Lecture 16 Cosmological Observations Curvature, Topology and Dynamics Curvature: CMBR Topology: Cosmic Cristalography & Circles in the Sky Expansion History (Dynamics) H 0 H(z), q 0, Λ Matter-Energy Content Age Light Elements Primordial Abundance Reionization Non Cosmological Backgrounds Depto. de Astronomía (UGto) Astronomía Extragaláctica y Cosmología Observacional
Curvature, Topology & Dynamics According to GR, spacetime is what mathematicians call a manifold, characterized by a metric and a topology the metric gives the local shape of spacetime (the distances and time intervals), relating a curvature to the presence of matter and energy the topology gives the global geometry (shape and extension) of the Universe The FRW model specifies completely the metric, but not the global curvature parameter (k) and a free function given the expansion history (a), which represents the dynamics of the Universe The curvature parameter is related to the radius of curvature of the Universe, defined as R curv2 = a 2 = 1 k = +1, 0, 1 kc 2 H 2 ΣΩ i + Ω Λ 1 which can have the values: R curv2 > 0 R curv = R curv2 < 0 R curv is the radius of the hypersphere (closed/spherical geometry) there is no R curv (flat/euclidean geometry) R curv is an imaginary number (open/hyperbolic geometry) concerning to the topology, in the first case the Universe has a finite volume, while in the others the Universe may either be finite or infinite in spatial extent
Curvature, Topology & Dynamics Curvature Some possible topologies for flat curvature simply connected (only one geodesics) multiply connected (more than one geodesics) The spherical (positive curvature) spaces and Euclidean (flat) spaces are all classified, but the hyperbolic (negative curvature) ones are not
Curvature, Topology & Dynamics) Curvature Topology Dynamics k < 0 (negative) finite/infinite open k = 0 (Euclidean) finite/infinite open k > 0 (positive) finite closed/open
Curvature: CMBR Cosmologists have measured R curv using the largest triangle available: one with us at one corner and the other two corners in the CMBR the characteristic angular size of the temperature fluctuations (hot and cold spots) can be predicted theoretically: if the space is flat, this characteristic size (or, more rigorously, the first peak in the CMBR power spectrum) subtends about 0.5 (~ Moon size); positively and negatively curved spaces have larger and smaller values, respectively Observed values are so close to 0.5 that we still cannot tell whether space is perfectly flat or very slightly curved either way...
Topology: Cosmic Cristalography & Circles in the Sky If the Universe is positively curved or Euclidean it is, in principle, possible to verify if it is simply or multiply connected by the the cosmic cristalography method given a certain class of extragalactic objects, with known distances, one may analyze the distribution of distances of these objects: if the Universe is multiply connected (and its curvature radius is smaller than the deepness limit of the sample) certain values of distances will occur much more frequently than the others Another possible verification for signs of multiple conexity is the search for circles in the sky in the CMBR if the fundamental polyhedron has a size such that its faces intercept the last scattering surface, we may see circles (marked by different temperatures) in these interceptions
Dynamics: Expansion History Current Hubble parameter (H 0 ): In order to measure the current expansion rate (Hubble constant ) one needs to have accurate distances and radial velocities for a sample of extragalactic objects covering distances large enough for having v pec << v H and still in the Local Universe radial velocities are directly measured from the redshifts of object spectra distances are very hard to measure many methods are available, but all of them have large uncertainties. There are two general classes of methods: the ones that use a series of distance measurements, each calibrated to measures at shorter distances, which compose a distance ladder, and the direct ones
Dynamics: Expansion History the Cepheids P-L Relation, Tully-Fisher, Fundamental Plane and Ia Supernovae methods are of the first class, using calibrations from parallaxes (Hipparchus satellite), statistical parallaxes, main sequence fitting, etc
Dynamics: Expansion History the Surface Brightness Fluctuations, Baade-Wesselink, Time Delay of Gravitational Lenses and X-Ray + S-Z methods are of the second class, based only on physical assumptions
Dynamics: Expansion History HST Key Project [Freedman et al. 2001, ApJ 553, 47]
Dynamics: Expansion History d = cz/h 0 [1 + ½ (1 + q 0 ) z] BCGs (50 s 70 s) SNe I (80 s 90 s) SNe Ia (90 s 00 s) SNe Ia: L max d t L relation correction (lacks theoretical basis!)
Dynamics: Expansion History Expansion History H(z): Supernovae Cosmology Project [Perlmutter et al. 1998, Nature 391, 51] [Perlmutter et al. 1999, ApJ 517, 565] High-z Supernovae Project [Riess et al. 1998, AJ 116, 1009]
Dynamics: Expansion History q(t) = ½ ΣΩ i (t) Ω Λ (t)
Dynamics: Matter-Energy Content Radiation density: The density parameter for the radiation is easily found from the temperature of the CMBR Neutrino density: T CMBR = 2.725 ± 0.002 K Ω rad = 4.15 10 5 h 2 [Mather et al. 1999, ApJ 512, 511] The density parameter of neutrinos depend on their exact mass. If all ν species are massless, then their energy density is smaller than the γ energy density by a factor 3 (7/8) (4/11) 4/3 (the first term for 3 generations of ν, the 7/8 because the Fermi-Dirac integral is smaller than the Bose-Einstein one by this factor, and the third term for difference in temperatures of the 2 particles). Thus Ω ν = 1.68 10 5 h 2 Nevertheless, observations of ν from both the Sun [Bahcall 1989, Neutrino Astrophysics] and from our atmosphere [Fukuda et al. 1998, Ph. Rev. L 81, 1562] strongly suggest that ν of different flavors (generations) oscillate into each other. This can happen only if ν have mass (although probably very small)
Dynamics: Matter-Energy Content Baryonic density: There are now four established ways of measuring the baryon density, and these all seem to agree reasonably well [Fukugita, Hogan & Peebles 1998, ApJ 503, 518] groups and clusters of galaxies most of the baryons in groups and clusters are in the form of a hot intergroup/cluster gas. The current estimates give Ω b ~ 0.02 Lyα-Forest in the spectra of distant quasars these estimates suggest Ω b h 1.5 ~ 0.02 [Rauch et al. 1997] anisotropies in the CMBR the second peak is direct related to the baryon density; preliminary results give Ω b h 2 ~ 0.024±0.004 [] light elements abundance are also sensitive to the baryon density, and that estimates give Ω b h 2 ~ 0.0205 ± 0.0018 Since these measurements refer to different redshifts (baryon density fall with a 3 ), they are in good agreement Ω b ~ 0.019 h 2
Dynamics: Age Universe Age: Since we have the density parameters of the Universe, we can estimate the its age from the lookback time of the big-bang t L = 1/H 0 0 dz / (1+z) [Ω rad (1+z) 4 + Ω mat (1+z) 3 Ω k (1+z) 2 + Ω Λ ] ½ the best estimates from the concordance model (Ω k = 1.0, Ω mat ~ 1/3 and Ω Λ ~ 2/3) are t 0 = 13.7 Gy
Dynamics: Age Galaxy Age: Beyond estimates from H(z), one can obtain lower limits for the Universe age from the age of our Galaxy three methods are usually used for that nucleocosmochronology abundance ratios of long-lived radioactive species (formed by fast n capture, r-process, in SNe explosions of the early generation stars) can be predicted and compared with their present observed ratios 235 U 0 = 235 U G exp(-t G /τ U ) ( 232 Th/ 238 U) 0 = ( 232 Th/ 238 U) G exp[-t G /(1/τ Th 1/τ U )] where 0 indices are current observed abundances, G indices are original abundances, τ are the (half-lives / ln2) and t G is the Galaxy age. Half-lives of 235 U, 238 U and 232 Th are, respectively 0.704, 4.468 and 14.05 Gy, respectively (all of them decay to a stable isotope of Pb) Cayrel et al [2001, Nature 409, 691], p.e., using these elements and also Os and Ir derived the age t G = 13.3 ± 3 Gy
Dynamics: Age Globular Clusters age the oldest stars of the Galaxy are in the Globular Clusters. These systems form very rapidly in the beginning of the galaxy life, since their collapse time scale is only about several million years. Their age can be derived from their H-R diagram, considering that all of their stars were born at the same time the turn-off point, obtained by a isochrone fitting, gives the age of the GC. In the oldest GC the main-sequence turn-off point has reached a mass of about 0.9 M (Z ~ Z /150)
Dynamics: Age Krauss & Chaboyer [2003, Science 299, 65], p.e., find t AG = 13.4 +3.4-2.2 Gy [Chaboyer 1998, Cosmological Parameters and Evol. of the Universe, IAU Symp 183] the 17 oldest GC
Dynamics: Age disc age the age of the Galaxy disc may be estimated by the luminosity function of white dwarf stars. These stars represent the final evolutionary state of most main-sequence stars (M < 8 M ), and their luminosity decreases approximately as L M t 7/5 [Mestel 1952, MNRAS 112, 583] Hansen et al [2002, ApJL 574, L155], p.e., find t D = 7.3 ± 1.5 Gy (and t AG = 12.5 ± 0.7 Gy for M5)
Dynamics: Age quasars the currently farthest quasar was found at z = 6.4 [SDSS] The lookback time of this object is about 12.9 Gy, which means that its formation was at most 0.8 Gy after the Big-Bang.
Light Elements Abundance primordial nucleosynthesis (200-1000 s, 1 10 9-5 10 8 K) 12 D 23 He 24 He 37 Li Deuterium: [D/H] p = 3.39 ± 0.25 10 5 [Burles & Tytler 1998, ApJ 499, 699] [Burles & Tytler 1998, ApJ 507, 732]
Light Elements Abundance Helium: There is a relation between the abundance of metals, Z, and the abundance of He, Y (both are produced by stars) By extrapolating the Y to Z = 0 (using the O, for example) we get the primordial abundance of He Y p [Izotov & Thuan 1998, ApJ 500, 188] [Peimbert et. al 2007, ApJ 666, 636]
Light Elements Abundance
Reionization The Dark Ages: after recombination, HI absorbs almost all the light of the first stars (Universe is dark and opaque) Energy sources for reionization: quasars: by assuming a universal LF for quasars and extrapolating to reionization era, they seem not to be numerous enough to ionize the IGM alone pop III stars (zero-metallicity, high-mass, very hot stars): can account for reionization with a reasonable IMF, although not observed yet
Reionization Observables: quasars spectra (Gunn- Peterson trough)*: before reionization, HI absorption suppress all the light blueward of Lyα (z reion > 6, from SDSS quasars)** CMBR: small scale anisotropies are erased, while polarization anisotropies are introduced (z reion = 11-7 from WMAP3)*** 21-cm line: ideal probe, for the near future * [Gunn & Peterson 1965, ApJ 142, 1633] ** [Becker et al. 2001, AJ 122, 2850] *** [Spergel et al. 2007, ApJS 170, 377]
Non Cosmological Backgrounds
Other References Papers: A.R. Liddle 1999, astro-ph/9901124 (inflation) M.S. Turner 1999, PASP 111, 264 P.J.E. Peebles 1999, PASP 111, 274 S.M. Carroll 2000, astro-ph/0004075 (cosmological constant) M. Tegmark 2002, astro-ph/0207199 M.S. Turner 2002, astro-ph/0202007 Gallerani et al. 2006, MNRAS 370, 1401 Books: S. Dodelson 2003; Modern Cosmology, Academic Press M. Roos, 1999; Introduction to Cosmology, Wiley Press M. Plionis & S. Cotsakis 2002, Modern Theoretical and Observational Cosmology, ASSL Kluwer Academic Publishers M.H. Jones & R.J.A. Lambourne 2003. An Introduction to Galaxies and Cosmology, Cambridge Univ. Press