Formation and Evolution of the Large Scale Structure

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Formation and Evolutionof theLarge Scale
Structure
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Large Scale Structure of the Universe
Somewhat after recombination -- density
perturbations are small on nearly all spatial
scales. Dark Ages, prior to z10 -- density
perturbations in dark matter and baryons grow on
smaller scales perturbations have gone
non-linear, dgtgt1 small (low mass) dark matter
halos form massive stars form in their potential
wells and reionize the Universe. z3 -- Most
galaxies have formed they are bright with
stars this is also the epoch of highest quasar
activity galaxy clusters are forming. Growth of
structure on large (linear) scales has nearly
stopped, but smaller non-linear scales continue
to evolve. z0 -- Small galaxies continue to get
merged to form larger ones in an open and lambda
universes large scale (gt10-100Mpc) potential
wells/hill are decaying, giving rise to late ISW.
Picture credit A. Kravtsov, http//cosmicweb.uch
icago.edu/filaments.html
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Matter Power Spectrumfrom inflation to today
A different convention plot P(k)k3
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Evolution of density fluctuations the set-up

Growth rate of a density perturbation depends on
the epoch (i.e. what component dominates global
expansion dynamics at that time), and whether a
perturbation k-mode is super- or sub-horizon.
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How did the matter power spectrum go from
Harrison-Zeldovich to this
?
lambda domination
log(t)
lambda-matter equality
z1
matter domination
recombination production of CMB
z1200
sub-horizon
matter-radiation equality
z4 x 103
super-horizon
radiation domination
end of inflation
zgtgt1010
infla- tion
Planck time
log(rcomov)
Growth rate of a density perturbation depends on
the epoch (i.e. what component dominates global
expansion dynamics at that time), and whether a
perturbation k-mode is super- or sub-horizon.
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Linear growth of density perturbationsSuper-hori
zon, w comp. dominated, pre post recomb.
Friedmann eq different patches of the Universe
will have slightly different average densities
and curvatures
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Linear growth of density perturbationsSub-horizo
n, radiation dominated, pre recombination
dark matter has no pressure of its own it is
not coupled to photons, so there is no restoring
pressure force at all.
Jeans linear perturbation analysis applies
log(t)
zero
CMB
radiation dominates, and because radiation does
not cluster ? all dk0
MRE
inflation
log(rcomov)
but the rate of change of dks can be non-zero
growing decaying mode mode
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Linear growth of density perturbationsSub-horizo
n, matter dominated, pre post recomb.
dark matter has no pressure of its own it is
not coupled to photons, so there virtually no
restoring pressure force.
Jeans linear perturbation analysis applies
log(t)
zero
also, can assume that total density is the
critical density at that epoch
CMB
MRE
inflation
log(rcomov)
Two linearly indep. solutions growing mode
always comes to dominate ignore decaying mode
soln.
Structure growth begins and ends with matter
domination
growing decaying mode mode
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Linear growth of density perturbationsSub-horizo
n, lambda dominated, pre post recomb.
dark matter has no pressure of its own it is
not coupled to photons, so there is virtually no
restoring pressure force.
Jeans linear perturbation analysis applies
log(t)
zero
can assume the amplitude of perturbations is
zero, because lambda, which dominates, does not
cluster
CMB
MRE
inflation
log(rcomov)
Two linearly indep. solutions growing mode
always comes to dominate ignore decaying mode
soln.
growing decaying mode mode
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Linear growth of density perturbationsSub-horizo
n, curvature dominated, pre post recomb.
dark matter has no pressure of its own it is
not coupled to photons, so there virtually no
restoring pressure force.
Jeans linear perturbation analysis applies
log(t)
zero
can assume the amplitude of perturbations is
zero, because curvature, which dominates, does
not cluster
CMB
MRE
inflation
log(rcomov)
Two linearly indep. solutions growing mode
always comes to dominate ignore decaying mode
soln.
growing decaying mode mode
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Linear growth of density perturbationsdark
matter, baryons, and photons
log(t)
CMB
MRE
amplitude of perturbation
inflation
log(rcomov)
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Evolution of matter power spectrum
log(t)
high-k small scale perturbations grow fast,
non-linearly
P(k)
Now
z1
k
baryonic oscillations appear the
P(k) equivalent of CMB T power spectrum
CMB
P(k)
MRE
k
sub-horizon perturb. do not grow during
radiation dominated epoch
P(k)
k
P(k)
k
Harrison-Zeldovich spectrum P(k)k from
inflation
P(k)
EoIn
k
log(rcomov)
log(k)
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Transfer Functions
Transfer function is defined as follows, where
the two relevant epochs are the end of inflation
and matter-radiation equality, and later epoch if
there shape changes in P(k).
Peacock astro-ph/0309240
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Growth of large scale structure
Dark Matter density maps from N-body
simulations Recent epoch dark matter or dark
energy dominated?
During matter dominated epoch, fractional
overdensity grows as the scale factor. The
corresponding potential fluctuations stay
constant, because decrease in average density and
increase in linear size combined compensate for
d a
Standard spatially flat Wmatter1.0
fractional overdensity 1/(1z)
350 Mpc
the Virgo Collaboration (1996)
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Growth of large scale structure
Dark Matter density maps from N-body simulations
Lambda (DE) spatially flat Wmatter0.3
fractional overdensity const
Standard spatially flat Wmatter1.0
fractional overdensity 1/(1z)
350 Mpc
the Virgo Collaboration (1996)
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Growth of large scale structure
In linear theory gravitational potential decays
if DE or negative curvature dominate late time
expansion
Lambda (DE) spatially flat Wmatter0.3
gravitational potential (1z)
Standard spatially flat Wmatter1.0
gravitational potential const
350 Mpc
the Virgo Collaboration (1996)
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Late Integrated Sachs-Wolfe (ISW) Effect
If a potential well evolves as a photon
transverses it, the photons energy will change
Sachs Wolfe (1967) ApJ 147, 73 Crittenden
Turok (1996) PRL 76, 575
photon gains energy after crossing a potential
well
potential well
Look for correlation between CMB temperature
fluctuations and nearby structure. Detection of
late ISW effect in a flat universe is direct
evidence of Dark Energy
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Detecting late ISW
Late ISW is detected as a cross-correlation,
CCF on the sky between nearby large scale
structure and temperature fluctuations in the
CMB.
HEAO1 hard X-rays full sky median z0.9
NVSS 1.4 GHz nearly full sky radio galaxies
median z0.8
Lines are LCDM predictions, not fits to
data Note points are highly correlated
Boughn Crittenden (2005) NewAR 49, 75,
astro-ph/0404470
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Evolution of matter power spectrum
log(t)
high-k small scale perturbations grow fast,
non-linearly
P(k)
Now
z1
k
baryonic oscillations appear the
P(k) equivalent of CMB T power spectrum
CMB
P(k)
MRE
k
sub-horizon perturb. do not grow during
radiation dominated epoch
P(k)
k
P(k)
k
Harrison-Zeldovich spectrum P(k)k from
inflation
P(k)
EoIn
k
log(rcomov)
log(k)
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Growth of perturbationswith and without DM
log(t)
lambda dom.
inflation
matter domination
radiation domination
CMB
MRE
Planck time
end of inflation
lambda-matter equality
log(rcomov)
without dark matter
with dark matter
Growth of baryonic perturbations without
DM given that the observed fluctuations in the
potential at the CMB (z1000) on horizon scales
are 10-5 , and assuming linear growth of
perturbations gives snowsCMB (1z) 0.01.
However, today on these scales we see rms
overdensities 10-100 times larger.
Coles Lucchin
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Baryonic Acoustic Oscillations
One wave around one center Wave starts
propagating at Big Bang end at recombination.
The final length is the sound crossing horizon at
recomb. (Change of color means recombination.)
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Matter power spectrum - observations
Baryonic Acoustic Oscillations (BAO) SDSS and 2dF
galaxy surveys
from k-space to real space
BAO bump
gal. corr. fcn.
comoving r (Mpc/h)
Eisenstein et al. astro-ph/0501171
Percival et al. astro-ph/0705.3323
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Clustering of SDSS galaxies epochs ofequality
and recombination
Luminous red galaxies, z 0.35
sound horizon size at recombination
Wmh20.12, 0.13, 0.14
galaxy correlation function
Wmh20.130/-0.011
Eisenstein et al. astro-ph/0501171