Cosmology from Gravity, Galaxies and Gas

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Cosmology from Gravity, Galaxies and Gas

• Gravitational instability in an expanding
  universe
• Gastronomy A biased view of dark matters
• Galaxies
• Gas
• Geometry and Dynamics
• The Cosmic Background Radiation
• Supernovae
• The ISW effect
• Baryon oscillations

Ravi K. Sheth (UPenn)
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The SDSS
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You can observe a lot just by watching.
-Yogi Berra
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Galaxy clustering depends on type
Large samples now available to quantify this
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Light is a biased tracer
To use galaxies as probes of underlying dark
matter distribution, must understand bias
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N-body simulations of gravitational clustering
in an expanding universe
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Cold Dark Matter

• Simulations include gravity only (no gas)
• Late-time field retains memory of initial
  conditions
• Cosmic capitalism

Co-moving volume 100 Mpc/h
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Cold Dark Matter

• Cold speeds are non-relativistic
• To illustrate, 1000 km/s 10Gyr 10Mpc from
  z1000 to present, nothing (except photons!)
  travels more than 10Mpc
• Dark no idea (yet) when/where the stars
  light-up
• Matter gravity the dominant interaction

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Notice initial expansion followed by turnaround
and virialization
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Its a capitalists life

• Most of the action is in the big cities
• Newcomers to the city are rapidly stripped of
  (almost!) all they have
• Encounters generally too high-speed to lead to
  long-lasting mergers
• Repeated harassment can lead to change
• Real interactions take place in the outskirts
• A network exists to channel resources from the
  fields to feed the cities

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• Cosmology/particle physics from density profiles
  of halos, and from substructure in halos (i.e.
  dense regions), but beware of GASTROPHYSICS!

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Youve got to be very careful if you dont know
where youre going, because you might not get
there. -Yogi
Berra
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Assume a spherical cow.
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Assume a spherical herd of spherical cows
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Initial spatial distribution within patch (at
z1000)...
stochastic (initial conditions Gaussian random
field) study forest of merger history trees.
encodes information about subsequent merger
history of object
(Mo White 1996 Sheth 1996)
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Organized spherical collapse model for merger
history To this, add dynamical friction, tidal
stripping, interactions, etc.
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Only very fat cows are spherical.
but this turns out to be a detail.
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The Halo Mass Function
(Reed et al. 2003)

• Small halos collapse/virialize first
• Can also model halo spatial distribution
• Massive halos more strongly clustered

(current parametrizations by Sheth Tormen 1999
Jenkins etal. 2001)
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Universal form?

• Spherical evolution (Press Schechter 1974
  Bond et al. 1991)
• Ellipsoidal evolution (Sheth Tormen 1999
  Sheth, Mo Tormen 2001)
• Greatly simplifies analysis of cluster abundances
  (e.g. ACT)

Sheth Tormen 1999 Jenkins et al. 2001
Accurate for any cosmological model, fluctuation
spectrum, and time
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Most massive halos populate densest regions
over-dense
under-dense
Key to understand galaxy biasing (Mo White
1996 Sheth Tormen 2002)
n(md) 1 b(m)d n(m)
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Nobody goes there anymore its too crowded.
-Yogi Berra
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Halo clustering

• Massive halos more strongly clustered
• Clustering of halos different from clustering of
  mass
• On large scales xh(r) b2 xdm(r) bias is linear

massive halos
non-
linear theory
dark matter
Percival et al. 2003
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Halo clustering ? Halo abundances

• Clustering is ideal (only?) mass calibrator
  (Sheth Tormen 1999)

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Halo-model of galaxy clustering

• Two types of pairs only difference from dark
  matter is that now, number of pairs in m-halo is
  not m2
• ?dm(r) ?1h(r) ?2h(r)
• Spatial distribution within halos is small-scale
  detail

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SDSS Galaxy ClusteringOn large scales, bias
linear (as expected) more luminous galaxies
more strongly clustered Measurements constrain
galaxy formation in standard model
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Gravitational Lensing
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Lensing provides a measure of dark matter along
line of sight
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Image distortions correlated with dark matter
distribution e.g., lensed image ellipticities
aligned parallel to filaments, tangential to
knots (clusters)
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The shear power of lensing
stronger weaker Cosmology from
measurements of correlated shapes better
constraints if finer bins in source or lens
positions possible
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CL00241664
Lensed, distorted object is blue Note a
cluster is relatively easy to find from
photometry alone (cheaper than obtaining spectra)
because most galaxies in it have similar colors
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Strong lensing Multiple images
PG 115080 zsource 1.72 zlens 0.31
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• Focal length strong function of cluster-centric
  distance highly distorted images possible
• Strong lensing if source lies close to
  lens-observer axis weaker effects if impact
  parameter large
• Strong lensing Cosmology from distribution of
  image separations, magnification ratios, time
  delays but these are rare events, so require
  large dataset
• Weak lensing Cosmology from correlations
  (shapes or magnifications) small signal requires
  large dataset

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The Lyman-alpha forest
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Evolving forest
probes evolution of cosmological gas density
field
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SDSS Ly-a P(k)
Higher-z
Evolution consistent with LCDM model Non-trivial
because this is test at z3!
Lower-z
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Inhomo-geneity on various scales in the Universe
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• Combining any (or all) datasets with CMB provides
  long lever arm on primordial fluctuation spectrum
• Combining datasets also breaks degeneracies

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The Cosmic Background Radiation
Cold 2.725 K Smooth 10-5
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Lensing of the CMB
Primordial Lensed
Next generation of experiments should be able to
measure this effect
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Ly-a Lensing Galaxies Clusters
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The ISW effect
Cross-correlate CMB and galaxy distributions Inte
rpretation requires understanding of galaxy
population
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Cosmology from growth rate of gravitational
instability (which must overcome
expansion) Signal depends on b(a) D(a) d/dt
D(a)/a
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Cross-correlate LRGs with CMB
Measured signal combination of ISW and SZ
effects Estimate both using halo model
(although signal dominated by linear theory)
Signal predicted to depend on b(a) D(a) d/dt
D(a)/a
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Evolution and bias
Work in progress to disentangle evolution of
bias from z dependence of signal (Scranton
et al. 2004)
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Classical Cosmological Tests

• Standard candles or rods require 2 integrals over
  redshift
• Comoving distance
• dCom(z) (c/H0) 0 ?zdz H0/H(z)
• where H(z) describes expansion history
• H(z)/H02 WM(1z)3
• WDE exp ?da/a
  1w(a)
• Standard flat cosmological constant model has
  w(a) -1 and WDE 1 - WM

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Small fluctuations (10-5) are seeds from which
structure grows.
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Angular scale of first peak implies universe is
Flat
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Supernovae Ia are good standard candles
for no good reason !
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Cosmological Time Dilation
Agreement with standard template only if (1z)
time dilation factor included
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Measuring the expansion
Expansion rate changes with time Hubbles
constant same at all positions in space, but may
depend on time
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Evidence for acceleration today
and deceleration in the more distant past
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The future aint what it used to be.
-Yogi Berra
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Baryon Oscillations in the Galaxy Distribution
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but we need a tracer

• Luminous Red Galaxies
• Luminous, so visible out to large distances
• Red, presumably because they are old, so probably
  single burst population, so evolution relatively
  simple
• Large luminosity suggests large mass, so probably
  strongly clustered, so signal easier to measure
• Linear bias on large scales, so length of rod not
  affected by galaxy tracer!

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Oscillations in Fourier space P(k) are spike in
real space x(r)
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• Structure grew gravitationally from small
  fluctuations growth of structure was
  hierarchical
• Gastrophysics important for understanding galaxy
  propertiesgalaxy biasing (distribution of light
  not same as of mass)
• Various probes (different scales and different
  times) all indicate LCDM is good self-consistent
  model
• Next decade (large scale photometric and
  spectroscopic surveys) will bring constraints on
  model parameters from 10 to 1

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You should always go to other peoples
funeralsotherwise they wont go to yours.
-Yogi Berra