Diapositiva 1

1
Lecture 16 Cosmological Observations

• Curvature, Topology and Dynamics
• Curvature CMBR
• Topology Cosmic Cristalography Circles in the
  Sky
• Expansion History (Dynamics)
• H0
• H(z), q0, ?
• Matter-Energy Content
• Age
• Light Elements Primordial Abundance
• Reionization
• Non Cosmological Backgrounds

2

• 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
• which can have the values

Rcurv2 a 2 1 k
1, 0, 1 kc2 H2SOi O? 1
Rcurv2 gt 0 ? Rcurv is the radius of the
hypersphere (closed/spherical geometry) Rcurv
8 ? there is no Rcurv (flat/Euclidean
geometry) Rcurv2 lt 0 ? Rcurv is an imaginary
number (open/hyperbolic geometry)
3

• Curvature, Topology Dynamics

• Curvature
• Some possible topologies for flat curvature

simply connected (only one geodesics)
multiply connected (more than one geodesics)
4

• Curvature, Topology Dynamics)

Curvature Topology Dynamics k lt 0
(negative) finite/infinite open k 0
(Euclidean) finite/infinite open k gt 0
(positive) finite closed/open
5

• Curvature CMBR

• Cosmologists have measured Rcurv 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

6

• 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

7

• Dynamics Expansion History

• Current Hubble parameter (H0)
• 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 vpec ltlt vH
• 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

8

• 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

9

• 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

10

• Dynamics Expansion History

• HST Key Project

Freedman et al. 2001, ApJ 553, 47
11

• Dynamics Expansion History

• BCGs (50s 70s)
• SNe I (80s 90s)
• SNe Ia (90s 00s)

• SNe Ia
• Lmax dtL relation ? correction
• (lacks theoretical basis!)

12

• 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
13

• Dynamics Expansion History

14

• Dynamics Matter-Energy Content

• Radiation density
• The density parameter for the radiation is
  easily found from the temperature of the CMBR

TCMBR 2.725 ? 0.002 K ? Orad 4.15?105 h2
Mather et al. 1999, ApJ 512, 511

• Neutrino density
• The density parameter of neutrinos depend on
  their exact mass. If all ? species are massless,
• then their energy density is smaller
  than the ? energy density by a factor
  3?(7/8)?(4/11)4/3
• (the first term for 3 generations of
  ?, 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
• Nevertheless, observations of ? from both the
  Sun Bahcall 1989, Neutrino Astrophysics and
• from our atmosphere Fukuda et al. 1998,
  Ph. Rev. L 81, 1562 strongly suggest that ? of
• different flavors (generations)
  oscillate into each other. This can happen only
  if ? have
• mass (although probably very small)

O? 1.68?105 h2
15

• 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 Ob 0.02
• Lya-Forest in the spectra of distant quasars
  these estimates suggest Obh1.5 0.02
• Rauch et al. 1997
• anisotropies in the CMBR the second peak is
  direct related to the baryon density
• preliminary results give Obh2
  0.024?0.004
• light elements abundance are also sensitive to
  the baryon density, and that estimates
• give Obh2 0.0205 ? 0.0018
• Since these measurements refer to different
  redshifts (baryon density fall with a3), they
• are in good agreement

Ob 0.019 h2
16

• 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
• the best estimates from
• the concordance
• model (Ok 1.0,
• Omat 1/3 and
• O? 2/3) are
• t0 13.7 Gy

tL 1/H0 ?0?8 dz / (1z) Orad (1z)4 Omat
(1z)3 Ok (1z)2 O?½
17

• 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
• where 0 indices are current observed
  abundances, G indices are original abundances,
• t are the (half-lives / ln2) and tG is the
  Galaxy age. Half-lives of 235U, 238U and
• 232Th 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

235U0 235UG exp(-tG/tU) (232Th/238U)0
(232Th/238U)G exp-tG/(1/tTh 1/tU)
18

• 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)

19

• Dynamics Age

Krauss Chaboyer 2003, Science 299, 65, p.e.,
find tAG 13.43.4-2.2 Gy
Chaboyer 1998, Cosmological Parameters and Evol.
of the Universe, IAU Symp 183 the 17 oldest GC
20

• 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 lt 8 M?), and their
  luminosity decreases approximately
• as L ? M t7/5 Mestel 1952, MNRAS 112,
  583
• Hansen et al 2002, ApJL 574, L155, p.e.,
  find tD 7.3 ? 1.5 Gy
• (and tAG 12.5 ? 0.7 Gy for M5)

21

• 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.

22

• Light Elements Abundance

• primordial nucleosynthesis
• (200-1000 s, 1109-5108 K)
• 12D
• 23He
• 24He
• 37Li

Deuterium
D/Hp 3.39 ? 0.25 ? 105
Burles Tytler 1998, ApJ 499, 699 Burles
Tytler 1998, ApJ 507, 732
23

• 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 ? Yp

Izotov Thuan 1998, ApJ 500, 188
Peimbert et. al 2007, ApJ 666, 636
24

• Light Elements Abundance

25

• 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

26

• Reionization

• Observables
• quasars spectra (Gunn-Peterson trough) before
  reionization, HI absorption suppress all the
  light blueward
• of Ly?
• (zreion gt 6, from SDSS quasars)
• CMBR small scale anisotropies are erased, while
  polarization anisotropies are introduced
• (zreion 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
27

• Non Cosmological Backgrounds

28

• 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