Dark Energy - A Pedagogic Review

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Dark Energy - A Pedagogic Review

• Paul Frampton
• University of North Carolina at Chapel Hill

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Plan of the talk

• What observations and theoretical assumptions
  underly dark energy?
• If General Relativity hold at all scales, the
  most conservative assumption, then DE
  follows from SNe1A or independently from CMB
  combined with LSS.
• What is the equation of state for DE?
• Should we seriously query general relativity at
  large distance scales?

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Einstein - Friedmann Equation

• The Einstein field equations relate geometry
  (LHS) to distribution of mass-energy (RHS)

• Addition to luminous dark matter
• - Cosmological constant, L?
• More generally, DARK ENERGY

• We hesitate to change this?
• - But checked accurately only at SS scales.
• higher-dimensional gravity?

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Observational issues

• How can we constrain dark energy?
• expansion history H(t)
• time-dependence of w(t) SNe1A
• does DE cluster no evidence for it?
• How does DE couple to gravity or to DM? Related
  to clustering.

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The issues

• What can we measure observationally?
• Time evolution of H(z)
• Temporal evolution and spatial distribution of
  structure
• Local tests of general relativity and the
  equivalence principle tho
• extrapolation from Solar System to Universe is
  some 13-15
• orders of magnitude comparable to extrapolation
  from weak scale to
• GUT scale. Usual prior is a desert hypothesis.

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? as dark energy Why 10-121 (Planck mass)4?

• Lamb shift and Casimir effect proved that vacuum
  fluctuations exist
• UV divergences are the source of the problem

?
a) 8? b) regularized at the Planck scale 1076
GeV4? c) regularized at the QCD scale 10-3
GeV4 ? d) 0 until SUSY breaking then 1
GeV4? e) all of the above 10 -47 GeV4? f)
none of the above 10 -47 GeV4? g) none of the
above 0 ?
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Coincidence problem

• Coincidence problem
• DE much earlier interferes with structure
  formation
• -- DE much later ?? still negligible and we would
  not be aware of it.
• Try to avoid anthropic arguments, however
  tempting!

,
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The Quintessence possibility

• Dynamical scalar field
• now called Quintessence generically
• E.g. Scaling potentials
• E.g. Tracker potentials

Wetterich 1988, Ferreira Joyce 1998
Ve-?Q
V((Q-a)bc) e-?Q
Albrecht Skordis 2000
VQ-?
Ratra Peebles 1988
.
Wang, Steinhardt, Zlatev 1999
Vexp(M/Q-1)
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Approaches to the coincidence problem

• Were not special universe sees periodic epochs
  of acceleration
• Were special the key is our proximity to the
  matter/ radiation equality
• Non-minimal coupling to matter
• e.g. Bean Magueijo 2001
• Non-minimal coupling to gravity
• e.g. Perrotta Bacciagalupi 2002
• k-essence A dynamical push after zeq with
  non-trivial kinetic Lagrangian term
  Armendariz-Picon, et al 2000

Dodelson , Kaplinghat, Stewart 2000
VM4e-?Q(1Asin ?Q)
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Modifications to gravity

• Quintessential inflation (e.g. Copeland et al
  2000)
• Randall Sundrum scenario
• r2 term increases the damping of ? as rolls
  down potential at early (inflationary) times
• inflation possible with V (?) usually too steep
  to produce slow-roll
• Cardassian expansion (e.g. Frith 2003)
• Adjustment to FRW, nlt0, affects late time
  evolution
• Curvature on the brane (Dvali ,Gabadadze Porrati
  2000)
• Gravity 5-D on large scales lgtlc i.e. modified at
  late times OF ALL PRESENT GRAVITY MODIFICATIONS
  MAY BE BEST MOTIVATED?

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Combining the dark matter and dark energy
problems?

• Unified dark matter/ dark energy
• at early times like CDM w0, cs20
• at late times like L w lt0
• E.g. Chaplygin gases
• an adiabatic fluid, parameters w0, a
• An example is an effective tachyonic action
  (Gibbons astro-ph/0204008 )

cs2 a w
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Phantom dark energy wlt-1

• Present data are consistent with w 1 as for
• a cosmological constant
• e.g. Scalar field lagrangian with the wrong
  sign in the kinetic term (Carroll, Hoffman,
  Trodden 2003)
  --But quantum instabilities require
  cut off scale 3MeV (Cline, Jeon Moore 2003)
• Brane world models can predict temporary wlt-1
  (Alam Sanhi 2002)

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W lt -1 case continued

• I shall spend more time on this exotic case
  because it is where the need for new physics is
  most dramatic.
• One interpretation of dark energy comes from
  string theory closed strings in a toroidal
  cosmology.
• (Bastero-Gil, Frampton and Mersini,Phys.Rev D65,
  106002 (2002). hep-th/0110167.
• This leads generically to w lt -1
• Frampton Phys. Lett. B555, 139 (2003).
  astro-ph/0209037

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Future fate of the dark energy
Without dark energy, the destiny of the universe
was tied to the geometry in a simple manner the
universe will expand forever if it is open or
flat. It will stop expanding and contract to a
Big Crunch if it is closed. With Dark Energy,
this connection between geometry and destiny is
lost and the future fate depends entirely on how
the presently-dominant dark energy will evolve.
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Future Fate (continued)

• This question is studied in
• Kallosh et al. astro-ph/0307185. Frampton and
  Takahashi,
  Phys. Lett. B557, 135 (2003).
  astro-ph/0211544.
• If w lt -1 is time independent, the scale factor
  diverges at a finite future time the Big Rip.
• Generally, this is at least as far in the future
  as the Big Bang is in the past.
• Such a cosmology has a philosophical appeal?
  More symmetry between past and future.
• With a time dependence to w(t) there are two
  other possible fates
• An infinite lifetime universe where dark energy
  is dominant at all future times.
• A disappearing dark energy where the universe
  becomes (again) matter dominated.

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Stability Issues for the case w lt -1

• The case w lt -1 gives rise to some exceptionally
  interesting puzzles for theoretical physics.
• There is the question of violating the energy
  conditions of GR. There exist inertial frames
  where the energy density is negative signaling
  vacuum instability. Frampton, Mod. Phys. Lett.
  A19, 801 (2004) hep-th/0302007.
• S.M. Carroll, M. Hoffman and M. Trodden.
  astro-ph/0301273.

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Stability (continued)

• Let us make two assumptions as illustrative that
  there exists a stable ground state and that the
  dark energy decays to it by 1st order PT.
• We can then use old arguments from e.g. P.H.
  Frampton, Phys, Rev. Lett. 37, 1378 (1976) to
  investigate nucleation.
• If there is even the tiniest interaction between
  DE and other interactions, nucleation would have
  occurred long ago unless the appropriate radius
  is at least galactic in size or bigger.

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Stability issues for w lt -1

• In this model of DE, because the energy density
  of DE is so small compared to e.g. the energy
  density in a common magnetic field of say 10T,
  the 1st order PT can be adequately suppressed
  only
• by decoupling DE completely from all
• but gravitational forces OR by arguing that
  a collision would need to be between galaxies or
  larger objects to be effected.
• Certainly no terrestrial experiment can be
  effected by DE background.

• Of course, this is merely a toy model but the
  general conclusion is probably correct that
  there can be no microscopic or macroscopic effect
  of the dark energy.
• This makes the DE even more difficult to
  investigate except through astronomical
  observations.

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SN1a first evidence for dark energy

• Perlmutter at al
• Riess et al.
• Over 100 SNe1a out to Z of 1.7

• Advantages
• single objects (simpler than galaxies)
• observable over wide z range
• Challenges
• Extinction from dust
• chemical composition/ evolution
• understanding mechanism behind
• Phillips relation for light curves

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Further evidence for Dark Energy

• CMB data from WMAP, combined with LSS of galaxy
  surveys 2dF and SDSS, tell us
• the Universe is very close to flat and that
  matter contribute only about 0.3
• Therefore, there is a missing 0.7 of dark energy,
• A conclusion completely independent of the SNe1a
  data which precipitated the discovery in 1998.

• WMAP analyses have produced an impressive list of
  cosmic parameters with unprecedent high accuracy.
• The dawn of Precision Cosmology
• A reminder that one prior is that general
  relativity holds at all length scales.

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VERY preliminary evidence for w lt -1?
WMAP TT SN1a
WMAP TT
ElgarØy and Multimäki 2004
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Solar system test of DGP Gravity

• Anomalous perihelion precession in modified
  gravity theories (Dvali et al 2002)
• Lunar laser ranging
• Unfortunately solar system tests are only known
  ways for testing general relativity.

-
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Conclusions Theory and Observation

• The theoretical community is yet to come up with
  a definitive proposal to explain the
  observations. String theory has been
  disappointing regarding this opportunity.
• The nature of dark energy is so profound for
  cosmology and particle physics we need the SN1a
  results improved on (SNAP, JDEM, -- NASA needs
  the resources!), as well as complemented by a
  range of observational constraints on CMB (WMAP2,
  Planck).
• The equation of state will be decisive. If w -1
  its a cosmological constant with its fine-tuning
  and coincidence problems. If w gt -1 quintessence
  will have a shot in the arm.
• If the data would settle down to a value w lt -1,
  we could be at the dawn of a revolution in theory
  with general relativity at the largest length
  scales called into question.