Low-z BAOs: proving acceleration and testing Neff

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Low-z BAOsproving acceleration and testing Neff

• Will Sutherland (QMUL)

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Talk overview

• Cases for low-redshift BAO surveys
• Smoking-gun test of cosmic acceleration - assumes
  only homogeneity isotropy, not GR.
• Testing fundamental assumptions from CMB era, in
  particular the number of neutrino species.

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2005 first observation of predicted BAO
feature by SDSS and 2dFGRS
(Eisenstein et al 2005)
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BAO feature in BOSS DR9 data 6
sigma (Anderson et al 2012)
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BAO observables transverse and radial
Spherical average gives rs / DV ,
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BAOs strengths and weaknesses

• BAO length scale calibrated by the CMB .
• Uses well-understood linear physics (unlike
  SNe).
• - CMB is very distant hard to independently
  verify assumptions.
• BAO length scale is very large, 153 Mpc
• Ruler is robust against non-linearity, details
  of galaxy formation
• Observables very simple galaxy redshifts and
  positions.
• - Huge volumes must be surveyed to get a precise
  measurement.
• - Cant measure BAO scale at z 0
• BAOs can probe both DA(z) and H(z) no
  differentiation needed for H(z). More sensitive
  to features in H(z) enables consistency tests
  for flatness, homogeneity.

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Precision from ideal BAO experiments
(Weinberg et al 2012)
Right panel idealized assumes matterbaryon
densities known exactly
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Cosmic speed trapProving cosmic acceleration
with BAOs only

• Assuming homogeneity, evidence for accelerating
  expansion is strong SNe, CMBlow-z measurements
  .
• SNe require acceleration independent of GR (if no
  evolution, and photon number conserved)
• CMB LSS acceleration evidence very strong,
  but requires assumption of GR.
• Possible loophole to allow non-accelerating model
  
• Assume SNe are flawed by evolution and/or photon
  non-conserving processes (peculiar dust,
  photon/dark sector scattering).
• AND GR not correct, so CMB inferences are
  misleading.
• This is contrived, but we should close this
  loophole

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Cosmic expansion rate da/dt
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Cosmic expansion rate, relative to today
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BOSS Busca et al 2012 Caveat assumed flatness
and standard rs
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Speed-trap motivations

• Radial BAO scale directly measures rs H(z) / c
• Ratio of two such measurements will cancel rs ,
  and detect acceleration directly.
• BUT, there is a practical problem
• very feeble acceleration at z gt 0.3
• Not enough volume to measure radial BAOs at z lt
  0.3 .
• Cant measure rs H0 at z 0.
• Spherical-average BAOs can prove acceleration IF
  we assume almost-flatness, but we dont want to
  rely on this.
• Workaround use radial BAO at z 0.7, compare
  to spherical-average BAO observable at z 0.2 .

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Limit relating DV(z1) and H(z2) for any
non-accelerating model
Comoving radial distance
No acceleration requires
therefore
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Assuming homogeneity, angular-diameter distance
is
No acceleration requires
Therefore
Open curvature ( ) gt 1
Closed curvature
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radial BAO observable
Spherical-average BAO observable, at z1
Divide
Use previous limit for DV
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Rearrange square-bracket onto LHS now RHS
becomes 1 O(z2), depends very weakly on
curvature.
Define XS as excess speed , ratio of BAO
observables
Flat models RHS 1 exactly . Open models RHS
lt 1 limit gets stronger. Closed models RHS gt
1 need to constrain this. But, closed models
have a maximum angular diameter distance lt Rc
/ (1z) , so z 3 galaxy sizes eliminate
super-closed models.
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(Sutherland, MN 2012, arXiv1105.3838)
Blue/green predictions for LambdaCDM / wCDM
Red upper limits for non-accelerating model,
various (extreme) curvatures.
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Speed-trap result

• If we assume
• Homogeneity and isotropy
• Redshift due to cosmic expansion, and constant
  speed of light
• BAO length conserved in comoving coordinates
• No acceleration after redshift z2
• Then
• Observable BAO ratio must be below red-lines
  above
• If observed XS gt 3 sigma above red-line ,
• at least one of four statements above
  is false.
• Signal 10 percent need lt 3 (ideally 2)
  precision on ratio of two BAO observables.
  Challenging, but definitely achievable.

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Hou et al 2011 Effect of varying Neff on CMB
damping tail.
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Measuring the absolute scale of BAOs

• BAO length scale is essentially the sound horizon
  at drag redshift zd 1020.
• If we assume
• Standard GR
• Standard neutrino content
• Standard recombination history
• Nearly pure adiabatic fluctuations
• Negligible early dark energy
• Negligible variation in fundamental constants
• Then BAO length depends on just two numbers, ?m
  and ?b both well determined by WMAP and Planck.
  
• WMAP results give rs(zd) 153 2 Mpc (1.3
  percent). Planck gives rs(zd) 151.7 0.5 Mpc
  (0.33 percent).

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Measuring the absolute scale of BAOs (2)

• Above assumptions are (mostly) testable from CMB
  acoustic peaks structure.
• But theres a risk of circular argument a wrong
  assumption may be masked by fitting biased
  values of cosmological parameters especially H0
  also Om, w etc.
• Highly desirable to actually measure the BAO
  length with a CMB-independent method.
• Obvious way measure transverse BAOs and DL(z)
  at same redshift distance duality gives DA(z)
  and absolute BAO scale.
• Would like to work at lower z , and use DV(z)
• Snag DV(z) is not directly measurable with
  standard distance indicators.

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Effect of non-standard radiation density
Definition of Neff
Matter density
Sound horizon in terms of rad. density and zeq
Define and use base parameter set
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(WMAP7 Komatsu et al 2010)
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WMAP7 likelihood contours
Strong degeneracy between Neff and ?m but zeq
is basically unaffected.
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WMAP7 likelihood contours
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Not exact, but accurate summary

• If we drop the assumption of standard Neff, then
  
• WMAP still tells us redshift of matter-radiation
  equality 3200, (Planck 3350) , but the
  physical matter and radiation densities are much
  less precise.
• Keeping CMB acoustic angle constant requires
  physical dark energy density to scale in
  proportion to matter radiation.
• best-fit inferred H0 scales as v(Xrad)
• Sound horizon rs scales as 1/ v(Xrad) .
• The BAO observables dont change inferred Om ,
  w are nearly unbiased (Eisenstein White 2004).
• If a 4th neutrino species, equivalent to 13.4
  increase in densities, 6.5 increase in H (e.g.
  70 to 74.5) and 6.1 reduction in cosmic
  distances/ages. Substantial effect !

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Neff affects all dimensionful parameters

• Nearly all our WMAP SNe BAO observables are
  actually dimensionless (apart from photonbaryon
  densities)
• redshift of matter-radiation equality
• CMB acoustic angle
• SNe give us distance ratios or H0 DL /c .
• BAOs also give distance ratios.
• All these can give us robust values for Os , w,
  E(z) etc almost independent of Neff .
• But there are 3 dimensionful quantities in FRW
  cosmology
• Distances, times, densities.
• Two inter-relations distance/time via c ,and
  Friedmann equation relates density timescale,
  via G.
• This leaves one short, i.e. any number of
  dimensionless distance ratios cant determine
  overall scale.
• Usually, scales are (implicitly) anchored to the
  standard radiation density, Neff 3.04 . But if
  we drop this, then there is one overall unknown
  scale factor.

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Neff , continued

• Photon and baryon densities are determined in
  absolute units but these dont appear separately
  in Friedmann eq., only as partial sums.
• Rescaling total radiation, total matter and dark
  energy densities by a common factor leaves WMAP,
  BAO and SNe observables (almost) unchanged but
  changes dimensionful quantities e.g. H.
• Potential source of confusion use of h and ?s.
  These are unitless but they are not really
  dimensionless, since they involve arbitrary
  choice of H 100 km/s/Mpc , and corresponding
  density.

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What BAOs really measure

• Standard rule-of-thumb is CMB measures ?m , and
  the sound horizon then BAOs measure h only
  true assuming standard radiation density.
• Really, CMB measures zeq adding a low-redshift
  BAO ratio measures (almost) Om. These two tell
  us H0 / v(Xrad) , but not an absolute scale.
• Thus, measuring the absolute BAO length provides
  a strong test of standard early-universe
  cosmology, especially the radiation content
  (Neff).
• Measuring just H0 is less good, since it mixes
  Neff, w and curvature. The absolute BAO scale
  probes only the early universe.

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Measuring the absolute BAO scale (3)

• Need two observations a relative BAO ratio at
  some redshift, and an absolute distance
  measurement to a matching redshift.
• It is generally easier to measure cosmic
  distances at lower z 0.25, which favours BAOs
  at moderate redshift.
• For SNe, the issue is evolution, so shorter time
  lever arm is favourable.
• SNe are better in near-IR (Barone-Nugent et al
  2012) sweet spot at z0.3 where rest-frame J, H
  appear in observed H,K.
• For lens time delays, degeneracy with cosmology
  zl ltlt zs is favourable for absolute distances.
• The ideal distance indicators long-term may be
  gravitational wave standard sirens precision
  limited by SNR , favours lower z.
• It is feasible to reach 1.5 precision on BAO
  ratio at z 0.25 this is probably better than
  medium-term distance indicators.

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Measuring the absolute scale of BAOs (4)

• Most robust quantity from a BAO survey is rs /
  DV(z) this is (almost) theory-independent.
• DV is related to comoving volume per unit
  redshift
• Could measure DV exactly if we had a population
  of standard counters of known comoving number
  density. But prospects dont look good galaxy
  evolution.
• At very low z, DV c z / H0 . But error is 6
  at z 0.2 much too inaccurate.
• Next well find much better approximations for
  DV(z)

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Pretty good approximations (lt 0.5 percent at z lt
0.4)
Suitable choice of zs can eliminate H and gives
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Relative accuracy of approximation
1 percent
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Relative accuracy of approximation
1 percent
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Better approximation
1 percent
Accuracy lt 0.2 percent at z lt 0.5
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An easy route to Om
h becomes a derived parameter
Define e as error in approximation
BAO ratio is
This is exact (apart from non-linear shifts in rs
) and fully dimensionless all H and ?s
cancelled.
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An easy route to Om
For WMAP baryon density, the above
simplifies to the following , to 0.4 percent

• This is all dimensionless, and nicely splits
  z-dependent effects
• Zeroth-order term is just Om-0.5 (strictly Ocb
  , without neutrinos)
• Leading order z-dependence is E(2z/3)
• The eV is second-order in z, usually z2 / 25
  and almost negligible
• at z lt 0.5

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An easy route to Om
Repeat approximation from previous slide
Substituting in the WMAP range for zeq , and the
BAO measurement at z 0.35 from Padmanabhan et
al (2012), and discarding the sub-percent eV ,
this gives
And just square and rearrange to
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Why DV approximation is good post-hoc
explanation using Taylor series
Deceleration and Jerk parameters
For reasonable models, abs lt 4 leading
order error lt z2 / 27
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Conclusions

• BAOs are a gold standard for cosmological
  standard rulers. Very well understood
  observations huge in scope but clean.
• Most planned BAO surveys are targeting z gt 0.7,
  to exploit the huge available volume and
  sensitivity to dark energy w.
• However, there are still two good cases for
  optimal low-z BAO surveys at z 0.25 (e.g.
  extending BOSS to South and lower galactic
  latitude)
• A third direct test of cosmic acceleration,
  without GR assumption. (arXiv1105.3838)
• In conjunction with precision distance
  measurements, can provide a test of the CMB
  prediction rs 151 Mpc, and/or a clean test for
  extra dark radiation, independent of DE and
  curvature.
• (arXiv1205.0715)

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Thank you !
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