The Theory/Observation connection lecture 4 dark energy: linking with observations

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The Theory/Observation connectionlecture 4dark
energy linking with observations

• Will Percival
• The University of Portsmouth

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Lecture outline

• Dark Energy review
• cosmological constant?
• quintessence?
• tangled defects?
• phantom dark energy?
• modified gravity?
• problems with the data?
• Geometrical tests
• SN1a
• BAO

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Cosmological constant

• Originally introduced by Einstein to make the
  Universe static
• Constant vacuum energy density, which is
  homogeneous and has constant density in time
• Equation of state
• Particle physics provides a natural candidate
  zero-point vacuum fluctuations for bosonic or
  fermionic fields
• typical scale of cosmological constant is
  (Mcutoff)4, where Mcutoff is UV cutoff of theory
  describing field
• Planck mass gives ?planck (1019GeV)4
• Observations show

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quintessence

• adaption of scalar field theory developed for
  inflationary theories for late-time dark energy
• very weak potential required, with very small
  effective mass
• field can be frozen at early times
• or it can slowly roll down the potential, with
  energy density tracking dominant fluid until
  recently (tracker models)
• equation-of-state generally evolves, although
  can be constant (with special choice of
  potential)
• In fact, any w(z)gt-1 history can be obtained
  with right choice of potential

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quintessence
Albrecht Weller 2002, astro-ph/0106079
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Parameterizations of w
If you dont know the physics, you dont have a
well-defined set of models to test, its a
free-for-all
can parameterise using w(a) w0 w1(1-a)
Bassett et al. 2004, astro-ph/0407364
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Tangled defects

• Network of defects formed in phase transition
  grows with expansion of Universe
• For strings, lengths grow as a, and energy as
  a-2, so w-1/3, and no acceleration (just)
• For walls, area grows as a2, and energy drops as
  a-1, so w-2/3, which can produce acceleration
• but observations show w -1

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Phantom dark energy

• motivated by early supernovae data which favored
  strong acceleration
• wlt-1
• density increases as Universe expands
• can lead to divergence in finite time - big rip
• theoretically difficult to justify
• violate weak energy condition
• lead to ghosts - negative norm energy states
• can be classically and quantum mechanically
  unstable
• If observations continue to show strong
  acceleration at low redshifts, may need a phase
  shift in theory

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modified gravity
Can separate cosmological constant from
stress-energy tensor
Can then imagine moving it to the other side of
the equation
Should we consider alternatives if were going to
be modifying gravity, rather than postulating a
new component of energy?
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modified gravity
Example from history Mercury perihilion Newton
dark planet? No! Modified gravity (GR)
Today, we need a modified Friedmann equation
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modified gravity
Modified gravity replace R with f(R) in action
for gravity. Gives
DGP modifed gravity (5D braneworld)
Problem we can always explain Adark by either
stress-energy component or change to gravity.
Only way of telling apart is by structure
formation (see next lecture)
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Problems with the data

• data depends on astrophysics, so subject to
  systematics
• but, more than one test, so need a conspiracy
  that all the astrophysics points you to
  acceleration
• Still, worth reviewing all data

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With this in mind, lets have a look at the
evidence for acceleration
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All strong evidence is geometrical
All of the evidence depends on the expansion
geometry, specifically through the Friedmann
equation
equation of state of dark energy p w(a) ?
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SNLS Hubble diagram
Astier et al (2006) AA, 447, 31
OM 0.263 0.042 (stat) 0.032 (sys) ltwgt-1.02
0.09 (stat) 0.054 (sys) (with BAO Flat
Universe)
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Supernovae observations

• Initially assumed all SN1a have same intrinsic
  peak brightness
• Now refined so that

Apparent magnitude of supernova
Stretch parameter s corrects for lightcurve
shape via ?
Luminosity distance to supernova
Absolute magnitude of supernova (assumed constant
for all SN1a)
cB-V colour corrects for extinction/intrinsic
effects via ?
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Supernovae systematics

• Experimental Systematics
• Calibration, photometry, Malmquist-type effects
• Contamination by other SNe or peculiar SNe Ia
• Minimized by spectroscopic confirmation
• Non-SNe systematics
• Peculiar velocities Hubble Bubble Weak lensing
• K-corrections and SN spectra
• UV uncertain golden redshifts spectral
  evolution?
• Extinction/Colour
• Effective RV Intrinsic colour versus dust
• Redshift evolution in the mix of SNe
• Population drift environment?
• Evolution in SN properties

From talk by Mark Sullivan
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Hubble diagram by galaxy type

• SNe in passive galaxies show a smaller scatter
• Intrinsic dispersion consistent with zero
• (Does intrinsic dispersion in SNe arise from
  dust?)
• Cleaner sample But SNe in passive galaxies are
  at high-z (20 two component model) very few
  locally

Star-forming hosts
Passive hosts
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Cosmological distribution of galaxy types
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Future supernovae prospects

• Short-term
• Current constraints on ltwgt ltwgt-1 to 6-7
  (stat)
• (inc. flat Universe, BAOWMAP-3)
• At SNLS survey end, statistical uncertainty will
  be 4-5
• 500 SNLS 200 SDSS larger local samples
• Improved external constraints (BAO, WL)
• Longer term
• No evolutionary bias in cosmology detected
  (tests continue!)
• SNe in passive galaxies seem more powerful
  probes, but substantially rarer (esp. at high-z)
• Colour corrections are the dominant uncertainty
• Urgent need for zlt0.1 samples with wide
  wavelength coverage
• Not clear what the next step at high-z should
  be

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Galaxy clustering
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The power spectrum turn-over
In radiation dominated Universe, pressure support
means that small perturbations cannot collapse.
Jeans scale changes with time, leading to smooth
turn-over of matter power spectrum.
varying the matter density times the Hubble
constant
However, it is hard to disentangle this shape
change from galaxy bias and non-linear effects
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Problem galaxy bias
Galaxies do not form a Poisson sampling of the
matter field
Peaks model large scale offset in 2-pt
clustering strength (next lecture)
Also non-linear effects in the matter
Also effects from the transition from mass to
galaxies
Angulo et al., 2007, MNRAS, astro-ph/0702543
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Baryon Acoustic Oscillations
Wavelength of baryonic acoustic oscillations is
determined by the comoving sound horizon at
recombination
varying the baryon fraction
At early times can ignore dark energy, so
comoving sound horizon is given by
Sound speed cs
Gives the comoving sound horizon 110h-1Mpc, and
BAO wavelength 0.06hMpc-1
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Comparing CMB BAO
CMB
SDSS GALAXIES
CREDIT WMAP SDSS websites
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Comparing BAO at different redshifts
SDSS main galaxies 2dFGRS
SDSS LRGs
Tell us more about the acceleration, rather than
just that we need it!
z0.35
z0.2
CREDIT WMAP SDSS websites
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BAO as a standard ruler
Changes in cosmological model alter measured BAO
scale (?dcomov) by Radial direction (evolution
of Universe) Angular direction (line of sight)
Gives rise to the rings of power
Hu Haiman 2003, astro-ph/0306053
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BAO as a standard ruler
BAO position (in a redshift slice) therefore
constrains some multiple of
Changes in cosmological model alter measured BAO
scale (?dcomov) by Radial direction (evolution
of Universe) Angular direction (line of sight)
If we are considering radial and angular
directions using randomly placed galaxy pairs, we
constrain (to 1st order)
Varying rs/DV
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Why BAO are a good ruler
Linear baryon acoustic oscillations are ratio of
linear matter power spectrum to a smooth fit
Suppose that we measure an observed power that is
related to the linear power by (halo model)
Linear bias model also predicts this form
Then observed oscillations are related to linear
BAO by
For linear bias model, peculiar velocities of
galaxies gives Gaussian damping with width 10Mpc
No change in position of oscillations, just a
damping term.
To change the observed positions of BAO, we need
sharp features in the observed power
Eisenstein, Seo White 2006, astro-ph/0604361 Per
cival et al. 2007, astro-ph/0705.3323
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Going to 2nd order
Perturbative treatment of (CDMbaryon) fluid
system
(e.g., Suto Sasaki 1991)
New approach
Based on field-theoretical approach,
Standard PT calculation can be improved by
re-summing an
infinite class of perturbative corrections at all
orders.
Renormalized Perturbation Theory (RPT)
Crocce Scoccimarro (2006ab,2007)
Related works McDonald, Matarrese Pietroni,
Valageas, Matsubara (07)
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Going to 2nd order
At second order we get mode mixing, which causes
shifts in the power spectrum BAO peaks
Shifts are lt1, and can be calculated
Not important for current data, but need to be
included for future analyses
Crocce Scoccimarro 2007 astro-ph/0704.2783
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BAO from all the SDSS DR5 galaxies
Compared with WMAP 3-year best fit linear CDM
cosmological model. N.B. not a fit to the data,
but a prediction from WMAP.

• Interesting features
• Overall P(k) shape
• Observed baryon acoustic oscillations (BAO)

Percival et al., 2007, ApJ, 657, 645
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BAO from the 2dFGRS SDSS
BAO detected at low redshift 0ltzlt0.3 (effective
redshift 0.2)
BAO detected at high redshift 0.15ltzlt0.5
(effective redshift 0.35)
BAO from combined sample (detected over the whole
redshift range 0ltzlt0.5)
Percival et al., 2007, MNRAS, astro-ph/0705.3323
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BAO distance scale constraints
Constraint including observed peak distance
constrain from CMB rs/dA(cmb)0.0104
?CDM
OCDM
SCDM
Constraint fitting rs/DV(z)
Constraint from DV(0.35)/DV(0.2)
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Future BAO prospects

• Short-term
• SDSS-II improves low redshift measurements by
  factor 2
• 1000000 galaxy redshifts to z0.5
• Wiggle-Z survey detects BAO at higher redshift
• 400 000 galaxy redshifts to z1
• weak constraints
• Longer term
• Photometric surveys (e.g PanSTARRS, DES) find
  2--3 distance constraints out to z1
• Future spectroscopic surveys (e.g. HetDex,
  BOSS, WFMOS, Space) push to 1 distance
  constraints over a wide range of redshift
  (0.5ltzlt3)
• With 1 constraints need to include 2nd order
  effects in analysis of BAO positions

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Further reading

• Supernovae
• Astier et al. (2005), astro-ph/0510447
• BAO
• Blake Glazebrook (2003), astro-ph/0301632
• Seo Eisenstein (2003), ApJ, 598, 720
• Hu Haiman (2003), astro-ph/0306053