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Title: Constraining the Inflationary Gravitational Wave Background: CMB and Direct Detection


1
Constraining the Inflationary Gravitational Wave
Background CMB and Direct Detection
  • Nathan Miller
  • Keating Cosmology Lab
  • CASS Journal Club
  • 3/13/07

2
References
  • 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

3
Outline
  • Introduction
  • Comparison Between CMB and Direct Detection
  • What can be constrained by measurements
  • Foregrounds

4
380 kyr
13.7 Gyr
5
Inflation
  • 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

6
Inflationary Dynamics
  • Inflation occurs when cosmological expansion
    accelerates
  • Driven by a spatially homogeneous scalar field,
    F, the inflaton

7
Slow-Roll Inflation
Rewriting with F as time variable
8
Primordial 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

9
Slow-Roll Hierarchy and Flow Equations
Definition of Parameters
Derivatives
10
Evaluating 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

11
Relating Slow-Roll to Observables
  • Observables can be written in terms of slow-roll
    parameters
  • 2nd order in slow-roll
  • C4(ln2?)-5

12
Results of Slow-Roll Flow Equations
Kinney 2002
13
Detection 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

14
CMB
  • 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
15
Gravitational 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

16
How a blackbody becomes polarized (Thomson
scattering)
Plane of Polarization
electron
unpolarized
100 polarized
Polarization cos2T Quadrupole Scattering
Courtesy of Brian Keating
17
How is the CMB polarized by GW?
e-
Gravitational Wavevector
Courtesy of Brian Keating
18
GW CMB Plasma
This process leads to.
Courtesy of Brian Keating
19
Gravitational Waves CMB
Caldwell Kamionkowski
Temperature and Polarization caused by single
wave in z direction.
Courtesy of Brian Keating
20
Polarization 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
21
WMAP Limits
NO Detection of the B mode
22
Future CMB Experiments
Measurements of the B-mode power spectrum are the
focus of future CMB grounds/balloon/space based
experiments
23
Direct 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

24
Inflationary 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
25
Michelson Interferometer
  • Split a single laser beam in two
  • Send beam over paths 90o to each other
  • Reflect beams back and produce an interference
    pattern

26
LISA, 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
27
Direct 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)

28
Big Bang Observer
29
Deci-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
30
Current Limits and Projected Sensitivities
Solid Lines are current limits Dashed Lines are
projections
31
From 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

32
Extrapolation vs. Numerical Method
  • Extrapolation
  • Numerical

33
r vs. ?GW
7
Extrapolation
From Slow roll
34
Amplitude as a function of Frequency
10-15
10-17
35
OGW Comparison
0.99 lt ns(kCMB) lt 1.01
36
Combining 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

37
GWB 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

38
Constraints on GWB amplitude from CMB/LSS
CMB Data Sets WMAP, ACBAR, CBI, VSA,
BOOMERanG Galaxy Power Spectrum Data 2dF, SDSS,
and Lyman-a
39
Adiabatic 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
40
Current and CMBPol Limits
41
Structure 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
42
Hubble 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
43
F vs. N
rgt10-2
rlt10-4
44
V(F)
r0.02
r0.001
rlt10-4
Planck
CMBPol
CMBPol
Foreground Sensitivity Limit
45
Types 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

46
Parameter 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
47
OGW-nt parameter space
Solid-blue Power Law Dotted Magenta
Chaotic Dot-dashed cyan Symmetry Breaking Dashed
Yellow Hybrid Everything evaluated at
BBO/DECIGO Scales
48
Consistency Relation
Consistency Relation
49
Determining 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

50
Uncertainty of R
Uncertainty implied with ns0.950.1
51
Problems
  • nt(CMB)?nt(DD)
  • Magnitude is different by an order of magnitude
  • R is always less than unity

Friedman, Cooray, Melchiorri 2006
52
Foreground 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

53
CMB Foregrounds
Synchrotron
WMAP 23 GHz
Dust
Finkbeiner-Davis-Schlegel Dust Map
54
Foreground Power Spectrum
Solid Synchrotron, Dashed Dust
55
Removal 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

56
Other Stochastic Gravitational Wave Backgrounds
Potentially detectable by LISA and LIGO
nt3
57
Conclusion
  • 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
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