Cosmology from Gravity, Galaxies and Gas

1. Cosmology from Gravity, Galaxies and Gas • Gravitational instability in an expanding universe • Gastronomy: A biased view of dark matters • Galaxies • Gas • Geometry and Dynamics • The Cosmic Background Radiation • Supernovae • The ISW effect • Baryon oscillations Ravi K. Sheth (UPenn)

2. The SDSS

3. You can observe a lot just by watching. -Yogi Berra

4. Galaxy clustering depends on type Large samples now available to quantify this

5. Light is a biased tracer To use galaxies as probes of underlying dark matter distribution, must understand ‘bias’

6. N-body simulations of gravitational clustering in an expanding universe

7. Cold Dark Matter • Simulations include gravity only (no gas) • Late-time field retains memory of initial conditions • Cosmic capitalism Co-moving volume ~ 100 Mpc/h

8. Cold Dark Matter • Cold: speeds are non-relativistic • To illustrate, 1000 km/s ×10Gyr ≈ 10Mpc; from z~1000 to present, nothing (except photons!) travels more than ~ 10Mpc • Dark: no idea (yet) when/where the stars light-up • Matter: gravity the dominant interaction

10. Cosmology/particle physics from density profiles of halos, and from substructure in halos (i.e. dense regions), but beware of GASTROPHYSICS!

12. You’ve got to be very careful if you don’t know where you’re going, because you might not get there.-Yogi Berra

13. Assume a spherical cow….

14. Assume a spherical herd of spherical cows…

15. Initial spatial distribution within patch (at z~1000)... …stochastic (initial conditions Gaussian random field); study `forest’ of merger history ‘trees’. …encodes information about subsequent ‘merger history’ of object (Mo & White 1996; Sheth 1996)

16. Organized spherical collapse; model for merger history To this, add dynamical friction, tidal stripping, interactions, etc.

17. Only very fat cows are spherical…. …but this turns out to be a detail.

18. (Reed et al. 2003) The Halo Mass Function • Small halos collapse/virialize first • Can also model halo spatial distribution • Massive halos more strongly clustered (current parametrizations by Sheth & Tormen 1999; Jenkins etal. 2001)

19. Universal form? • Spherical evolution (Press & Schechter 1974; Bond et al. 1991) • Ellipsoidal evolution (Sheth & Tormen 1999; Sheth, Mo & Tormen 2001) • Greatly simplifies analysis of cluster abundances (e.g. ACT) Sheth & Tormen 1999 Jenkins et al. 2001 Accurate for any cosmological model, fluctuation spectrum, and time

20. Most massive halos populate densest regions over-dense under-dense Key to understand galaxy biasing (Mo & White 1996; Sheth & Tormen 2002) n(m|d) = [1 + b(m)d] n(m)

21. Halo clustering • Massive halos more strongly clustered • Clustering of halos different from clustering of mass • On large scalesxh(r) ~ b2 xdm(r); bias is linear massive halos non- linear theory dark matter Percival et al. 2003

22. Halo clustering  Halo abundances Clustering is ideal (only?) mass calibrator (Sheth & Tormen 1999)

23. Halo-model of galaxy clustering • Two types of pairs: only difference from dark matter is that now, number of pairs in m-halo is not m2 • ξdm(r) =ξ1h(r) + ξ2h(r) • Spatial distribution within halos is small-scale detail

24. SDSS Galaxy ClusteringOn large scales, bias linear (as expected); more luminous galaxies more strongly clustered Measurements constrain galaxy formation in ‘standard’ model

25. Gravitational Lensing

26. Lensing provides a measure of dark matter along line of sight

27. Image distortions correlated with dark matter distribution; e.g., lensed image ellipticities aligned parallel to filaments, tangential to knots (clusters)

28. The shear power of lensing stronger weaker Cosmology from measurements of correlated shapes; better constraints if finer bins in source or lens positions possible

29. CL0024+1664 Lensed, distorted object is blue Note: a cluster is relatively easy to find from photometry alone (cheaper than obtaining spectra) because most galaxies in it have similar colors

30. Strong lensing: Multiple images PG 115+080 zsource = 1.72 zlens = 0.31

31. Focal length strong function of cluster-centric distance; highly distorted images possible • Strong lensing if source lies close to lens-observer axis; weaker effects if impact parameter large • Strong lensing: Cosmology from distribution of image separations, magnification ratios, time delays; but these are rare events, so require large dataset • Weak lensing: Cosmology from correlations (shapes or magnifications); small signal requires large dataset

32. The Lyman-alpha forest

33. Evolving forest … …probes evolution of cosmological gas density field

34. SDSS Ly-a P(k) Higher-z Evolution consistent with LCDM model Non-trivial because this is test at z~3! Lower-z

35. Inhomo-geneity on various scales in the Universe

36. Combining any (or all) datasets with CMB provides long lever arm on primordial fluctuation spectrum • Combining datasets also breaks degeneracies

37. The Cosmic Background Radiation Cold: 2.725 K Smooth: 10-5

38. Lensing of the CMB Primordial Lensed Next generation of experiments should be able to measure this effect

39. The ISW effect Cross-correlate CMB and galaxy distributions Interpretation requires understanding of galaxy population

40. Cosmology from growth rate of gravitational instability (which must overcome expansion): Signal depends on b(a) D(a) d/dt [D(a)/a]

41. Evolution and bias Work in progress to disentangle evolution of bias from z dependence of signal (Scranton et al. 2004)

42. Classical Cosmological Tests • Standard candles or rods require 2 integrals over redshift: • Comoving distance: dCom(z) = (c/H0) 0 ∫zdz H0/H(z) where H(z) describes expansion history: [H(z)/H0]2 = WM(1+z)3 + WDEexp{ ∫da/a [1+w(a)]} ‘Standard’ flat cosmological constant model has w(a) = −1 andWDE = 1 − WM

43. Small fluctuations (10-5) are seeds from which structure grows.

45. Angular scale of first peak implies universe is Flat

46. Supernovae Ia are good standard candles … … for no good reason …!

47. Cosmological Time Dilation Agreement with standard template only if (1+z) time dilation factor included

48. Measuring the expansion Expansion rate changes with time: Hubble’s constant same at all positions in space, but may depend on time

50. Evidence for acceleration today… … and deceleration in the more distant past