Seb Oliver

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Distant Universe

• Seb Oliver
• Lecture 19 Structure Formation

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Isotropy

• The Universe appears to be the same in all
  directions
• Not true on small scales e.g. galaxies / not
  galaxies
• numbers of galaxies in North number in South
• Especially in CMBR
• DT / T lt 10-4

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Structure Formation
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Structure Formation

• Gravitational Instability
• Primordial Fluctuations
• Modification of Fluctuations
• Linear evolution
• Non-Linear Evolution
• CMB as a probe of Structure formation Geometry

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Quantification of Clustering
Structures in 1-D
Long-wavelength
Larger amplitude/power
Short-wavelength
smaller amplitude/power
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Quantification of Clustering
This distribution has a lot of long wavelength
power And a little short wavelength power
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Terminology

• We want to quantify the Power
• On different scales
• either as l (scale-length) or k (wave number)

• Fluctuations field

• Fourier Transform of density field

• Power Spectrum

Measures the power of fluctuations on a given
scale k
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Terminology

• Horizon information can only travel at a finite
  speed, so there is a limiting distance that we
  can see which is the distance that light can
  travel since the beginning of the Universe.
• This distance is called the particle horizon and
  changes with time

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Primordial Fluctuations

• Possibilities are quantum mechanical Gaussian
  Fluctuations which arise naturally in
  Inflationary theories
• A second possiblity is defects which might arise
  from phase transitions in the early Universe
• Cosmic strings 1-D
• Domain walls 2-D
• Or textures 3-D

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Primordial Fluctuations

• A common assumption is that the fluctuations have
  the same amplitude
• d 10-4 when they enter the horizon
• This gives a scale-free or Harrison-Zeldovich
  spectrum

Harrison-Zeldovich
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Types of Primordial Fluctuation

• Adiabatic
• Corresponding to changes in volume in the early
  universe. Changes number density of photons and
  matter particles equally but their mass densities
  change differently
• Iso-curvature
• Start with no perturbations in the density field
  but with fluctuations in the matter opposed to
  the radiation dg -dm
• Iso-thermal
• Radiation field unperturbed, fluctuations in
  matter only (rarely considered)

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Modifications of Fluctuations

• Prior to matter radiation equality perturbations
  are prevented from growing due to radiation
  pressure
• Pressure opposes gravity effectively for all
  wavelengths below the Jeans Length

Equation of state
Speed of sound
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Modifications of Fluctuations

• Jeans length is the scale at which sound waves
  can cross an object in about the time for
  gravitational collapse
• In a radiation dominated Universe
• And Jeans Length is close to Horizon size
• At matter-radiation equality the sound speed
  starts to drop fluctuations can grow
• Horizon scale at matter-radiation equality
  defines a particular scale of fluctuations

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Modifications of Fluctuations

• After matter-radiation equality
• Baryons still affected by photon pressure due to
  Thomson scattering and perturbations oscillate as
  sound waves. After zrecombination the
  fluctuations can grow
• Dark matter will also have small-scale
  structure suppressed. When particles are
  relativistic they will free-streeam out of
  fluctuations erasing them
• Silk-Damping similarly photons are not completely
  bound to baryons and will show reduced
  fluctuations

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Modifications of Fluctuations
Dark matter
Baryons
Matter dominated
Radiation dominated
Post-recombination
Baryons collapse into potential wells of DM
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Post-Recombination

• Any fluctuations or potential wells in the
  dark-matter field will gravitationally attract
  baryons. So quickly the density fields will be
  similar again
• All above effects can be represented by the
  Transfer Function

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Transfer Function
CDM
MDM
Baryons
HDM
Small scales
Large scales
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Post-Recombination P(k)
CDM
CDM iso-curvature
HDM
Small scales
Large scales
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Linear Evolution

• Having some of the nasty physics out of the way
  we know the initial conditions
• Small fluctuations dltlt1 can be treated as
  perturbations to the FW cosmology
• All scales grow equally
• For matter-dominated Universe and adiabatic
  fluctuations

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Non-Linear Evolution

• The full study of structuire formation requires
  the use N-body simulations to understand the
  evolution with dgt1
• But we can consider a simple model analytically
• The spherical collapse model

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Spherical collapse model

• Solution of GR for a sphere is exactly the same
  as for a closed Friedman-Robertson-Walker
  Cosmology
• Friedman Equation
• From problem sheet 1

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Spherical collapse model
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Spherical collapse model
Linear theory
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Spherical collapse model

• Turn-around
• Sphere reaches maximum radius and starts
  collapsing
• 2? p
• t pB
• At this point d5.5, dlin1.06

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Spherical collapse model

• Collapse
• Collapses to a singulartity
• 2? 2p
• t 2pB
• dinfinity
• dlin1.69

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Spherical collapse model

• Halt to collapse
• Evenutally collapse is halted by pressure.
• Kintetic energy of collapse is turned into
  thermal energy
• Virial therom
• V-2 KE
• 2? 3p/2
• t 2pB
• d147
• dlin1.58

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Cl Spectra
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The Current Understanding
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Thats All Folks