Constraining the Inflationary Gravitational Wave Background: CMB and Direct Detection
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Transcript of Constraining the Inflationary Gravitational Wave Background: CMB and Direct Detection
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Constraining the Inflationary Gravitational Wave Background:
CMB and Direct DetectionNathan Miller
Keating Cosmology LabCASS Journal Club
3/13/07
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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
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Outline
• Introduction
• Comparison Between CMB and Direct Detection
• What can be constrained by measurements
• Foregrounds
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13.7 Gyr
380 kyr
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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
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Inflationary Dynamics
• Inflation occurs when cosmological expansion accelerates
• Driven by a spatially homogeneous scalar field, Φ, the “inflaton”
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Slow-Roll Inflation
Rewriting with Φ as “time” variable
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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
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Slow-Roll Hierarchy and Flow Equations
Definition of Parameters Derivatives
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Evaluating the Flow Equations
• Randomly choose starting slow-roll parameters• Evolve forward in time (dN < 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
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Relating Slow-Roll to Observables
• Observables can be written in terms of slow-roll parameters
• 2nd order in slow-roll• C=4(ln2+γ)-5
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Results of Slow-Roll Flow Equations
Kinney 2002
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Detection of Inflation
1. Indirectly through the B-mode of the CMB is a goal of next generation CMB experiments
2. Direct detection with future space based GW detectors has become a subject of serious study
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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
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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
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How a blackbody becomes polarized (Thomson scattering)
100% polarized
Plane of Polarization
unpolarized
Polarization ~ cos2Θ – Quadrupole Scattering
electron
Courtesy of Brian Keating
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How is the CMB polarized by GW?
Gravitational Wavevector
e-
Courtesy of Brian Keating
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GW + CMB Plasma
This process leads to….Courtesy of Brian Keating
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Gravitational Waves + CMB
Caldwell & Kamionkowski
Temperature and Polarization caused by single wave in +z direction.
Courtesy of Brian Keating
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Polarization Patterns
E-mode B-mode
• Density fluctuations give scalar perturbations => E-mode• Gravity Waves give tensor perturbation => B, E modes
• Polarization Generation by Thomson Scattering
Wayne Hu
Courtesy of Brian Keating
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WMAP Limits
NO Detection of the B mode
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Future CMB Experiments
Measurements of the B-mode power spectrum are the focus of future CMB grounds/balloon/space based experiments
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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
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Inflationary Gravitational Wave Background and Direct Detection
• Don’t measure r– Only measure tensors
• Energy density of the gravitational wave background
• Function of wavenumber
Tensor Power Spectrum today
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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
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LISA, Space-Based Laser Interferometer
LISA
• 3 Spacecrafts, each containing a reference mass
• Laserbeams are directed at other 2 spacecraft’s 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
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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)
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Big Bang Observer
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Deci-hertz Interferometer Gravitational Wave Observatory
10-
18
10-
24
10-
22
10-
20
10-
4
104
102
100
10-
2Frequency [Hz]
Str
ain
[H
z-1
/2]
LISA Terrestrial Detectors (e.g. LCGT)
Gap
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Current Limits and Projected Sensitivities
Solid Lines are current limits
Dashed Lines are projections
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From CMB to Direct Detection
• To make comparisons between CMB and Direct Detection, need relation between r and ΩGW
• Simplest is extrapolating measured tensor power spectrum to DD scales
• Can use slow roll to calculate variables at different scales
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Extrapolation vs. Numerical Method
• Extrapolation • Numerical
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r vs. ωGW
Extrapolation From Slow roll 7
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Amplitude as a function of Frequency
10-17
10-15
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ΩGW Comparison
0.99 < ns(kCMB) < 1.01
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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 Φ(N)
• They also can be combined to help test the single-field consistency relation
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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 ΩGW
• Non-Adiabatic– Effects may differ from those of massless neutrinos
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Constraints on GWB amplitude from CMB/LSS
CMB Data Sets: WMAP, ACBAR, CBI, VSA, BOOMERanG
Galaxy Power Spectrum Data: 2dF, SDSS, and Lyman-α
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Adiabatic vs. Homogeneous
• Adding Galaxy Survey + Lyman-α increases uncertainty over using just CMB– Discrepancy between
data sets
• 95% Confidence Limit of ΩGWh2<6.9x10-6 for homogeneous initial conditions
Dotted Line: only CMB data
Solid Line: +Galaxies and Lyman-α
Dash-Dot: +Marginalize over non-zero neutrino masses
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Current and CMBPol Limits
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Structure of the Potential
• Trajectories of the Hubble constant as a function of N can be determined by measurements of CMB+DD
• Different models satisfying observational constraints on ns, αs and large r can have much different ωgw at DD scales
– How does this affect the history of H
– H is related to V
• Φ vs. N significantly different depending on rCMB
N0
(N0)
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Hubble Constant Trajectories
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
0.15 ≤ r ≤ 0.25
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Φ vs. N
r>10-2r<10-4
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V(Φ)
r=0.02 r=0.001 r<10-4
Planck CMBPol CMBPol
Foreground Sensitivity Limit
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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 αs 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
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Parameter Space Occupied by Different Types of Inflation
Solid-blue: Power LawDotted Magenta: ChaoticDot-dashed cyan: Symmetry BreakingDashed Yellow: Hybrid
Everything evaluated at CMB scales
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ΩGW-nt parameter space
Solid-blue: Power LawDotted Magenta: ChaoticDot-dashed cyan: Symmetry BreakingDashed Yellow: Hybrid
Everything evaluated at BBO/DECIGO Scales
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Consistency Relation
Consistency Relation
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Determining R
• Proposal to use both CMB and DD to constrain consistency relation
• With 10% foreground contamination, CMBPol could measure R=1.0±80.0
• Determine r from CMB scales, nt from direct detection scales
• Laser interferometer can measure nt to
• Connecting ntBBO
to ntCMB adds additional uncertainty
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Uncertainty of RUncertainty implied with ns=0.95±0.1
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Problems
• nt(CMB)≠nt(DD)
• Magnitude is different by an order of magnitude
• R is always less than unity
Friedman, Cooray, Melchiorri 2006
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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
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CMB ForegroundsSynchrotron
Dust
WMAP 23 GHz
Finkbeiner-Davis-Schlegel Dust Map
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Foreground Power Spectrum
Solid: Synchrotron, Dashed: Dust
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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
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Other Stochastic Gravitational Wave Backgrounds
nt=3
Potentially detectable by LISA and LIGO
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Conclusion
• Combining CMB and DD much about inflation can be learned
• Different things can be constrained that can’t 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
• Won’t happen for ~20 years– BBO/DECIGO aren’t anytime soon– CMBPol is still a long ways away