Constraining Modified Growth Patterns with Tomographic Surveys GGI - PowerPoint PPT Presentation

Constraining Modified Growth Patterns with Tomographic Surveys GGI Dark Energy Conference March, 3rd 2009 Alessandra Silvestri in collaboration with: Levon Pogosian, GongBo Zhao, Joel Zylberberg astro-ph/0809.3791 astro-ph/0709.0296, PRD’07

Outline Cosmic Acceleration: ? Modified Gravity ? Dark Energy? Λ Can we distinguish between them? Large Scale Structure! f(R) theories : as a learning-ground for signatures of modifications Growth of Structure: Background: degenerate the dynamics is changed, leading to with LCDM a characteristic scale-dependent pattern Searching for modified growth patterns

Cosmic Acceleration Supernova Cosmology Project Kowalski, et al., Ap.J. (2008) 1.5 SNeIa, CMB, Union 08 LSS SN Ia compilation + 1.0 standard GR applied to a SNe homogeneous and isotropic � � Universe Kowalski et al . 2008 0.5 Ω 0 m ≈ 0 . 3 CMB F Ω 0 X ≈ 0 . 7 l Eisenstein et al . a t BAO 2005 0.0 ρ 0 = ρ 0 � � 0.0 0.5 1.0 Ω 0 m ≡ � m 3 H 2 0 M 2 ρ 0 P cr

Cosmic Acceleration A very good fit to all these data is a Universe in which 70% of the energy budget is in the COSMOLOGICAL CONSTANT, LCDM Anyhow it is important to explore the whole space of explanations that fit these data and could have testable features... Dark Energy Modified Gravity 1 ˜ 1 ˜ G µ ν T µ ν = T µ ν G µ ν = M 2 M 2 P P X matter fields with dynamics such as to modification of GR on large cause the late universe to accelerate scales, admitting self-accelerating (quintessence, solutions k-essence, ...) Generalized Dark Energy LCDM + vs. (or uncoupled DE) Modified Gravity

What do we learn from f(R) gravity ?

f(R) Gravity S = M 2 � � dx 4 √− g [ R + f ( R )] + d 4 x √− g L m [ χ i , g µ ν ] P 2 (S.Capozziello, S.Carloni & A.Troisi, astro-ph/0303041 S.Carroll, V.Duvvuri, M.Trodden & M.S.Turner, Phys.Rev.D70 043528 (2004)) (1 + f R ) R µ ν − 1 2 g µ ν ( R + f ) + ( g µ ν � − ∇ µ ∇ ν ) f R = T µ ν { M 2 P ∇ µ T µ ν = 0 f R ≡ d f dR The Einstein equations are fourth order. The trace-equation becomes: dynamical ! T R = T M 2 (1 − f R ) R + 2 f − 3 � f R = P M 2 P

Background Viability There is an extra scalar d.o.f.: the scalaron f R � λ C ≡ 2 π 3 f RR ≈ 2 π m f R 1 + f R ...extra dynamics and fifth-force... to have a stable high-curvature regime, i.e. to go through a standard matter era, to have a positive effective Newton constant, and to satisfy LGC w e ff ≃ − 1 (Dolgov & Kawasaki, Phys.Lett.B 573 (2003), Navarro et al. gr-qc/0611127, Sawicki and Hu astro-ph/0702278 Starobinsky astro-ph/0706.2041, Chiba, Smith, Erickcek astro-ph/0611867 Amendola et al. astro-ph/0603703-0612180, Amendola & Tsujikawa astro-ph/0705.0396)

Can we distinguish them from LCDM? While at the background level viable f(R) must closely mimic LCDM, the difference in their prediction for the growth of large scale structure can be significant The scalaron sets a transition scale, inducing a characteristic scale- dependent pattern-dependent pattern of growth coupled DE On scales below the Compton wavelength of the scalaron, the modifications contribute a slip between the Newtonian potentials and the growth is enhanced by the fifth-force ISW, P(k), ISW-galaxy & WL

Dynamics of Linear Perturbations....Sub-Horizon k 2 � 1 + H ′ � δ ′′ δ ′ m + m + a 2 H 2 Ψ = 0 H 1 + 4 k 2 f RR − 3 1 E m δ m k 2 Ψ = a 2 F 1 + 3 k 2 f RR F 2 a 2 F = k 2 1 k 2 f RR { time and scale dependent a 2 m 2 a 2 F rescaling of Newton constant Ψ = 1 + 2 k 2 f RR Φ a 2 F 1 + 4 k 2 f RR a 2 F β k 2 k 2 Ψ = 1 + 2 = 1 + 4 Φ G e ff a 2 m 2 3 a 2 m 2 3 k 2 k 2 1 + 4 G 1 + a 2 m 2 3 a 2 m 2 (coupled quintessence: Amendola,L. PRD’04)

w eff = − 1 � Φ + ( a, k ) ∆ m ( a, k ) /a � f 0 R = − 10 − 4 Φ + ( a i , k ) ∆ m ( a i , k ) /a i f(R) LCDM k (h/Mpc) k (h/Mpc) 0.5 0.5 0.2 0.2 0.1 0.1 0.05 0.05 0.02 0.02 0.01 0.01 5 4 3 2 1 0 5 4 3 2 1 0 z z 0.8 0.9 1

Characteristic signatures Overall we observe a scale-dependent pattern of growth. The modifications introduced by f(R) models are similar to those introduced by more general scalar-tensor theories and models of coupled DE-DM The dynamics of perturbations is richer, and different observables are described by different functions, not by a single growth factor! Φ + combining different measurements we can build discriminating probes of gravity

Searching for modified growth patterns What is the potential of current and upcoming tomographic surveys to detect departures from GR (LCDM,quintessence) in the growth of structure?

Parametrization slip between Newtonian potentials: γ ( a, k ) ≡ Φ Ψ effective Newton constant: G → G · µ ( a, k ) in standard GR : γ ( a, k ) = 1 µ ( a, k ) = 1 Parametrization: inspired by scalar-tensor theories / massive coupled quintessence k 2 Φ Yuk ∼ 1 = 1 + β G e ff � 1 + ( β − 1) e − r/ λ � a 2 m 2 k 2 G 1 + r a 2 m 2 γ ( a, k ) ≡ 1 + β 2 λ 2 2 k 2 a s µ ( a, k ) ≡ 1 + β 1 λ 2 1 k 2 a s 1 + λ 2 1 + λ 2 2 k 2 a s 1 k 2 a s Fisher analysis for the parameters: { s, β 1 , β 2 , λ 2 1 , λ 2 2 }

Observables: theoretical predictions m + k 2 Ψ = 0 ∆ ′′ m + H ∆ ′ { k 2 Ψ = − a 2 OBSERVABLES G · µ ( a, k ) ∆ m 2 M 2 P Φ = γ ( a, k ) · Ψ We wish to combine multiple-redshift information on Galaxy Count, Weak Lensing, CMB and their cross correlations Y (ˆ n 2 , z 2 ) X (ˆ n 1 , z 1 ) Therefore the observables are the ANGULAR POWER SPECTRA: dk � C XY k ∆ 2 R I X l ( k ) I Y ( θ ) = 4 π l ( k ) l � z ∗ dz W ( z ) j l [ kr ( z )] ˜ I X l ( k ) = c x R X ( k, z ) 0

Surveys background: SNeIa (SNAP) + CMB (Planck) Galaxy Count (GC) & Weak Lensing (WL): DES (Dark Energy Survey, Sept. 2009, 0.1 < z <1.3) LSST (Large Synoptic Survey Telescope, proposed, z ~ 3) ∆ T CMB: Planck (ESA, , ) ∼ 2 × 10 − 6 θ ∼ 5 ′ T

Fiducials γ ( a, k ) ≡ 1 + β 2 λ 2 2 k 2 a s µ ( a, k ) ≡ 1 + β 1 λ 2 1 k 2 a s 1 + λ 2 1 + λ 2 2 k 2 a s 1 k 2 a s f(R) fiducials: fixed coupling: β 1 = 4 3 , β 2 = 1 2 1 mass evolution: m 2 ∼ f RR ∝ a − 6 s ∼ 4 mass scale today: λ 1 � O (10) Mpc (LGC) (LGC) λ 1 � O (10 3 ) Mpc

Constraints 68% Confidence Contours for the 5 modified-growth parameters

f(R)

f(R)

Relative Errors with all data combined

Reconstructed G and gravitational slip λ 2 1 ∼ 10 3 DES λ 2 1 ∼ 10 4 LSST 5 4 3 2 1 5 4 3 2 1 0 4 3 2 1 0 4 3 2 1 0 redshift

Summary The degeneracy among models of cosmic acceleration is broken at the level of Large Scale Structure. Weak Lensing (WL), Galaxy Count (GC), the Integrated Sachs Wolfe effect (ISW) & their cross-correlations offer a powerful testing ground for GR on large scales. We have learned that upcoming and future surveys can place non trivial bounds on modifications of the growth of structure even in the most conservative case, i.e. considering only linear scales. These results are model-dependent, but they motivate us to pursue model-independent methods such as PCA (Principal Component Analysis) results coming soon, stay tuned :-)

THANK YOU !