Title: Constraining the Inflationary Gravitational Wave Background: CMB and Direct Detection
1Constraining the Inflationary Gravitational Wave
Background CMB and Direct Detection
- Nathan Miller
- Keating Cosmology Lab
- CASS Journal Club
- 3/13/07
2References
- Smith, Kamionkowski, Cooray Direct Detection of
the Inflationary Gravitational Wave Background
2005 - Smith, Peiris, Cooray Deciphering Inflation with
Gravitational Waves CMB Polarization vs. Direct
Detection with Laser Interferometers 2006 - Chongchitnan and Efstathiou Prospects for Direct
Detection of Primordial Gravitational Waves 2006 - Smith, Pierpaolo, Kamionkowski A New Cosmic
Microwave Background Constraint to Primordial
Gravitational Waves 2006 - Friedman, Cooray, Melchiorri WMAP-normalized
Inflationary Model Predictions and the Search for
Primordial Gravitational Waves with Direct
Detection Experiments, 2006
3Outline
- Introduction
- Comparison Between CMB and Direct Detection
- What can be constrained by measurements
- Foregrounds
4380 kyr
13.7 Gyr
5Inflation
- Alan Guth, 1981
- Early exponential expansion of the universe
- Solves many cosmological problems
- Horizon, Flatness, Magnetic Monopole
- Production of primordial gravitational waves
- Only early universe scenario that produces these
gravitational waves - Creates CMB B-modes
- Predicts stochastic gravitational wave background
with a nearly scale-invariant spectrum
6Inflationary Dynamics
- Inflation occurs when cosmological expansion
accelerates - Driven by a spatially homogeneous scalar field,
F, the inflaton
7Slow-Roll Inflation
Rewriting with F as time variable
8Primordial Power Spectra
- Power spectra are evaluated when the wavelength
in question leaves the horizon - Can be parametrized by a power law with the
spectral indices slowly changing as a function of
wavenumber
9Slow-Roll Hierarchy and Flow Equations
Definition of Parameters
Derivatives
10Evaluating the Flow Equations
- Randomly choose starting slow-roll parameters
- Evolve forward in time (dN lt 0) until end of
inflation or reaches a late time fixed point - Evaluate Observables
- If evolution reaches a late-time fixed point,
calculate the observables at this point - If inflation end, evaluate the flow equations
backward N e-folds from the end of inflation.
Calculate the observables at this point - Exact value of N to use is unknown (reheating) so
a range is used
11Relating Slow-Roll to Observables
- Observables can be written in terms of slow-roll
parameters - 2nd order in slow-roll
- C4(ln2?)-5
12Results of Slow-Roll Flow Equations
Kinney 2002
13Detection of Inflation
- Indirectly through the B-mode of the CMB is a
goal of next generation CMB experiments - Direct detection with future space based GW
detectors has become a subject of serious study
14CMB
- Universe was much smaller, hotter
- Photons in equilibrium with the proton/electron
plasma - As universe expanded, wavelength expanded,
eventually energy smaller than required to keep
equilibrium in proton/electron plasma - Photons free-streamed to us today
- Density perturbations before recombination give
rise to photon anisotropies
Boomerang 03 Flight
15Gravitational Waves on the CMB
- CMB B-mode or Curl Polarization
- Generated by Primordial GWB at large (1o) angular
scales - Density perturbations do not create B-modes
- Detection is limited by
- Lensing at small (5) scales
- Large Scale Structure
- Neutrinos
- Foregrounds
-
16How a blackbody becomes polarized (Thomson
scattering)
Plane of Polarization
electron
unpolarized
100 polarized
Polarization cos2T Quadrupole Scattering
Courtesy of Brian Keating
17How is the CMB polarized by GW?
e-
Gravitational Wavevector
Courtesy of Brian Keating
18GW CMB Plasma
This process leads to.
Courtesy of Brian Keating
19Gravitational Waves CMB
Caldwell Kamionkowski
Temperature and Polarization caused by single
wave in z direction.
Courtesy of Brian Keating
20Polarization Patterns
- Polarization Generation by Thomson Scattering
E-mode
B-mode
Wayne Hu
- Density fluctuations give scalar perturbations
gt E-mode - Gravity Waves give tensor perturbation gt B, E
modes
Courtesy of Brian Keating
21WMAP Limits
NO Detection of the B mode
22Future CMB Experiments
Measurements of the B-mode power spectrum are the
focus of future CMB grounds/balloon/space based
experiments
23Direct Detection
- Directly measure the change in lengths caused by
wave passing through - Frequency probed is about 0.1 1 Hz
- 1014 Mpc-1
- Ground and space based experiments
- Only space based considered for detection of GWB
24Inflationary Gravitational Wave Background and
Direct Detection
- Dont measure r
- Only measure tensors
- Energy density of the gravitational wave
background - Function of wavenumber
Tensor Power Spectrum today
25Michelson Interferometer
- Split a single laser beam in two
- Send beam over paths 90o to each other
- Reflect beams back and produce an interference
pattern
26LISA, Space-Based Laser Interferometer
- 3 Spacecrafts, each containing a reference mass
- Laserbeams are directed at other 2 spacecrafts
reference masses - Spacecraft shine back their own lasers, matching
phase with laser of main craft - Main craft compares light from other crafts to
determine through interference pattern change in
distance - Secondary craft also shine their lasers at each
other to determine their own separation
LISA
27Direct Detection Sensitivities
- Constraining inflation for 3 different possible
detectors are discussed - BBO
- BBO-grand (10 times more sensitive)
- Ultimate DECIGO (40-100 times more sensitive)
28Big Bang Observer
29Deci-hertz Interferometer Gravitational Wave
Observatory
LISA
Terrestrial Detectors (e.g. LCGT)
Strain Hz-1/2
Gap
10-4
102
104
100
10-2
Frequency Hz
30Current Limits and Projected Sensitivities
Solid Lines are current limits Dashed Lines are
projections
31From CMB to Direct Detection
- To make comparisons between CMB and Direct
Detection, need relation between r and OGW - Simplest is extrapolating measured tensor power
spectrum to DD scales - Can use slow roll to calculate variables at
different scales
32Extrapolation vs. Numerical Method
33r vs. ?GW
7
Extrapolation
From Slow roll
34Amplitude as a function of Frequency
10-15
10-17
35OGW Comparison
0.99 lt ns(kCMB) lt 1.01
36Combining CMB Direct Detection
- Using both measurements of the CMB and BBO/DECIGO
can probe inflaton potential with NO assumptions
about power-law behavior or a model shape for the
potential - Slow-roll inflation
- Through Hubble Constant and F(N)
- They also can be combined to help test the
single-field consistency relation
37GWB and Initial Conditions
- GWB behaves as a free-streaming gas of massless
particles - Similar to massless neutrinos
- Adiabatic Initial Conditions
- Indistinguishable from massless neutrinos
- CMB/LSS constraint to number of massless neutrino
species translates directly to a constraint on
OGW - Non-Adiabatic
- Effects may differ from those of massless
neutrinos
38Constraints on GWB amplitude from CMB/LSS
CMB Data Sets WMAP, ACBAR, CBI, VSA,
BOOMERanG Galaxy Power Spectrum Data 2dF, SDSS,
and Lyman-a
39Adiabatic vs. Homogeneous
- Adding Galaxy Survey Lyman-a increases
uncertainty over using just CMB - Discrepancy between data sets
- 95 Confidence Limit of OGWh2lt6.9x10-6 for
homogeneous initial conditions
Dotted Line only CMB data Solid Line Galaxies
and Lyman-a Dash-Dot Marginalize over non-zero
neutrino masses
40Current and CMBPol Limits
41Structure of the Potential
- Trajectories of the Hubble constant as a function
of N can be determined by measurements of CMBDD - Different models satisfying observational
constraints on ns, as and large r can have much
different ?gw at DD scales - How does this affect the history of H
- H is related to V
- F vs. N significantly different depending on rCMB
(N0)
N0
42Hubble Constant Trajectories
0.15 r 0.25
Trajectories with sharp features in H(N) in the
last 20 e-folds of inflations will be the first
to be ruled out be BBO/DECIGO
43F vs. N
rgt10-2
rlt10-4
44V(F)
r0.02
r0.001
rlt10-4
Planck
CMBPol
CMBPol
Foreground Sensitivity Limit
45Types of Inflation
- Each type of inflation can predict observables in
allowed range - Measurements of Ps and ns at CMB/LSS scales along
with upper limits to r and as constrain inflaton
potential and derivatives at time CMB/LSS scales
exited the horizon - Can use fact that 35 e-folds of inflation
separate CMB/LSS and BBO/DECIGO to find potential
when BBO/DECIGO scales exited the horizon
46Parameter Space Occupied by Different Types of
Inflation
Solid-blue Power Law Dotted Magenta
Chaotic Dot-dashed cyan Symmetry Breaking Dashed
Yellow Hybrid Everything evaluated at CMB scales
47OGW-nt parameter space
Solid-blue Power Law Dotted Magenta
Chaotic Dot-dashed cyan Symmetry Breaking Dashed
Yellow Hybrid Everything evaluated at
BBO/DECIGO Scales
48Consistency Relation
Consistency Relation
49Determining R
- Proposal to use both CMB and DD to constrain
consistency relation - With 10 foreground contamination, CMBPol could
measure R1.080.0 - Determine r from CMB scales, nt from direct
detection scales - Laser interferometer can measure nt to
- Connecting ntBBO to ntCMB adds additional
uncertainty
50Uncertainty of R
Uncertainty implied with ns0.950.1
51Problems
- nt(CMB)?nt(DD)
- Magnitude is different by an order of magnitude
- R is always less than unity
Friedman, Cooray, Melchiorri 2006
52Foreground Contamination
- Foregrounds contaminate measurements
- Foregrounds in CMB
- Dust, Synchrotron
- Limits minimum achievable r detected
- Foregrounds in DD also may limit detection
- Inspiralling binary systems of white dwarfs,
neutron stars, or black holes - Must be able to subtract to high accuracy
- Other sources of a stochastic GWB
53CMB Foregrounds
Synchrotron
WMAP 23 GHz
Dust
Finkbeiner-Davis-Schlegel Dust Map
54Foreground Power Spectrum
Solid Synchrotron, Dashed Dust
55Removal Techniques
- Many different CMB foreground removal techniques
- Map Space
- Template Fitting
- Linear Combination
- FastICA
- Maximum Entropy Method
- Monte Carlo Markov Chain
- l Space
- Minimize Power
56Other Stochastic Gravitational Wave Backgrounds
Potentially detectable by LISA and LIGO
nt3
57Conclusion
- Combining CMB and DD much about inflation can be
learned - Different things can be constrained that cant be
done with just CMB - History of Hubble Constant
- Inflaton Potential
- Consistency relation(?)
- Foregrounds will limit ultimate detection limit
- Background might limit detection of the
background - Wont happen for 20 years
- BBO/DECIGO arent anytime soon
- CMBPol is still a long ways away