A look into the Dark Universe

Transcription

1 Zentrum für Astronomie, Institut für Theoretische Astrophysik Universität Heidelberg

2 Dark Energy dark energy: assumed to drive accelerated cosmic expansion scalar field having negative pressure? early dark-energy models: finite dark-energy density even at early times behaviour not generally covered by common models (parameters w and dw/dz)

3 Dark Energy dark energy: assumed to drive accelerated cosmic expansion scalar field having negative pressure? early dark-energy models: finite dark-energy density even at early times behaviour not generally covered by common models (parameters w and dw/dz)

4 Dark Energy: Consequences pressure of a (homogeneous), self-interacting scalar field: p = wρc 2 = T V T + V ρc2

5 Dark Energy: Consequences pressure of a (homogeneous), self-interacting scalar field: p = wρc 2 = T V T + V ρc2 Friedmann s equation, expansion function E(a) = [ Ωr0 a 4 + Ω m0 a 3 + Ω d0e 3 d ln a[1+w(a)] + Ω ] 1/2 k0 a 2

6 Dark Energy: Consequences pressure of a (homogeneous), self-interacting scalar field: p = wρc 2 = T V T + V ρc2 Friedmann s equation, expansion function E(a) = [ Ωr0 a 4 + Ω m0 a 3 + Ω d0e 3 d ln a[1+w(a)] + Ω ] 1/2 k0 a 2 effects on cosmology: time and distances t = 1 da H 0 ae(a), D com = da a 2 E(a)

7 Dark Energy: Consequences pressure of a (homogeneous), self-interacting scalar field: p = wρc 2 = T V T + V ρc2 Friedmann s equation, expansion function E(a) = [ Ωr0 a 4 + Ω m0 a 3 + Ω d0e 3 d ln a[1+w(a)] + Ω ] 1/2 k0 a 2 effects on cosmology: time and distances t = 1 da H 0 ae(a), D com = da a 2 E(a) effects on cosmology: structure growth (a 3 Eδ ) = 3Ω m0δ 2a 2 E

8 Dark Energy: Expansion Function, Growth Factor

9 Dark Energy: Expansion Function, Growth Factor

10 Early Dark Energy: Model Specification parameterisation: averaged Ω d during structure formation, Ω d,sf few per cent (Wetterich, Doran et al.), Ω d,sf ln aeq ln a tr Ω d (a)d ln a ln a tr ln a eq models are compatible with data both have Ω d,sf Ω m0 = 0.33, h = 0.67, n = 1.05, σ 8 = Ω m0 = 0.36, h = 0.62, n = 0.99, σ 8 = 0.78

11 Early Dark Energy: Model Specification parameterisation: averaged Ω d during structure formation, Ω d,sf few per cent (Wetterich, Doran et al.), Ω d,sf ln aeq ln a tr Ω d (a)d ln a ln a tr ln a eq models are compatible with data both have Ω d,sf Ω m0 = 0.33, h = 0.67, n = 1.05, σ 8 = Ω m0 = 0.36, h = 0.62, n = 0.99, σ 8 = 0.78

12 Early Dark Energy: Models tracker solutions: dark energy density follows dominant component

13 Early Dark Energy: Models tracker solutions: dark energy density follows dominant component parameterising by w(z = 0) and constant dw/dz(z = 0) may be misleading

14 Early DE: Constraints from Data limits on Ω d,sf from WMAP3, CMB, 2dFGRS, SDSS, SN-Ia data (Robbers, Doran, Wetterich 2006)

15 Spherical Collapse study evolution of homogeneous, spherical overdensity: falls behind cosmic expansion, turns around, virialises at collapse time parameters: linear density contrast at collapse virial overdensity in collapsed halo

16 Spherical Collapse Model initial overdensity δ ini determined such that collapse occurs at chosen redshift z c overdensity linearly extrapolated to collapse redshift: δ c = D + (z c )δ ini overdensity within collapsed (virialised) halos: vir in Einstein-de Sitter universe: ( ) 2/3 3π 1.686, vir = 18π δ c = virialisation in presence of cosmological constant or Dark Energy? (cf. Maor & Lahav 2005)

17 Virial Overdensity virial overdensity in collapsed halos: assuming dark energy does not clump and thus not contribute to virialisation (cf. Maor & Lahav 2005)

18 Linear Overdensity linear overdensity at collapse: initial overdensity fixed by halo formation redshift

19 Linear Growth Factor growth factor divided by scale factor, normalised early (bottom) or late (top)

20 Asymptotic Behaviour at early times, a 1: linear growth factor D + (a) a n with n = Ω de(a) (cf. Ferreira & Joyce 1998) starting at a eq with the same overdensity, early DE falls behind by ( ) 1 n a a eq compared to ΛCDM at collapse, z c ac 1 1 and δ c (z c a eq ) m with m = 3 5 Ω de(a) for z c = 10 and Ω de (a eq ) 0.01 δ c 1.62 in agreement with numerical solution

21 Times and Distances at fixed H 0, universe may be 1 Gyr younger than standard ΛCDM

22 Times and Distances at fixed H 0, universe may be 1 Gyr younger than standard ΛCDM angular-diameter and luminosity distances, relative to ΛCDM

23 Halo Properties expected mean concentration parameter (according to Eke et al.)

24 Simulations halos evolving from identical initial conditions in different cosmologies simulations (Dolag et al.) quantitatively confirm increased concentrations

25 Mass Function, Merger Rates Sheth-Tormen mass function, relative to ΛCDM

26 Mass Function, Merger Rates Sheth-Tormen mass function, relative to ΛCDM occurrence of major mergers in clusters

27 Mergers and Strong Lensing mergers temporarily increase strong-lensing cross sections (Torri et al.)

28 Mergers and Strong Lensing mergers temporarily increase strong-lensing cross sections (Torri et al.) cluster cross sections in dark-energy models (Meneghetti et al.)

29 Lensing by high-z Clusters RDCS 1252 (z = 1.24)

30 Lensing by high-z Clusters

31 Lensing by high-z Clusters importance of mergers for the lensing optical depth (Fedeli et al.)

32 Cluster-Count Evolution decrease in cluster number (M > h 1 M ) from redshift 0 to 1: cluster population evolves substantially less; same effect for galaxies at higher redshifts!

33 Planck s Counts cumulative number counts expected from Planck

34 Planck s Counts cumulative number counts expected from Planck relative increase compared to ΛCDM

35 SZ Cluster Extraction simulated CMB map

36 SZ Cluster Extraction superposed SZ signal (Schäfer et al.)

37 SZ Cluster Extraction recovered SZ signal superposed SZ signal (Schäfer et al.)

38 The CBI Anomaly Boomerang, COBE-DMR, Dasi, Maxima, CBI data CBI data at l = simulations with σ 8 = 0.9 (bottom) and σ 8 = 1.0 (top) (Bond et al. 2005)

39 Weak Lensing coherent distortion of background galaxies distortion power spectrum: P κ (l) f(w)p δ (l/w)dw measurable two-point statistics: ξ(φ) l 2 P κ (l)j 0 (lφ)d ln l nonlinear evolution relevant on scales below 10

40 Weak-Lensing Power Spectrum weak-lensing power l 2 P κ (l) relative to ΛCDM source redshifts z s = 1 (lower curves) and z s = 1.5 (upper curves)

41 Conclusions models with early Dark Energy: finite dark-energy density even at high redshifts tracker solutions: DE density follows dominant comp. compatible with all relevant data normalised to CMB spherical collapse: virial overdensity moderately, linear overdensity significantly changed consequences: distance, times reduced halo concentrations increased halo-count evolution slowed down apparent discrepancy between linear and non-linear normalisation