Understanding Gravity on Cosmic Scales Rachel Bean Cornell University Work in collaboration with Istvan Laszlo (Cornell) Eva-Marie Mueller (Cornell) Scott Watson (Syracuse) Donnacha Kirk & Sarah Bridle (UCL) Rachel Bean: Itzykson 2012 ANRV352-AA46-11 ARI 25 July 2008 2:1 2.0 a CosmicNo geometry: Expansion history constraints Big Bang Standard candles 1.5 0 b BAO Ω Λ 1.0 –0.5 CMB SNe w Standard rulers 0.5 –1.0 CMB SNe BAO Flat 0 –1.5 0 0.5 1.0 0 0.1 0.2 0.3 0.4 0.5 Ω ΩM M Kowalski 2008 Figure 8 Rachel Bean: Itzykson 2012 (a) Constraints upon !M and !" in the consensus model (cosmological constant/cold dark matter model) using baryon acoustic oscillations (BAO), cosmic microwave background (CMB), and supernovae (SNe) measurements. (b) Constraints upon !M and constant w in the fiducial dark energy model using the same data sets. Reproduced from Kowalski et al. (2008). by University of Tokyo on 01/22/12. For personal use only. in these two models; although the mix of data used here differs from that in Table 1 (supernovae are included in Figure 8), the resulting constraints are consistent. Regarding Sandage’s two numbers, H0 and q0, Table 1 reflects both good agreement with and a smaller uncertainty than the direct H0 measurement based upon the extragalactic distance scale, H0 72 8 km/s/Mpc (Freedman et al. 2001). However, the parameter values in Table 1 are Annu. Rev. Astro. Astrophys. 2008.46:385-432. Downloaded from www.annualreviews.org = ± predicated on the correctness of the CDM paradigm for structure formation. The entries for q0 in Table 1 are derived from the other parameters using Equation 6. Direct determinations of q0 require either ultraprecise distances to objects at low redshift or precise distances to objects at moderate redshift. The former are still beyond reach, whereas for the latter the H0/q0 expansion is not valid. If we go beyond the restrictive assumptions of these two models, allowing both curvature and w to be free parameters, then the parameter values shift slightly and the errors increase, as expected. In this case, combining WMAP, SDSS, 2dFGRS (Two-Degree-Field Galaxy Redshift Survey), 0.016 and SNe Ia data, Spergel et al. (2007) yield w 1.08 0.12 and !0 1.026+0.015, whereas = − ± = − WMAP SDSS only bounds H to the range 61 84 km/s/Mpc at 95% confidence (Tegmark + 0 − et al. 2006), comparable to the accuracy of the HST Key Project measurement (Freedman et al. 2001). Once we abandon the assumption that w 1, there are no strong theoretical reasons for = − restricting our attention to constant w. A widely used and simple form that accommodates evolu- tion is w w (1 a)w (see Section 6). Future surveys with greater reach than that of present = 0 + − a experiments will aim to constrain models in which !M, !DE,w0, and wa are all free parame- ters (see Section 8). We note that the current observational constraints on such models are quite www.annualreviews.org Dark Energy 401 • k2φ = 4πGQa2ρ∆ (18) − 1 d(aθ) (1 + R) = k2 ψ (19) a dτ 2 k2ψ = k2Rφ shear stresses (20) − 2 R(a)= (21) 3β(a) 1 − 1 Q(a)=1 (22) − 3β(a) k2 [˙α + (1 + R) α Rη]= 12πGa2ρ(1 + w)σ (23) H − − ds2 = a(τ)2[ (24) − Understanding cosmic acceleration ds2 = a(τ)2[1 + 2ψ(x,t)]dτ 2 + a(τ)2[1 2φ(x,t)]dx2 (25) Cosmic− acceleration = a modification of Einstein’s− equations Gµν =8πGTµν (26) Deviations New matter? from GR? interactions? Λ? mat f(gµν,R,Rµν) + Gµν =8πGTµν (27) Inhomogeneous universe? Broad aim =Phenomenology Distinguish which sector: new gravity,mat newDE matter or Λ? Gµν =8πG Tµν + Tµν (28) Ambitious aim = Theoretical model Learn something more about the underlying theory? Rachel Bean: Itzykson 2012 1 S = d4x√ g R + d4x√ g (29) − 16πG − Lmat 1 S = d4x√ g (R + f (R))+ d4x√ g (30) − 16πG 2 − Lmat 1 S = d4x√ g f (φ)R + d4x√ g (31) − 16πG 1 − Lmat 1 S = d4x√ g R + d4x√ g (32) − 16πG − Lmat,DE I-2 1 S = d4x√ g R + d4x√ g (30) − 16πG − Lmat (31) 1 S = d4x√ g (R + f (R))+ d4x√ g (32) − 16πG 2 − Lmat (33) 1 S = d4x√ g f (φ)R + d4x√ g (34) − 16πG 1 − Lmat (35) (5)3 mp S = d5x g(5) R(5) + d4x√ g (36) − 2 − Lmat (37) 1 S = d4x√ g R + d4x√ g (38) − 16πG − Lmat,DE Distinguishinga¨ with4πG expansion history = (ρ +3P ) (39) a − 3 m m • Alter Friedmann and acceleration equations at late times a¨ 4πG a¨ = 4πG (ρ +3P + ρDE +3PDE) (40) a= − 3 (ρm +3Pm)+stuff a − 3 or a¨ 4πG stuff + = (ρ +3P ) ? (41) a − 3 m m e.g. f(R) gravity a2 3 1 a¨ 4πG H2f + f + Hf˙ + f¨ + = (ρ +3P ) − R 6 2 R 2 R a − 3 e.g. DGP gravity H˙ a¨ 4πG + = (ρ +3P ) − rc a − 3 Rachel Bean: Itzykson 2012 I-3 There are benefits to asking more questions… Rachel Bean: Itzykson 2012 Three groups of extra galactic observations for testing gravity II: Growth, up to some I: Background expansion III: Growth directly normalization CMB angular diameter Galaxy autocorrelations CMB ISW autocorrelation distance Galaxy – ISW x-corrln Weak lensing Supernovae luminosity autocorrelation distance Xray and SZ galaxy cluster measurements Peculiar velocity distribution/ BAO angular/radial scale bulk flows Ly-alpha measurements Rachel Bean: Itzykson 2012 Phenomenological model of modified gravity • Perturbed metric ds2 = (1 + 2ψ)dt2 + a2(1 2φ)dx2 − − • Aim to describe phenomenological properties common to theories • A modification to Poisson’s equation, Q k2φ = 4πGQa2ρ∆ − Q≠1: can be mimicked by additional (dark energy?) perturbations, or modified dark matter evolution • An inequality between Newton’s potentials, R ψ = Rφ R≠1: not easily mimicked. – potential smoking gun for modified gravity? – Significant stresses exceptionally hard to create in non-relativistic fluids e.g. DM and dark energy. Rachel Bean: Itzykson 2012 Cosmological tests of gravity • Non-relativistic tracers: Galaxy positions and motions – Measure ψ ∼ Gmat =QRGN – Biasing of tracer (galaxy) issue δg = bδm • Relativistic tracers: Weak lensing and CMB – Sensitive to (φ+ψ) ∼Glight =Q(1+R)GN and time derivs – In theory direct tracer of potential, but still uncertainties • stochasticity relating luminous and all mass rg Dekel & Lahav ’99 • plenty of systematics (photoz, IAs…) • Complementarity of tracers key to testing gravity Rachel Bean: Itzykson 2012 ʹ ͹ Ǥ ʹ Ǧ ǡ ȋ !"#$%ʹͲͲͺȌǤ ǡ Ǥ Ǧ δͶΨȋ δͳͲΨȌ ǣ x ͵ &'()*Ǥ x Ͷ Ǧ+ Ǥ x ͷ+&'()*ǦǤ Complications : photometric redshifts • Faster but less precise alternative to spectroscopic z z • Essential for tomography – Measuring evolution on dark energy – Cross-correlations between z bins Spectroscopic useful for disentangling systematics and cosmology Photometric z !"#$%&' ()*' ' +&,-'./01.'-/&'2&%,0%3456&'0,'-/".'2/0-078'49#0%"-/3',0%'-/&'Credit: LSST Consortiumugrizy'.:.-&3'$."5#' • Sensitive to modeling&32"%"649'-&3294-&.'$5%&94-&;'-0'-/0.&'$.&;'"5'-/ &'."3$94-"05<'1/&%&'1&'4229:'=0-/'34#5"-$;&'45;' .$%,46&' =%"#/-5&..' 2%"0%.*' >&?&6-"5#' #494@"&.' "5' -/&' 54%%01' =4;' 2/0-078' .-%"2' A9&,-B' 45;' 4;;"5#' – galaxy distribution,;&&2' C' D' 2/0-03&-%:' "32%0E&.' -/".' ,$%-/&%' 4.' ./015' 05' %"#/-*' F5' &46/' 64.&<' &32"%"649' .2&6-%49' -&3294-&.'4%&'$.&;<'50-'-/&'-&3294-&.'-/4-'#&5&%4-&;'-/&'."3$94-&;'64-490#.' Stage IV – photo-z statistical accuracy, systematic offsets and catastrophic errors dn/dz 30 z Rachel Bean: Itzykson 2012 Disentangling dark energy and cosmic tests of gravity from weak lensing systematics 5 The noise for each survey is modeled as statistical errors Survey Parameters Stage III Stage IV given by Area(sq. deg.) 5000 20000 2 "i"j γrms √2z0 0.8 0.9 N# = δij , (25) zmin 0.001 0.001 2nj zmax 33 ninj 1 N# = δij , (26) Ng 10 35 nj N 510 n " ph N i j =0, (27) σz0 0.07 0.05 # γrms 0.23 0.35 where γrms is the root mean square uncertainty in the shear measurement of the galaxies and nj is number of galaxies Table 1. Summary of the photometric large scale structure sur- th per steradian in j photometric redshift bin so i ni = Ng . vey specifications assumed for the Stage III and Stage IV survey: The survey specifications assumed in our analysis for survey area; median survey redshift, √2z ;minimumandmaxi- 0 the Stage III and IV surveys are given in TableP 1. mum redshifts observed, z and zmax;numberofgalaxies,per min We include complementary constraints from tempera- square arcminute, Ng;numberofphotometricredshiftbins,Nph; standard photometric redshift measurement error at z =0,σz0, ture (T) and E-mode polarisation (E) measurements from and the r.m.s. shear measurement error, γrms. aPlanck-likeCMBsurveyuptol =3000.Assummarised in Table 2, we model this by considering the three lowest frequency bands of the Planck HFI instrument, three chan- ν(GHz) 100 143 217 nels for temperature data and 2 for E mode polarisation,as described in the Planck Bluebook 7.Weassumeeachfre- f 0.8 0.8 0.8 sky quency channel has Gaussian beams of width θFWHM and θFWHM(arc min) 10.7 8.0 5.5 error in X = T,E of σX ,sothatthenoiseinchannelc is σ (µK) 5.4 6.0 13.1 T given by σE (µK) - 11.4 26.7 Disentangling dark energy and cosmic tests of gravity from weak lensing systematics 5 2 The noise for each survey is modeled as statistical errors XX,c Survey Parameters Stage III Stage IV 2 #(#+1)θFWHM,c/8ln(2) N# =(σX,cθFWHM,c) e given by , (28) Area(sq.