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

The Theory/Observation connection
lecture 4
dark energy: linking with observations
Will Percival
The University of Portsmouth
Lecture outline
 Dark Energy review
– cosmological constant?
– quintessence?
– tangled defects?
– phantom dark energy?
– modified gravity?
– problems with the data?
 Geometrical tests
– SN1a
– BAO
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
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)>-1 history can be obtained with right choice
of potential
quintessence
Albrecht & Weller 2002,
astro-ph/0106079
Parameterizations of w
If you don’t know the
physics, you don’t have
a well-defined set of
models to test, it’s a freefor-all
can parameterise using
w(a) = w0 + w1(1-a)
Bassett et al. 2004, astro-ph/0407364
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
Phantom dark energy
 motivated by early supernovae data which favored
strong acceleration
 w<-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
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 we’re going to be modifying
gravity, rather than postulating a new component of energy?
modified gravity
Example from history: Mercury perihilion
Newton + dark planet?
No! Modified gravity (GR)
Today, we need a modified Friedmann
equation
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)
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
With this in mind, lets have a look at the evidence
for acceleration …
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) 
SNLS Hubble diagram
First-Year SNLS Hubble Diagram
Astier et al (2006)
A&A, 447, 31
ΩM = 0.263 ± 0.042 (stat) ± 0.032 (sys)
<w>=-1.02 ± 0.09 (stat) ± 0.054 (sys) (with BAO + Flat Universe)
Supernovae observations
 Initially assumed all SN1a have same intrinsic peak
brightness
 Now refined so that
Luminosity
distance to
supernova
Apparent
magnitude of
supernova
Stretch parameter s:
corrects for lightcurve
shape via 
Absolute magnitude of
supernova (assumed constant
for all SN1a)
c=B-V colour: corrects
for extinction/intrinsic
effects via 
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
–Light-curves/Colors/Luminosities
From talk by Mark Sullivan
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
Passive hosts
Star-forming
hosts
Cosmological distribution of galaxy types
Future supernovae prospects
Short-term:
 Current constraints on <w>: <w>=-1 to ~6-7% (stat)
(inc. flat Universe, BAO+WMAP-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 z<0.1 samples with wide wavelength coverage
– Not clear what the “next step” at high-z should be
Galaxy clustering
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
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
Baryon Acoustic Oscillations
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QuickTime™ and a
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are needed to see this picture.
“Wavelength” of baryonic acoustic
oscillations is determined by the
comoving sound horizon at
recombination
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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
CMB
SDSS GALAXIES
Comparing CMB & BAO
CREDIT: WMAP & SDSS websites
z=0.2
SDSS LRGs
SDSS main galaxies + 2dFGRS
Comparing BAO at different redshifts
Tell us more about the
acceleration, rather than
just that we need it!
z=0.35
CREDIT: WMAP & SDSS websites
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
BAO as a standard ruler
Changes in cosmological model
alter measured BAO scale
(∆dcomov) by:
BAO position (in a redshift slice)
therefore constrains some multiple
of
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
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
No change in position of oscillations,
just a damping term.
For linear bias model,
peculiar velocities of
galaxies gives Gaussian
damping with width ~10Mpc
To change the observed positions of BAO, we need sharp
features in the observed power
Eisenstein, Seo & White 2006, astro-ph/0604361
Percival et al. 2007, astro-ph/0705.3323
Going to 2nd order …
Perturbative treatment of
(CDM+baryon) fluid system
   (1)   ( 2)   (3)  
（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)
Going to 2nd order …
At second order we get mode
mixing, which causes shifts in
the power spectrum BAO
peaks
Shifts are <1%, and can be
calculated
Not important for current data,
but need to be included for
future analyses
Crocce & Scoccimarro 2007; astro-ph/0704.2783
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:
1.
Overall P(k) shape
2.
Observed baryon
acoustic oscillations
(BAO)
Percival et al., 2007, ApJ, 657, 645
BAO from the 2dFGRS + SDSS
BAO detected at low redshift
0<z<0.3 (effective redshift 0.2)
BAO detected at high redshift
0.15<z<0.5 (effective redshift 0.35)
BAO from combined sample
(detected over the whole redshift
range 0<z<0.5)
Percival et al., 2007, MNRAS, astro-ph/0705.3323
BAO distance scale constraints
CDM
SCDM
OCDM
Constraint including
observed peak
distance constrain
from CMB
rs/dA(cmb)=0.0104
Constraint fitting
rs/DV(z)
Constraint from
DV(0.35)/DV(0.2)
Future BAO prospects
Short-term:
 SDSS-II improves low redshift measurements by factor ~2
– 1000000 galaxy redshifts to z~0.5
 Wiggle-Z survey detects BAO at higher redshift
– 400 000 galaxy redshifts to z~1
– weak constraints
Longer term:
 Photometric surveys (e.g PanSTARRS, DES) find ~2--3% distance
constraints out to z~1
 Future spectroscopic surveys (e.g. HetDex, BOSS, WFMOS, Space) push to
1% distance constraints over a wide range of redshift (0.5<z<3)
 With 1% constraints need to include 2nd order effects in analysis of
BAO positions
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