Phenomenological Classification of Inflationary Potentials

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Phenomenological Classification of Inflationary
Potentials

• Katie Mack (Princeton University)
• with George Efstathiou (Cambridge University)
• Efstathiou Mack, JCAP 05, 008 (2005)
• astro-ph/0503360

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The Lyth Bound Revisited

• Katie Mack (Princeton University)
• with George Efstathiou (Cambridge University)
• Efstathiou Mack, JCAP 05, 008 (2005)
• astro-ph/0503360

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Outline

• Current status of inflation
• What the observations can tell us
• Linking observations to fundamental theory (Lyth
  Bound)
• Phenomenological approach
• Implications for future theoretical work

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The inflationary paradigm today

• Inflation is successful
• offers solution to
• horizon problem
• flatness problem
• general predictions have been upheld
• flat universe
• gaussian and adiabatic metric fluctuations
• nearly scale-independent spectrum
• but which inflation theory are we talking about?

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The inflationary paradigm today

• Inflation is successful
• offers solution to
• horizon problem
• flatness problem
• general predictions have been upheld
• flat universe
• gaussian and adiabatic metric fluctuations
• nearly scale-independent spectrum
• but which inflation theory are we talking about?

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WMAP to the rescue!
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the good news

• Tensor modes
• produced by gravitational waves
• no contribution from density perturbations
• Detection would
• confirm prediction of primordial gravitational
  waves in inflation
• give the energy scale of inflation

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the bad news
WMAP alone
WMAP2dFLya
we cannot yet distinguish between broad classes
of inflationary theories that have different
physical motivations. Peiris et al. (2003)
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Seljak et al., 2004 (astro-ph/0407372)
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B-Mode Polarization
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Current upper limits
r 0.36
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Beyond WMAP

• Currently proposed experiments (ground and
  balloon-borne) can reach r0.01 at 3s level
• Space-based, with improved foreground knowledge,
  could get to r10-3 at 3s
• (Verde, Peiris Jimenez, astro-ph/0506036)

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You may askWhat about gravitational wave
detectors?

• Of the planned experiments, only Big Bang
  Observer (next generation after LISA) has any
  chance of detecting primordial GWs

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Linking observation to physics

• Future experiments may detect primordial
  gravitational waves, but what would this tell us
  about inflation itself?
• Goal Find a way to link the observables to the
  fundamental physics without assuming a particular
  model

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Phenomenological Approach

• Produce a set of inflationary models to be as
  general as possible
• Require only
• single field
• inflation sustained long enough to solve horizon
  problem ( 55 e-foldings)
• Calculate r and ?f, compare with Lyth Bound

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The Lyth Bound

• David Lyth (1996) suggests rough relation
• for ?N 4 (CMB multipoles 2 to 100)
• Considering the full course of inflation, with
  at least 50-60 e-folds, ?f could exceed this by
  an order of magnitude
• If slow-roll parameter
• is monotonically increasing, a stronger
  condition is required

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The Lyth Bound

• General expectation
• large r gt large ?f
• High values of r require changes in the field
  value of order mPl

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Monte Carlo Reconstruction Results (106 models)
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But in the real world

• Can improve the scatter by comparing with
  observables
• From Seljak et al. 2004, astro-ph/0407372

0.92 lt ns lt 1.06 -0.04 lt nrun lt 0.03
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Remaining models

• Now have tighter empirical relationship between r
  and ?f
• ?f/mPl 6 r1/4
• (for r gt 10-3)

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What have we learned?

• To obtain a large value of r, you need a large
  variation in the scalar field
• For r 10-3, need ?f of order unity
• If any conceivable CMB polarization experiment
  is to detect tensor modes, ?f must be large

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Implications for inflation

• Large field variations cannot be described by
  low-energy effective field theory, where the
  potential is written as
• with . This is invalid for
  .
• Does that mean we need new physics?
• Not necessarily quantum gravity corrections may
  still be small as long as V lt mpl4
• But we will need a new way to talk about such
  models.

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The bottom line

• Future CMB polarization experiments can only
  probe high field inflation models (e.g., chaotic
  inflation)
• Understanding the physics of such models is
  important if such experiments are to tell us
  anything useful about the mechanism behind
  inflation

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Single-field inflation

• Scalar field f rolling down potential V(f)
• Slow rolling of inflaton field causes inflation
• Some commonly considered models
• V f2
• V f4

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Mechanics of inflation

• Change in Hubble Parameter depends on change in
  scalar field (speed of roll)
• In slow-roll inflation, take H constant, slow
  roll of inflaton

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• Expand Hubble Parameter in power series
• Use slow-roll parameters to represent this
  expansion

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acceleration
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E mode and B mode polarization
E modes (no curl)
B modes (no divergence)
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WMAP vs. Planck
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Planck projected B-mode measurement
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Other experiments
Clover
None of these experiments likely to probe below r
10-2
QUIET
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Cooray, astro-ph/0503118
Limits on future gravitational wave experiments
r 0.13 r 5 10-4 r 10-5