Running, CMB and the Lyman Alpha Forest

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Running, CMB and the Lyman Alpha Forest

• Inflation Is running reasonable?
• Sloan Digital Sky Survey Lyman alpha forest

With Kev Abazajian, Evalyn Gates, Ewan Stewart,
Lam Hui, Adam Lidz
Scott Dodelson Workshop on CMB, Minnesota March
19, 2003
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Evidence for running comes from CMB on large
scales and Lyman alpha forest on small scales
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Even physicists not interested in inflation
should care about running.
Running is degenerate with neutrino mass
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Running and Neutrino Mass
Introducing running as an additional free
parameter loosens bound on neutrino mass.
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Inflationary models predict little running
Deviations from scale invariance represent the
first term in the slow roll expansion

• E.g. chaotic inflation with f4 potential

Nnumber of e-folds prior to end of inflation,
of order 60
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For general potentials
Dodelson Stewart (2001),Stewart (2001)
Unless there is a feature in the spectrum, we
expect running (n) to be of order (n-1)2. If n
is of order (n-1), then expect n also to be of
order (n-1).
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We have no models for inflaton potential

• Circumvent the potential take initial conditions
  for slow roll parameters and evolve (Kinney,
  2002)
• Run 1,000,000 models
• Compute observables for every run

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Inflation can generate many different values of
n, the spectral index
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Inflation typically generates n very close to
zero (WMAP value -.04)
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If n is big, what about n?
15/million runs which fall within WMAP 1-sigma
range
Suggests If n is large, so is n.
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How big is big?

• Recall
• Require

where k1/k0 is the range of scales probed by
observationsabout four orders of magnitude.
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SDSS Lyman Alpha Forest
3000 QSOs withabsorption lines from redshifts 2
to 4.2
Hui et al.
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Goal 1D Flux power spectrum

• Subtract mean flux and divide by mean flux. This
  gives d open squares
• Composite QSO spectrum crosses
• Principle Component Analysis Allow each QSO
  spectrum to vary linear combination of training
  set reference points

Simple thing works. Composite spectrum works very
well.
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Systematics Check
Cross-correlate distant lines of sight. No
intrinsic correlations any observed must be due
to improper continuum fitting.
Possible problems on large scales. No problems on
small scales.
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Results

• Dashed lines are from Kecksolid from SDSS
• 3 sets of curves from low (bottom) to high (top)
  redshift
• SDSS goes to larger scales, but doesnt have
  small scales resolution

Good agreement with Keck!
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Six more redshift bins
High z
Low z
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Parameterize with amplitude at every redshift
scales as (1z)4
(Parenthetically No evidence for Helium
reionization)
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Convert 1D Flux Spectrum to 3D Linear Matter
Power Spectrum

• Run many simulations with CDM-like spectra
• Extract Flux power spectra from each simulation
• Fit amplitude and slope of power at 1 Mpc

Lidz et al.
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Mild Evidence for Linear Growth
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3D Linear Power Spectrum
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Constraints on running
? WMAPACBARCBI SDSS Lyman alpha ? 7
cosmological parameters ? Consistent with no
running
Abazajian et al (March 19, 1110 CST)
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Conclusion

• Large running unlikely from inflation. If running
  (n) is large, why not jerking (n)?
• SDSS superb probe of Ly-alpha preliminary
  results consistent with Croft amplitude, but with
  shallower slope. Very preliminary results no
  running
• We must all become familiar with inflation, CMB,
  LSS, dark energy, polarization, in addition to
  smooth cosmology

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