The Dark Side of the Universe

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The Dark Side of the Universe
Katherine Freese Michigan Center for Theoretical
Physics University of Michigan
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BIG BANG
14 BILLION YEARS AGO
Hot primordial soup Universe is
Cooling and Expanding
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QUARK/HADRON TRANSITION
t 0.01 sec
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Galaxy formation t 1 million years
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Raisin Bread Model of the Universe

• As the loaf rises, raisins move steadily apart
  from one another, with the loaf maintaining the
  same configuration.

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Cosmological Principles

• Universe is homogeneous
• looks the same at every point
• (on average)
• Universe is isotropic
• looks the same in every direction

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The Great Wall
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Homogeneous Universe
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• At the turn of the Millenium, recent experiments
  answered some of the BIG QUESTIONS
• What is the geometry of the universe?
• What is the mass of the observable universe?
• How big is the universe?
• BUT many questions remain what is the universe
  made of?

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Geometry of the Universe
1930 Three possible geometries for the
universe 2000 The geometry of the universe is
FLAT!!!!!!
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Universe has Flat Geometry

• Universe is NOT two-dimensional.
• Goes out to infinity in all three directions
• Shortest distance between two
• points is a straight line.
• No curvature required,
• no weird geometry.

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Geometry is Determined by Matter Content

• Warping of Spacetime

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Matter Bends Light
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Objects appear to be in different positions
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As we look backwards in time

• All points in infinite universe getting closer
  and closer
• --- yet universe can still be infinite all
  the
• way back!
• Eventually, the density at each point is so great
  we lose description (maybe string theory?)
• Big Bang at every point in the universe.

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Big Bang happens everywhere at once (not at a
single point)
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Dark Matter in Galaxies

• What do galaxies look like?
• Rotation Curves and galactic dark matter
• Evidence for dark matter in clusters of galaxies
• What can the Dark Matter be?

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Our Galaxy The Milky Way
The mass of the galaxy
solar masses
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Galaxies
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Scematic of typical galaxy
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Galaxies have Dark Matter Haloes
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Rotation Curves

• How do we know that galaxies have dark matter
  haloes? Rotation Curves.
• Example Solar System Rotation Curve
• 95 of the mass of galaxies is made of an unknown
  component!!!

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Solar System Rotation Curve
Average Speeds of the Planets
As you move out from the Sun, speeds of the
planets drop.
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Solar System
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Tyco Brahe(1546-1601)
Lost his nose in a duel, and wore a gold and
silver replacement. Studied planetary
orbits. Died of a burst bladder at a dinner
with the king.
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Rotation Curves of Galaxies
Orbit of a star in a Galaxy speed is Determined
by Mass
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Speed is determined by Mass
The speed at distance r from the center of the
galaxy is determined by the mass interior to
that radius. Larger mass causes faster orbits.
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Vera Rubin
Studied rotation curves of galaxies, and found
that they are FLAT!
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95 of the matter in galaxies is unknown dark
matter!

• Rotation Curves of Galaxies

OBSERVED FLAT ROTATION CURVE
EXPECTED FROM STARS
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Suns orbit is sped up by dark matter in the
Milky Way
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Dark Matter in Clusters of Galaxies

• Rotation Curves of Galaxies in the Cluster
• Lensing
• Gravitationally Confined Hot Gas in Clusters

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Lensing Another way to detect dark matter it
makes light bend
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Lensing by dark matter
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Dark Matter in a Rich Cluster
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Hubble Space Telescope
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Hot Gas in Clusters The Coma Cluster
Without dark matter, the hot gas would evaporate.
X-ray Image from the ROSAT satellite
Optical Image
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The Dark Matter Problem

• 95 of the mass in galaxies and clusters
• of galaxies are made of an unknown dark matter
  component
• Known from rotation curves,
• gravitational lensing,
• hot gas in clusters.

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Formation of Structure Numerical Simulations
Dark Matter particles come together to make
galaxies, clusters, and larger scale structures
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The Dark Matter is NOT

• Diffuse Hot Gas (would produce x-rays)
• Cool Neutral Hydrogen (see in quasar absorption
  lines)
• Small lumps or snowballs of hydrogen (would
  evaporate)
• Rocks or Dust (high metallicity)
• (Hegyi and
  Olive)

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What Can the Dark Matter Be?

• MACHOs Massive Compact Halo Objects
• made of ordinary matter
• OR
• WIMPs Weakly Interacting Massive Particles made
  of exotic matter

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MACHOs

• Faint stars
• Planetary Objects (Brown Dwarfs)
• Stellar Remnants
• White Dwarfs
• Neutron Stars
• Black Holes

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Is Dark Matter Made of Stars? NO!

• Faint Stars Hubble Space Telescope
• Planetary Objects
• parallax data
• microlensing experiments
• Together, these objects make up less than 3 of
  the mass of the Milky Way.

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Microlensing experiments
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Microlensing Event
Only three percent of the Halo can be made of
faint stars or brown dwarfs.
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Stellar Evolution

• Currently, the Sun is undergoing fusion
• 4 Hydrogen burning to Helium

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Stellar Remnants

• Three possible outcomes
• White Dwarf Once the Sun runs out of nuclear
  fuel, it will collapse to a white dwarf
• (electron degeneracy pressure)
• Neutron Star Stars three times as heavy as the
  Sun collapse to neutron stars
• (neutron degeneracy pressure)
• Black Hole Stars twenty times as heavy as the
  Sun collapse to black holes.
• These three dark matter candidates are all about
  as massive as our Sun.

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Black Hole Structure
The gravity of the black hole is so strong that
anything entering inside the event horizon
can never escape, not even light!
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Artists Impression of a Black Hole
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Black Hole at Center of Galaxy
At the center of every galaxy is a very massive
black hole, as massive as a million suns.
These massive black holes form from mergers and
are NOT the dark matter.
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Is Dark Matter made of Stellar Remnants? NO

• Their progenitors overproduce infrared radiation.
• Their progenitors overproduce element abundances
  (C, N, He)
• Enormous mass budget.
• Requires extreme properties to make them.
• NONE of the expected signatures of a stellar
  remnant population is found.

At most 20 of the dark matter can be white
dwarfs, neutron stars, or remnant blackholes.
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I HATE MACHOS!

• DESPERATELY LOOKING FOR WIMPS!

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WIMPs

• Weakly Interacting Massive Particles
• About 100 times as heavy as protons
• Go right through us
• The Death Theory one interacts in a human
  roughly every 70 years
• Motivated by supersymmetry from particle theory

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Supersymmetry

• Particle theory designed to keep particle masses
  at the right values
• Every particle we know has a partner
• photon photino
• quark squark
• electron selectron
• The lightest supersymmetric partner is a dark
  matter candidate.

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WIMP dark matter halo
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WIMPs
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Detection of WIMP dark matter
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Our Universe is Accelerating
Observations of Type IA Supernovae suggest that
the Universe is accelerating.

• Possible explanations
• I. Dark Energy
• Cosmological constant
• Decaying vacuum energy (Freese, Adams, Frieman,
  and Mottola 1987
• Quintessence (Ratra and Peebles, Steinhardt,
  Wang, et al.)
• II. Modification to the Einstein Equations

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Alternative modify the Friedmann equation

• We propose a modification to the Friedmann
  equations governing the expansion of the universe.

Usual Friedmann equation
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The Cardassian Alternative

• We propose a modification to the Friedmann
  equations governing the expansion of the universe.

No vacuum, No curvature
Matter and radiation only
Simplest version
(K. Freese and M. Lewis, PLB 540 (2002) p1.)
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Power Law Cardassian

• Geometry is flat, as required by the CMB no
  curvature term.
• NO VACUUM TERM
• MATTER ONLY
• The new term is initially negligible.
• Nucleosynthesis is unaffected by its presence.
• The Cardassian term begins to dominate recently,
  at z zcard O(1), as indicated by SN
  observations.
• This fixes B and essentially corresponds to the
  coincidence problem.
• Once the new term dominates, the universe expands
  according to

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The Critical Energy Density of the Universe

• The geometry of the Universe is flat. What
  energy density does this correspond to?
• Today,
• The energy density that satisfies this equation
  is, by definition, the critical density. Hence,
  the critical density is now a different number,
• The Universe can be flat and matter dominated,
  with a matter density that is 0.3 of the old
  critical density.

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Ratio of new to old critical density.
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Cluster Baryon Fraction Estimates

• Numerical simulations suggest that clusters are
  representative of the universe (Evrard, et al.,
  2001).
• Measurement of the cluster baryon fraction,
  coupled with observed light element densities
  from big bang nucleosynthesis can be used to
  estimate the overall matter density in the
  universe

• Taken at face value, assuming Ob 0.024,
  measurements of the cluster baryon fraction
  indicate that the matter density in the universe
  is (White, et al., 1993)

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• The Universe can be flat, matter dominated, and
  accelerating, with a matter density that is 0.3
  of the old critical density.

Matter can provide the entire closure density of
the Universe.
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Equivalent Formulation of Power Law Cardassian

• Equivalently, power law Cardassian can be written
  in the form

For reasonable parameters, Modifications are
only important for Hence, solar system physics
is completely unaffected.
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Generalized Cardassian

• More generally, we consider modifications to the
  Friedman equation,
• The function returns to the usual
  early on, but takes a different
  form that drives acceleration after z1. For
  example,

(Modified Polytropic Cardassian)
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Cardassian vs. Quintessence

• What is the difference between the Cardassian and
  quintessence models?
• Quintessence requires a dark energy component
  with a specific equation of state (
  ).
• The only ingredients in Cardassian cosmology are
  ordinary matter and radiation.
• As far as observations of a(t) are concerned,
  there is a correspondence between power law
  Cardassian and quintessence models.
• However, Poissons eqns., cluster abundances,
  ISW will be different for the two models.
• Generalized Cardassian models can be
  distinguished from generic quintessence models
  with upcoming precision cosmological experiments.

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Best Fit Values for Power Law Cardassian
Parameters

• Current estimates of the dark energy equation
  of state parameter imply,

WMAP constraints (Bennett, et al., 2003)

• Requiring now gives an estimate
  for zcard, the redshift at which the new term
  begins to dominate

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The Age of the Universe

• In the Cardassian model, the age of the universe
  is typically modified. An accelerating universe
  is generally older than one not accelerating.

• Here we assume
• Current measurements suggest

WMAP (Bennett, et al., 2003)
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The Position of the Doppler Peak in the CMB

• The accelerated expansion of the universe will
  shift the position of the first peak in the CMB.
  In a flat geometry, the angular size subtended by
  the sound horizon at the time of recombination is
  given by,

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Comparison of Generalized Cardassian Models with
Current Supernova Data
(Wang, Freese, Gondolo, and Lewis,
astro-ph/0302064)
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Determining the Sign of
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Estimating Dark Energy Density From Supernova
Data (SNAP)
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Additional Observational Tests

• Using CMBFast to further constrain Cardassian
  parameters in light of WMAP data.
• ISW effect may differentiate Cardassian from
  generic quintessence models.
• Number count tests
• DEEP2 (Marc Davis)
• Abundance of galaxy halos of fixed rotational
  speed Depend on the comoving volume element
• Alcock-Paczynski Test
• Compares angular size of a spherical object at
  redshift z to its redshift extent .
• Trick use correlation function of Lyman-alpha
  clouds as spherical objects (Crotts, Hui)

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Motivation for Cardassian Models

• 1) Modified Friedmann equations arise generically
  in theories with extra dimensions (Chung and
  Freese 1999).
• 2) Fluid description. Ordinary Friedmann
  equation, but energy density has additional terms
  (possibly due to dark matter with
  self-interactions characterized by negative
  pressure).

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Motivation for Cardassian Cosmology 1) Extra
Dimensions

• In a 5-dimensional universe with a metric,

where u is the coordinate in the direction of
the 5th dimension, one does not generically
obtain the usual FRW equation on the observable
brane (Chung and Freese, 1999).

• By suitable choice of the bulk energy momentum
  tensor, one may obtain an FRW equation on our
  brane of the form,
• for any n. More generally, one can obtain
  other modifications.

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Motivation for the Cardassian Term

• This result arises from the 5D Einstein
  equations together with the Israel boundary
  conditions relating energy-momentum on our brane
  to derivatives of the metric in the bulk.
• We stress that there is no unique 5D energy
  momentum tensor that gives rise to a Cardassian
  term. However, as an existence proof, we have
  constructed an inelegant example,

where,
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Cardassian Fine-tuning

• The power law Cardassian term begins to dominate
  when,

• The parameter B must be chosen by hand. This
  essentially corresponds to the coincidence
  problem.
• The size of B is set by the extra-dimensions, and
  clues to its value may come from understanding
  better the extra-dimensional physics.
• The mass scale corresponding to B is very small
  for nlt1/2, singular for n1/2, and becomes large
  for ngt1/2. For the good fit Cardassian
  parameters, n0.2

• These values for B correspond to an energy
  density in the bulk of

• The value is unmotivated, but not unreasonable.
• We stress again that the form of the bulk energy
  momentum is not unique!

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Motivation for Cardassian Cosmology 2) Fluid
Description

• We use the ordinary Friedmann equation,
• And take the energy density to be the sum of two
  terms

(Gondolo and Freese, hep-ph/0209322,
hep-ph/0211397)
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Conservation Laws

• Energy Conservation
• Modified Continuity equation
• Modified Eulers equation
• Particle Number Conservation
• Modified Poissons Equation
• Newtonian limit

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Example Fluid Description of Power Law Cardassian
Problem on Galactic Scales
New force destroys flat rotation curves. Hence,
fluid power law Cardassian must be thought of as
an effective model which applies only on large
scales.
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Example Fluid Description of MP Cardassian

• Parameter n important on large scales.
• Parameter q important on small scales rotation
  curves are fine.
• We are checking the power spectrum.

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Weak Energy Condition

• Some Cardassian models can satisfy the weak
  energy condition even
  with a dark energy component
• (matches data?)
• Example MP Cardassian

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Speculation Self Interacting Dark Matter?

• Dark matter may be subject to a new, long range,
  confining force (fifth force?)
• n.b. Analogous to quark confinement that exhibits
  negative pressure.
• Thermodynamic arguments determine the equation of
  state of the force mediators,

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Summary

• We have proposed a modification to the
  conventional FRW equations that allows for a
  flat, accelerating universe that contains only
  matter.
• The critical density of the universe has
  decreased so that ordinary matter may now result
  in a flat geometry.
• Cardassian models are consistent with both CMB
  and supernovae observations. Future data may
  distinguish between models.
• Nucleosynthesis, as well as structure formation
  prior to zcard is unaffected.
• The modification may result from the presence of
  extra dimensions.
• A fluid description has been developed, possibly
  due to self interacting dark matter.
• From a theoretical perspective it may be
  profitable to consider alternatives to
  conventional dark energy scenarios.
• Future directions
• A fundamental theory? Can we write down a
  Lagrangian?
• Detailed analysis of structure formation in the
  context of the model.

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Etymology

• Cardassians are an alien race indigenous to the
  Star Trek universe.
• They appear foreign to us, yet consist entirely
  of matter.
• They are bent on the accelerated expansion of
  their empire.

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Cardassian vs. Quintessence

• Can the Cardassian and quintessence models be
  distinguished?
• The models are fundamentally different.
• Cardassian modification of the Einstein equations
  will also result in a modification of the Poisson
  equation. Precision observations of cluster
  abundances, etc., may therefore serve to
  distinguish one model from the other.
• Late ISW effect might be different in the context
  of Cardassian model.

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The Cardassian Alternative

• We propose a modification to the
  Friedmann-Robertson-Walker (FRW) equations
  governing the expansion of the universe.

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Features of Cardassian Model

• The model contains only matter (i.e. no vacuum
  contribution)
• Geometry in the model is flat (as required by CMB
  measurements).

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The Critical Density of the Universe

• What energy density corresponds to a flat
  universe in our model? If the second term starts
  to dominate at a red-shift zeq,
• We find that the critical density has been
  modified from its usual value. In the Cardassian
  model, the new critical density is,

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The Critical Density of the Universe

• The universe can be flat and matter dominated,
  with a matter density that is a third of the old
  critical density!

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Best Fit Values for Cardassian Parameters
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Structure Formation in the Cardassian Model

• Prior to zeq 1 the Cardassian term is
  unimportant and therefore does not appreciably
  affect early structure formation.
• Because the term causes acceleration once it
  does dominate, perturbation growth is frozen out.

• Without a specific, motivating model for the
  Cardassian term, we cannot yet completely predict
  its effect on structure formation.