Dark Energy, Modified Gravity and The Accelerating Universe

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1 Dark Energy, Modified Gravity and The Accelerating Universe Dragan Huterer Kavli Institute for Cosmological Physics University of Chicago

2 Makeup of universe today Dark Matter (suspected since 1930s established since 1970s) Baryonic Matter (stars 0.4%, gas 3.6%) 22% 4% Dark Energy (suspected since 1980s established since 1998) 74% Also: radiation (0.01%)

3 Some of the early history of the Universe is actually understood better! Physics quite well understood 95% of contents only phenomenologically described

4 DE status ~8 years after discovery m-m (mag) High-Z SN Search Team Supernova Cosmology Project =0.3, =0.7 =0.3, =0.0 =1.0, =0.0 Measurements much better, LCDM still a good fit Strong indirect (non-sna Ia) evidence for DE from CMB+LSS (m-m) (mag) Vacuum energy dominated Physical mechanism responsible completely unknown Matter dominated z Riess et al 1998; Perlmutter et al 1999 A lot of work on modified gravity proposals and observational signatures

5 Current constraints Ω DE 0.7

6 What if gravity deviates from GR? For example: H 2 F (H) = 8πG 3 ρ, or H2 = 8πG 3 ( ρ + 3F (H) 8πG ) Modified gravity Dark energy

7 Modified gravity proposals Introduce modifications to GR (typically near horizon scale) to explain the observed acceleration of the universe Make sure Solar System tests are passed (can be hard) Constrain the MG theory using the cosmological data Try to distinguish MG vs. standard DE (can be hard!)

8 Example: f(r) gravity S = 1 16πG d 4 x g [R + f(r)] Einstein equations are now 4th order Two classes frr<0 (never Matter Dominated, long range forces) frr>0 (MD in the past, can evade Solar system tests) Carroll, Duvvuri, Trodden, Turner 2005; Mena, Santiago & Weller 2006; Navarro & van Acoleyen 2006; Song, Hu & Sawicki 2006; many others...

9 Example: DGP braneworld theory 1 extra dimension ( bulk ) in which only gravity propagates matter lives on the brane weakening of gravity at large distances = appearance of DE Credit: Iggy Sawicki Dvali, Gabadadze & Porrati 2000; Deffayet 2001

10 The structure of DGP H 2 H r c = 8πG 3 ρ 5D GR 4D GR rc is a free parameter (to be consistent with observation, rc ~ 1/H0) 2GM=r g r * r c Scalar-Tensor New scale r = ( r g r 2 c ) 1/3 5D GR Dvali, Gabadadze & Porrati 2000; Deffayet 2001 Credit: Iggy Sawicki

11 DGP linear growth 1 Growth relative to EdS g(a) y DE Mimicking DGP expansion LCDM LCDM DGP DGP DGP 4D dark energy ax Scale factor Lue, Scoccimarro & Starkman; Koyama & Maartens; Sawicki, Song & Hu

12 ISW in DGP LCDM Phi DGP Song, Sawicki, & Hu 2007

13 So DGP is (almost) ruled out Disfavored at a few sigma from distances (SNe etc) Disfavored at a few more sigma from CMB ISW Decisive rule-out will come from ISW cross-correlation at high z: Song, Sawicki, & Hu 2007

14 Dark Energy or Modified Gravity? A given DE and modified gravity models may both fit the expansion history data very well But they will predict different structure formation history, i.e. deviation from δ + 2H δ 4πρM δ = 0

15 In standard GR, H(z) determines distances and growth of structure δ + 2H δ 4πρ M δ = 0 So check if this is true by measuring separately Distances (a.k.a. kinematic probes) (a.k.a. 0 th order cosmology) Growth (a.k.a. dynamical probes) (a.k.a. 1 st order cosmology)

16 Price of ignorance of MG allows for modified gravity 0.2 w a neglects modified gravity having!"= w 0 Huterer & Linder, astro-ph/

17

18 Cosmological Probes of Dark Energy (and Modified Gravity)

19 Kinematic probes: SNe Ia High-Z SN Search Team Supernova Cosmology Project m-m (mag) =0.3, =0.7 =0.3, =0.0 =1.0, =0.0 (m-m) (mag) Get pure (luminosity) distances z

20 Kinematic probes: CMB and BAO T = K δt T pt correlation Θ Distance to recombination Credit: WMAP team Sound horizon Bennett et al 2003 (WMAP collaboration)

21 Structure formation probes: Galaxy cluster counts d 2 N dω dz = n(z) r(z)2 H(z) dn/dz (4000 deg 2 ) w=-0.8! M =1,! DE =0! M =0.3,! DE =0.7, w=-1 Credit: Quinn, Barnes, Babul, Gibson z Essentially fully in the nonlinear regime (scales ~1 Mpc)

22 Structure formation probes: Weak Gravitational Lensing P shear 0 W (r)p matter (r)dr True, nonlinear l(l+1)p l! /(2") 10-6 Linear theory 10-8 Credit: Colombi & Mellier Multipole l Mostly in the nonlinear regime (scales ~10 arcmin, or ~1 Mpc)

23 More general approach Measure the DE parameters from distances and growth separately OmegaDE Omega_de w_1 0.2 wa w_0 w Ishak, Upadhye and Spergel 2006; others...

24 Still more general approach: measure functions r(z) and g(z) see if they are consistent Knox, Song & Tyson 2005

25 Minimalist Modified Gravity vs. DE Describe deviations from GR via a single new parameter g(a) δ a = exp [ a 0 ] d ln a[ω M (a) γ 1] Excellent fit to standard DE growth function with γ = [1 + w(z = 1)] Also fits the DGP braneworld theory with γ = 0.13 Huterer & Linder, astro-ph/ see also Linder & Cahn, astro-ph/

26 (dn/dz)!z "=0.55!"=0.1!w=0.05!m # =0.3 ev Cluster counts z Weak lensing tomography l(l+1) P! ii / (2") # = 0.55 # = {i,i}= l

27 Constraints on the growth index sig(w0) sig(wa) sig(gamma) WL SNE Planck Clusters Recall, for DGP γ = 0.13 Huterer & Linder, astro-ph/

28 Discarding the small-scale info in weak lensing (error or bias in!) / "!, fid Degradation factor in! error k cut (h / Mpc) Using the Nulling Tomography of weak lensing (Huterer & White 2005)

29 South Pole Telescope Planck Supernova/Acceleration Probe LSST

30 Conclusions distinguishing dark energy from modified gravity is becoming one of the key goals of cosmology in years to come assuming nonlinear clustering that follows the usual prescription even with MG, we find that future probes can achieve very interesting constraints on this parameter restriction to linear scales severely degrades the errors, but well worth pursuing ambitious, general approach: measure functions r(z) and g(z), check if they are consistent minimalistic approach: measure a single parameter that describes departures between DE and MG bright future with upcoming powerful surveys

31 Physically motivated MG parametrization ds 2 = a 2 (τ) [ (1 + 2ψ)dτ 2 + (1 2φ)d x 2] ψ = (1 + ϖ)φ and assume ϖ = ϖ 0 ρ DE ρ M [l(l+1)c l /2!] 1/2 (µk) LCDM!0.1! l: multipole moment Caldwell, Cooray & Melchiorri, astro-ph/

32 Physically motivated MG parametrization CMB-galaxy cross-correlation 10!3 Weak lensing power spectrum 10!4 LCDM 0.1!0.1 l(l+1)c l /2! 10!5 10! l Caldwell, Cooray & Melchiorri, astro-ph/

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