Numerical Cosmology

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Numerical Cosmology

• Romeel Davé
• University of Arizona
• Tucson, Arizona, USA

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Our Universe As We Know It

• We live in an dark matter dominated,
  inflationary, Big Bang universe.
• Universe began 13.8 billion years ago, in an
  explosion of super-hot super-dense plasma.
• Space itself expanded, and continues to expand
  except where bound locally by gravity (e.g on
  Earth, or in our Galaxy).
• The expansion is governed by Hubbles Law
  vrecessionH(t)?d, where H is Hubbles
  constant.
• Echoes of the Big Bang are visible today as
  Cosmic Background Radiation

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Inflation(if you thought the Big Bang was wacky,
wait till you hear this!)

• Less than 1 second after the Big Bang, the
  Universe underwent a sudden burst of expansion,
  growing by gt1060 in a fraction of a second. It
  then resumed normal expansion.
• Quantum vacuum fluctuations (much like white
  noise on a TV) were frozen in at this epoch.
• It is these fluctuations that eventually give
  rise to galaxies, stars, and us!
• While there is no direct observation of
  inflation, it is required to explain causality
  within our observable Universe, among other
  things.

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Cosmic Background Radiation

• Comes to us from recombination epoch, when
  Universe became cool enough for protons and
  electrons to form H atoms.
• WMAP power spectrum shows wiggles characteristic
  of Big Bang.

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Dark Matter

• We are made of ordinary matter, or what
  Astronomers call baryonic matter. Baryonic
  matter interacts with electromagnetic radiation
  (light), via reflection, refraction, or
  absorption.
• But we are in the minority 90 of the Universes
  mass is non-baryonic dark matter!
• We cannot see dark matter directly we infer
  its presence from its gravitational effects on
  the baryonic matter we can see.

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Galaxy Rotation Curves A Dark Matter Indicator
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The Accelerating Universe

• Recently, astronomers have observed that our
  Universe is not just expanding, but accelerating!
• The Universe contains a vacuum energy, causing
  pressure that drives the acceleration (think of
  it as slow inflation).
• Einstein actually introduced such a term in his
  equations of General relativity to prevent the
  Universe from accelerating he called it his
  greatest blunder, since had he not done so, he
  would have predicted an expanding Universe!
• Ironically, this same term (with the opposite
  sign) is now invoked to produce an acceleration.

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The Fate of Our Universe?
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The Constituents of Our Universe

• Densities are measured in terms of the critical
  density, i.e. the amount of mass-energy it would
  take to just halt the expansion due to
  self-gravity.
• Matter density Wm0.27
• Baryonic matter density Wb0.04
• Vacuum energy density WL0.73
• Hubble constant (today) H072 km/s/Mpc

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Structure Formationand the Cosmic Web

• Initially, density fluctuations are small. They
  grow via gravitational instability.
• Matter collapses into pancakes, then onto
  filaments, creating a Cosmic Web.
• Eventually it breaks away from Hubble expansion
  and collapses on itself, forming a galaxy.
• Galaxies cluster hierarchically into groups,
  clusters, and even super-clusters.

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Galaxy FormationWhat about the Baryons?

• Gravitational instability of dark matter is
  halted by angular momentum.
• But dark matter cant form the things we see.
  Why? It cant dissipate!
• In the centers of galaxies, baryons dissipate
  their gravitational potential by radiative
  cooling, and can condense to form stars.
• A galaxy is born!

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Galaxy Redshift Surveys

• The hardest problem in astronomy What is the
  distance to an observed object?
• Can obtain a good estimate using Hubbles Law
  (vrH0d) If we measure recession velocity, we
  know distance!
• Recession results in characteristic emission
  being redshifted (i.e. Doppler shifted to longer
  wavelengths) by measuring the redshift, one gets
  velocity and hence distance.
• Redshift surveys are thus used to map the galaxy
  distribution.

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The Cosmos on a Computer

• Structure formation is highly nonlinear. Our
  solar systems overdensity is 108!
• Easiest way to model is to numerically follow
  growth of perturbations into nonlinearity.
• Model random subvolume of Universe using many
  particles, each representing a bit of mass
  (typically a million to a billion Suns!).
• Simulate Compute forces on particles from
  gravity, pressure advance particles positions
  repeat until end!

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Summary

• We live in a dark matter-dominated, inflationary
  Big Bang Universe. Moreover, the expansion
  appears to be accelerating.
• The parameters of our Universe can now be
  precisely determined from CBR anisotropy
  measurements and redshift surveys.
• The growth of structure can be modeled using
  computers, allowing theories to be tested and new
  phenomena to be elucidated.