron.Soc.Lett [77] Jeong, D., & Komatsu, E., 2006, ApJ, 651, 619; M. Crocce, [78] R. S. Koehler, P. Schuecker, and K. Gebhardt, [79] See