NCPP Primorsko

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NCPP




Primorsko

June 2007Topics in
Cosmology-2

• Daniela Kirilova
• Institute of Astronomy, BAS

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Outline

• Introduction to Cosmology
• The Universe Dynamics
• The Expanding Universe
  observational status
• Universe Parameters
• H constant
• Universe age
• The Expansion History of the
  Universe

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Cosmological Principle is exact at large scales
gt 200 Mpc (containing mlns of galaxies) It is
a property of the global Universe.

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2.1.The Universe Dynamics

• Dynamics is provided by GR.
• The Einstein field quations read
• ,
• Finding a general solution to a set of
  equations as complex as the Einstein field
  equations is a hopeless task. The problem is
  simplied greatly by considering mass
  distributions with special symmetries.
• The matter content is usually modelled as a
  perfect fluid with a stress-energy tensor in the
  rest frame of the fluid

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Differentiating Eq. (1) and subtracting Eq. (2)
we obtain an equation for the energy momentum
conservation or Friedmann expansion
driven by an ideal fluid is isentropic,
dS0Frequently used relation between the scale
factor andtemperature in an expanding Universe
R(t)1/T
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Number of relativistic degrees of freedom is a
function of T.

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• Thermodinamic relations for the energy density
  and number densities n
• These relations are a simple consequence of the
  integration of the Bose-Einstein or Fermi-Dirac
  distributions

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• The Friedmann equation, Eq. (1), can be
  interpreted within Newtonian mechanics. It takes
  the form of energy conservation for test
  particles bounded in the gravitational potential
  created by mass
• k1 corresponds to negative binding energy,
  recollapse and over-critical density, where
  
• 
  H2
• k-1 positive binding energy, expansion,
  under-critical density

Three cases should be distinguished which
foreordain the type geometry of the universe
Flat, an open universe, having Euclidean
geometry, infinite in space and time.
Spherical, a closed universe, finite but
unbounded in space and finite in time.
Hyperbolic, again an open universe, infinite in
space and in time, but curved.
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Possible scenarios green - a flat, critical
density universe in which the expansion is
continually slowing down blue - an open, low
density universe, expansion is slowing down,
but not as much because the pull of gravity is
not as strong. red - a universe with a large
fraction of matter in a form of dark energy,
causing an accelerated expansion .
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• According to Einstein's theory, the force law is
  modied. Not only does mass gravitate, but the
  pressure, too, makes its contribution to the
  gravitational force. This is a very important
  modication, since pressure can be negative,
  leading to anti-gravity and to accelerated
  expansion.

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The present value of this parameter H is called
the Hubble constant. It describes the rate of
expansion of the Universe, and can be related to
observations. Consider two points with a fixed
comoving distance The physical distance is
the relative velocity is
This is the famous Hubbles law To solve the
Friedmann equations, one has to specify the
Universe matter content and the equation of
state for each of the constituents.
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Equations of state
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Expansion History of the Universe
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(No Transcript)
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2.3.The Expanding Universe

• Observational status

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Hubble's Law 1912- Slipher spiral
nebula are receding 1920's- Hubble v-d
proportionality

• Distance-Velocity Relationship

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Distances to Galaxies

• Step by step approach (the distance ladder)
  based on the assumption that cepheids, RR Lyrae
  stars have the same properties in other galaxies.
  The same for the SN explosions. These
  assumptions are supported by essentially the same
  spectra and light curves.
• variable stars up to 20 Mpc
• SN I (had nearly the same peak luminosity
  ) up to 400 Mpc
• brightest Sc I spirals, which have about
  the same luminosity
• Tully-Fisher relation, between the
  rotational velocity of a spiral galaxy and its
  luminosity.
• Galaxies Velocities
• The shift of emission lines with respect to
  the frequency measurements by the local observer
  is related to velocity, and is used as an
  observable instead of the velocity.

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Apparent, absolute magnitudes and
photometric distance

• If we know the apparent magnitude m and the
  absolute magnitude M using we can evaluate d
  (photometric distance)
• where d is measured in parsecs.

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The Redshift

• Systematic recession of objects, or
  cosmological expansion, leads
• to redshift. Note that cosmological redshift
  is not entirely due to the Doppler effect, but,
  rather, can be interpreted as a mixture of the
  Doppler effect and of the gravitational redshift.
• zcv, for nonrelativistic velocities zlt0.2,
  otherwise

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Hubbles Original Diagram
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• From the
  Proceedings
• of the National
  Academy of Sciences
  Volume 15 March 15, 1929 Number 3
• A RELATION BETWEEN DISTANCE AND RADIAL
  VELOCITY AMONG EXTRA-GALACTIC
  NEBULAE
• By Edwin Hubble
• Mount Wilson Observatory, Carnegie
  Institution of Washington
  Communicated January 17, 1929
• ..The results establish a roughly linear
  relation between velocities and distances among
  nebulae
• The outstanding feature, is the
  possibility that the velocity-distance relation
  may represent the de Sitter effect, and hence
  that numerical data may be introduced into
  discussions of the general curvature of space. In
  the de Sitter cosmology, displacements of the
  spectra arise from two sources, an apparent
  slowing down of atomic vibrations and a general
  tendency of material particles to scatter. .
  .. the linear relation found in the present
  discussion is a first approximation representing
  a restricted range in distance.

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The Hubble Law

• cz H d
• v measured in km/s, d in Mpc, hence H is
  measured in km/s/Mpc.
• H0 100h km/s/Mpc, 0.4 lt h lt 1.0
• Corresponds to a homogeneous expanding universe
  (r, T decrease)
• Space itself expands
• The Hubble law provides a scheme to find the
  distance to a distant galaxy by measuring its
  redshift.
• Applicable for distances higher than those
  corresponding to peculiar velocities.
• d3000h-1 z Mpc
• dH(t) 3t2/H(t) at MD, dH(t) 2t1/H(t) at RD
• Hubble age 1/H0
• If r(t) and H(t) at any moment t, then
• Not applicable for gravitationally bound
  systems.

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Contemporary Hubble Diagrams
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2.4. Universe ParametersThe Hubble Constant

• One of the "key projects" of the Hubble Space
  Telescope is the
• Edwin Hubble's program of
• measuring distances to nearby galaxies.
• The current CMB results show the Hubble Constant
  to be
• H73 3/-4 (km/sec)/Mpc.

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Age of the Universe

• If the universe contains a form of matter similar
  to the cosmological constant, then the inferred
  age can be even larger.
• In general in the case matter density is less
  than 1

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The universe is at least as old as the oldest
globular clusters that reside in it.

• Life cycle of a star depends upon its mass
• All of the stars in a globular cluster formed at
  roughly the same time they can serve as cosmic
  clocks. The oldest globular clusters contain only
  stars less massive than 0.7 M. Observation
  suggests that the oldest globular clusters are
  between 11 and 13 billion years old.

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H-R diagrams for clusters Turnoff points
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• Structure of CMB fluctuations depend on the
  current density, the composition and the
  expansion rate.
• WMAP data with complimentary observations from
  other CMB experiments (ACBAR and CBI), we are
  able to determine an age for the universe closer
  to an accuracy of 1.
• Current estimate of age fits well with what we
  know from other kinds of measurements the
  Universe is about 13.7 billion years old!