Relativity

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Relativity CosmologyCHIPP meeting, April 7,
2006

• Ruth Durrer
• Départment de physique théorique
• Université de Genève

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Content

• Time in general relativity
• redshift in the gravitational field
• the equivalence principle
• Cosmology, an introduction
• the expanding universe
• the thermal history
• CMB anisotropies cosmological parameters
• Conclusions

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GR time delay

• To demonstrate the reality of gravitational
  redshift, Einstein suggested the following
  Gedankenexperiment (1907)Imagine a photon
  emitted at height H0, frequency ?0 (energy
  E0h?0) propagating to height H?h, where it is
  absorbed with frequency ?1. If there would be no
  redshift, ?1?0, we could generate a perpertuum
  mobile in the following way send the photon with
  energy h?0E0 to height ?h, convert it in a
  particle with mass m E0/c2, let the particle
  fall, it gains the potential energy mg?h, convert
  it back into a photon with energy E1 E0(1
  g?h/c2) gtE0 etc...
• To avoid this contradiction the photon must be
  redshifted in the gravitational potential
• ??g?h/c2 (' 10-19?h/1m )
• ?1 ?0(1-??) ?0(1-z) or ?1?0(1z)
• (First observations in the earths gravitational
  field, Pounds Snider 1965)

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• In the same way time slows down in a
  gravitational field,
• d? (1?)dt (For weak gravitational
  fields)
• This is most extreme at the horizon of a black
  hole where only a finite amount of time has
  elapsed when time for a far away observer is
  already infinite.
• Equivalence principle Free fall cannot be
  distinguished locally from an inertial system.
• Hence a horizontally emitted photon travels
  horizontally in a freely falling elevator, hence
  it is deflected for an observer at rest w.r.t.
  the earths gravitational field.
• Notions of time, space, causality are determined
  by a metric field g??(x) which itself is related
  to the energy distribution in the universe via
  the gravitational field equations.
• Light rays travel along curves with ds2g??(x)dx?
  dx? 0
• In flat space this reduces to c2t2 x2 0
• Apart from the scalar effects discussed here,
  gravity also has a vector component (Lense
  Thirring effect, Gravity Probe B), and a tensor
  component (gravitational waves).

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Cosmology

• With GR it is for the first time possible to find
  consistent (stable) solutions which describe a
  universe filled homogeneously with matter and
  radiation.
• The observed Universe is expanding and
  homogeneous and isotropic on large scales.
• It can be approximated by a Friedmann-Lemaître
  universe with small fluctuations.

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The thermal history of the Universe

• As you know, the universe is presently expanding.
  Two galaxies at a distance d recede from each
  other with a speed dH0, where H0 ' (727)km/s/Mpc
  is the Hubble parameter.
• In the past the Universe was not only much denser
  but also much hotter.
• If the Universe was dominated by matter and
  radiation in the past, it encountered a
  singularity (big bang) about 10-14 Gyrs in the
  past.
• At the temperature T' 3000K (t' 3105 years)
  electrons and protons recombined to neutral
  hydrogen and the universe became transparent for
  photons.
• At the temperature T' 109K ' 0.1 MeV (t' 3min.)
  deuterium became stable and most of the neutrons
  in the universe were burned into He4. with traces
  of deuterium, He3 and Li7.
• At T ' 1MeV neutrinos decoupled.
• At T ' 100MeV confinement
• At T ' 200GeV electroweak transition
• ...?
• Inflation

Observational cosmology is the search for
relics/fossils of these earlier phases.
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• The present temperature of the CMB is
• T0 (2.7372 0.001)K,
  T(z) T0(1z)
• It has the best thermal spectrum ever measured!.
• Dans le passé, lunivers nétait pas seulement
  beaucoup plus dense, mais
• aussi plus chaud que aujourdhui. A z gt zR '
  1300, TR ' 3500 ' 0.3eV, il y
• avait assez de photon avec une énergie au dessus
  du seuil de réionisation
• de lhydrogène (13.7eV) pour garder lunivers
  ionisé (tR 105 années).
• En régressant vers le passé, da densité de
  radiation croit comme (1z)4
• tandis que celle de la matière ne croit que comme
  (1z)3. A z gt zeq ' 104,
• lunivers est dominé par la radiation.
• A Tnuc ' 0.8MeV ' 109 K les éléments légers se
  forment à partir de protons
• et neutrons.
• A Tdec ' 1.4MeV les neutrinos découplent.
• A Tconf ' 200MeV le plasma de quarks et gluons
  est confiné en protons et neutrons.
• A Tew ' 200GeV la transition électrofaible a lieu

?
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CMB anisotropies

• Wmap 1 year
• (2003)

Wmap 3 year (2006)

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lightlike geodesics

• From the surface of last scattering into our
  antennas the CMB photons travel along geodesics.
  By integrating the geodesic equation, we obtain
  the change of energy in a given direction n
• Ef/Ei (n.u)f/(n.u)i Tf/Ti(1 DTf /Tf
  -DTi /Ti)
• This corresponds to a temperature variation.
  In first order perturbation theory one finds for
  scalar perturbations

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Polarisation

• Thomson scattering depends on polarisation a
  quadrupole anisotropy of the incoming wave
  generates linear polarisation of the outgoing
  wave.

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The power spectrum of CMB anisotropies
DT(n) is a function on the sphere, we can
expand it in spherical harmonics
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The physics of CMB fluctuations
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WMAP data
Temperature (TT Cl)
Polarisation (ET)
Hinshaw et al (2006)
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All temperature anisotropy data

• Hinshaw et al. (2006)

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Polarisation data

• Page et al. (2006)

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Measured cosmological parameters
(With CMB flatness or CMB Hubble)
Spergel et al. 06
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Curvature

• We cannot measure curvature or the
  cosmological constant with the CMB alone!

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Dark energy or a cosmological constant

• The CMB alone cannot determine the dark
  energy equation of state.

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Wmap other CMB data
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Wmap other data
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Conclusions

• Relativistic cosmology paints a rather accurate,
  consistent picture of a universe with the
  following properties
• Space is flat.
• The universe consists of 4 baryons, 22 dark
  matter and 74 dark energy.
• This is consistent with CMB, LSS, weak lensing,
  SnIa distance measurements, etc...
• Who ordered this bizarre mix???