Download Inflation Basics

The Future of the CMB
Marc Kamionkowski
(Caltech)
AIU ’08, Tsukuba, 13 March 2008
CMB that we see originates from edge of observable
Universe as it was ~400,000 years after the big bang,
~14 billion years ago
You are here
14 billion
light-years
Causally
connected
region
Observe:
•CMB smooth to 1st approximation
•Has small fluctuations
•BBN accounts for light-element abundances
Can infer:
•Primordial density perturbations exist
•Have small amplitude on largest scales
•Have small amplitude on smallest scales
•Have spectrum (in wavenumber k) no
steeper than scale invariant
Slow-roll
parameters
Inflationary
perturbations:
(open)
(flat)
First test of inflation:
Is the Universe flat?
T(n)=Σ almYlm(n)
Cl=<|alm|2>
CMB determination
of the geometry
(MK, Spergel,
and Sugiyama, 1994)
YES!
30 mK
BOOMERanG (2002)
Now even more precise from WMAP
Cosmological-parameter determination
(Jungman, MK, Kosowsky, Spergel 1996)
WMAP-3:
even better than we expected!!
WHAT
NEXT???
GEOMETRY
SMOOTHNESS
STRUCTURE
FORMATION
INFLATION
What is
Einfl?
STOCHASTIC GRAVITATIONAL WAVE
BACKGROUND with amplitude Einfl2
Detection of ultra-long-wavelength GWs from
inflation: use plasma at CMB surface of last
scatter
as sphere of test masses.
Temperature pattern produced by
one gravitational wave oriented in z
direction
z
No Gravity Waves
Gravity Waves
Detection of gravitational waves with
CMB polarization
(MK, Kosowsky, Stebbins, 1996; Seljak & Zaldarriaga 1996)
Temperature map:
“E Mode”
Polarization Map:
Density perturbations have no handedness” “B
so they cannot produce a polarization with a curl
mode”
Gravitational waves do have a handedness, so they
can (and do) produce a curl
Model-independent probe of gravitational waves!
“Curl-free” polarization patterns
“curl” patterns
Recall, GW amplitude is Einfl2
l2
GWs  T
And from COBE, Einfl<3x1016 GeV
GWs  unique polarization pattern. Is it detectable?
If E<<1015 GeV (e.g., if inflation from PQSB),
then polarization far too small to ever be detected.
But, if E~1015-16 GeV (i.e., if inflation has
something to do with GUTs), then polarization
signal is conceivably detectable by Planck
or realistic post-Planck experiment!!!
Big news:
If ns=0.95, and ε~η (and no
weird cancellation), then
ε~0.01, V~(2x1016 GeV)4,
and r=T/S~0.1.
I.e., GW background ~ “optimistic”
estimates
(e.g., Smith, Cooray,MK, arXiv:0802:1530)
WMAP
BICEP
QUIET1
QUEST (QUaD)
Planck
QUIET2
Hivon
SPIDER
(Kesden, Cooray, MK 2002;
Knox, Song 2002)
If GW amplitude small, may need
high-resolution T/P maps to
disentangle cosmic-shear
contribution to curl
component from that due to
inflationary gravitational waves.
Lensing shifts position on sky:
Where the projected grav potential is
and so lensing induces a curl
even if there was no primordial curl, with
power spectrum
How can we correct for it? T also lensed. In
absence of lensing,
but with lensing,
We can therefore reconstruct the deflection
angle….
Another possibility to correct for
cosmic shear
(Sigurdson, Cooray 2005)
• Use 21-cm probes of hydrogen distribution
to map mass distribution between here and
z=1100
The CMB:
What else is it good for?
WMAP-5: fraction of CMB photons
that re-scattered after recombination
(z~1100) is τ~0.1.
If electrons that re-scattered these CMB
CMB photons were ionized by radiation
from the first stars, then the first stars
formed at z=10
Probes of parity violation in
CMB
(Lue, Wang, MK 1999)
Might new physics responsible for inflation
be parity violating?
TC and TG correlations in CMB are
parity violating.
Can be driven, e.g., by terms of form
during inflation or
since recombination
WMAP search: Feng et al., astro-ph/0601095
Komsatsu et al. (WMAP-5)
High-frequency gravitational waves
and the CMB
GWs are tensor modes of perturbations.
“Conventional” way to probe GWs:
1) low-l plateau versus peaks
2) B mode polarization
New approach:
Small scale GW behave as massless
particles. They contribute to the energy
density of the Universe.
Limits on gravitational-wave energy density
Smith, Pierpaoli, MK
(PRL, 2006)
Particle Decays and the CMB
Xuelei Chen and MK, PRD 70, 043502 (2004)
L. Zhang et al., PRD 76, 061301 (2007)
also, Kasuya, Kawasaki, Sugiyama (2004)
and Pierpaoli (2004)
• Can we constrain dark-matter decay
channels and lifetimes from the CMB and
elsewhere?
Photons absorbed by IGM
Transparency
window
IGM
optical depth,
temperature,
and ionization
for decaying
particle
Ionization
induced by
particle
Decays
affects
CMB power
spectra
What Else??
Inflation predicts distribution of primordial
density perturbations is Gaussian (e.g., Wang
&MK, 2000).
But how do we
tell if primordial
perturbations
were Gaussian??

In single-field slow-roll inflation,
nongaussianity parameter (e.g., Wang-MK 1999):
fNL ~ ε (δρ/ρ)
~ 0.01 x 10-5
Will be small!! WMAP now at fNL ~50; Planck to get
to fNL ~O(1). So simplest models not to be tested,
but alternatives may produce larger fNL .
Gaussian random field
Φ=φ+ fNL (φ2-<φ2>)
Gravitational potential
How do we tell if primordial perturbations were Gaussian??
(1) With the CMB:
Advantage: see primordial perturbation directly
Disadvantage: perturbations are small
T/T
How do we tell if primordial perturbations were Gaussian??
(2) With galaxy surveys:
Advantage: perturbations are bigger
Disadvantage: gravitational infall induces
non-Gaussianity (as may biasing)
Evolved
Primordial
How do we tell if primordial perturbations were Gaussian??
(3) With abundances of clusters (e.g.,
Robinson, Gawiser & Silk 2000) or high-redshift
galaxies (e.g., Matarrese, Verde & Jimenez 2000):
Rare objects
form here
How do we tell if primordial perturbations were Gaussian??
(4) With distribution of cluster sizes
(Verde, MK, Mohr & Benson, MNRAS, 2001):
Broader distribution of >3
peaks leads to broader
formation redshift distribution
and thus to broader size
distribution
How do we tell if primordial perturbations were Gaussian??
How do these different avenues compare?
For just about any nonGaussianity with long range
correlations (e.g., from topological defects
or funny inflation), CMB> LSS (Verde, Wang,
Heavens & MK, 2000).
Cluster and high z abundances do better
at probing nonGaussianity from topological
defects than CMB/LSS, while CMB remains
best probe of that from funny inflation
(Verde, Jimenez, Matarrese & MK, MNRAS 2001).
Is the Universe Statistically Isotropic?
Pullen and MK, PRD (2007); Ando and MK PRL (2008)
Inflation usually predicts primordial perturbations are
statistically isotropic---they have no preferred direction:
Power spectrum P(k) function of wavenumber
k magnitude only; not its direction.
But what if this were violated (e.g., Ackerman, Carroll,Wise,
2007)? What if we had a power spectrum that depended on
the direction of k?
Statistically
isotropic
E.g.,
a power
quadrupole
If SI is violated:
And is straightforward to calculate the
Dll’ given P(k).
Departures from SI correlate different alm’s.
Pullen-MK: minimum-variance estimators
for the ξlml’m’ and also the gLM. E.g., WMAP
sensitive to g20~0.02 and Planck to g20~0.005 (1σ).
Ando-MK: nonlinear evolution of
primordial anisotropic power:
Pprim(k) 
Ptoday(k)
required to search galaxy surveys for SI departures.
Pullen-Hirata now testing SI with SDSS/WMAP
Direct Detection of Inflationary
Gravitational Waves?
(T. L. Smith, MK, Cooray, PRD 2006;
see also Efstathiou-Chongchitnan and Smith-Peiris-Cooray)
Mission concept studies:
•NASA: Big-Bang Observer (BBO)
•Japan: Deci-Hertz Gravitational-Wave
Observatory (DECIGO)
seek to detect directly inflationary gravitationalwave background at ~0.1-Hz frequencies
Survey some “toy” models for inflation:
“power-law”
“chaotic”
“hybrid”
“symmetry-breaking”
Tensor-to-scalar ratio r
chaotic
Power-law
Symmetry
breaking
chaotic
For dessert: something completely
different…..
Dark Matter, the Equivalence
Principle, and Dwarf Galaxies
Work done with Mike Kesden,
PRL 97, 131303 (2006) [astro-ph/0606566],
PRD 74, 083007 (2006) [astro-ph/0608095]
observed
3-5 kpc
dis
k
Local dark-matter 8.5 kpc
density: ~0.4 (GeV/c2)/cm3
Velocity dispersion:
v ~ 300 km/sec
But does dark matter fall same way
in gravitational field? Does the
force law,
hold for dark matter as well? And if
how would we know?
Instead, consider tidal streams of Sagittarius dwarf:
•Sgr is DM dominated so acts as DM tracer of Milky
Way potential, while stripped stars act as baryonic
tracers.
•Streams are long-lived and now well-observed with
2MASS and SDSS
•Detailed simulations compared with observations
already provide remarkably precise constraints to Sgr
mass, M/L, orbit, and Milky Way halo (e.g., Law,
Johnston, Majewski 2005)
Majewski et al. 2003
Where do tidal streams come from?
MW
trajectory
M=mass
R
Trailing
tail
Sgr
r
m=mass
Leading tail
Where do tidal streams come from?
MW
trajectory
M=mass
R
Trailing
tail
Sgr
r
m=mass
Leading tail
Conclusions
• Conservative “by-eye” comparison with
observation of roughly equal leading and trailing
stream constrains DM force law to be within
~10% of that for baryons
Summary
• CMB provides ever increasing evidence for inflation
• Departure from scale invariance significant, if real,
provides additional motivation for pursuing IGWs
• Cosmic shear of CMB provides exciting new target;
room for theoretical and data-analysis work
• Can begin to test Gaussianity of primordial
perturbations
• Can begin to test validity of statistical-isotropy
prediction
• Theorists need to be more imaginative: what else can
we do with the CMB? Where do we go next?