Is dark energy necessary to explain recent cosmological observations

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Is dark energy necessary to explain recent
cosmological observations?

• Morad Amarzguioui
• Institute of Theoretical Astrophysics
• University of Oslo

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Outline

• Theoretical foundations of cosmology
• Observations
• The concordance model
• Inhomogeneities in the matter distribution?

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General relativity

• Einstein's GR lays the foundations for most of
  our understanding of the Universe.
• Describes gravity not as a force but as a
  curvature of space and time
  
• Curvature Energy and pressure.
• Gravitational motion particles move freely in
  the curved space-time.

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Cosmological principle

• The field equation cannot be solved generally.
  Must make an assumption about the geometry and
  distribution of matter.
• Cosmological principle The Universe is
  homogeneous and isotropic.
• Leads to a very simple model for the Universe
  The Friedmann-Robertson-Walker (FRW) model.

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FRW space-time

• The geometry is described by the line element
• 
  
  
• This leads to the Friedmann equations
• 
  
  
  
  
• Assuming contribution from various energy
  components, the first equation can be written as

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Observations

• Observe radiation emitted by various sources.
• Three main observational sources
• Supernovae of type Ia (SNIa)
• Cosmic microwave backround radiation (CMB)
• Large-scale structure (LSS)
• Evolution of the Universe from emission to
  absorption affects the intensity and redshift of
  the photons. Observations constrain the
  evolution.

7

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Concordance model

• Combining the three sets of tests gives a best
  fit model which is flat and contain only approx.
  25 matter.
• The remaining 75 are in the form of a mysterious
  dark energy.

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Dark energy

• We don't know what dark energy is. Know only its
  properties.
• Supernova observations indicate that the
  expansion rate of the Universe increases with
  time. Dark energy must therefore act repulsively,
  causing the expansion to accelerate.
• From Friedmann's equations Has negative pressure
  with
• A candidate The cosmological constant.

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Cosmological constant

• Introduced by Einstein in 1917 to make his
  Universe model static.
• Expect such a term to appear naturally in the
  field equations.
• QFT predicts that there should be vacuum energy
  present due to vacuum fluctuations.
• Zel'dovich The vacuum energy behaves like the
  cosmological constant.

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Problems

• Fine-tuning problem A naïve calculation of the
  vacuum energy gives a value that is at least 120
  order of magnitude too large.
• Coincidence problem Why are the densities of
  vacuum energy and matter of the same order today.
  They scale as
• 
  
• Leaves only a tiny window of opportunity where
  they can be roughly equal. Why today?

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Is dark energy necessary?

• All values for the cosmological parameters are
  derived under the assumption that the Universe is
  homogeneous and isotropic.
• Instead of introducing additional energy
  components, maybe one should allow for more
  general matter distributions?
• Compatible with the observations without dark
  energy?

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Supernovae and acceleration

• SN observations imply that the expansion rate
  increases along the path of the photons
  from emission to absorption.
• In a homogeneous Universe, where the expansion
  rate is the same everywhere, this can only mean
  that the expansion rate increases with time.
• If we allow for an inhomogeneous Universe, the
  increase can be explained as a spatial variation
  in the expansion rate along the path. No
  accelerated expansion!

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Spherically symmetric models

• The simplest realistic inhomogeneous model is
  spherically symmetric.
• Geometry given by the Lemaître-Tolman-Bondi (LTB)
  metric
• Expansion is generally different in radial and
  transverse directions.

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Field equations

• The Friedmann equations generalize to
• serve the role as free parameters.
• Can define generalized density contrasts for
  matter and curvature from the Friedmann equations.

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Free parameters

• How do we expect and to behave?
• Use data from SNIa, LSS and CMB to constrain the
  parameters. The physical parameters probed by
  these observations are the expansion rate and the
  density parameters.
• The physical parameters are related to and
  via the Friedmann equations.

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Qualitative behaviour

• For compatibility with SNIa, the expansion rate
  must decrease radially from the observer.
• For compatibility with LSS, the density of matter
  today must be 0.2-0.3.
• For compatibility with CMB, the Universe must be
  flat and the expansion rate relatively low
  (h0.5).
• No tension between these requirements since the
  tests probe different spatial regions of the
  Universe.

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Combined

• The expansion rate decreases radially down to a
  low and constant value.
• The matter density is low near the observer and
  increases radially outward to a high and constant
  value.
• We live inside an underdense bubble in an
  otherwise homogeneous Universe!

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Best-fit model

• Better fit to SNIa than the homogeneous
  concordance model.
• Have not done an actual fit to the whole CMB
  power spectrum. Only to the first peak.
• Matter density close to the observer is
  .

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Off-center observers

• Moving the observer away from the center will
  change the SNIa and CMB observations.
• Anisotropic space-time --gt asymmetric photon
  paths --gt additional anisotropies in the CMB
  anisotropic relation between magnitudes and
  redshift for SNIa.
• These effects constrain the off-center placement
  to within 15 Mpc from the center.

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Conclusions

• Inhomogeneous models can to a certain degree
  explain the cosmological data without introducing
  dark energy.
• No accelerated expansion.
• We live inside an underdense region of the
  Universe.
• Restricted to a radius of 15 Mpc from the center.
• The Copernican principle is violated. We live in
  a special place.