Constraining the Inflationary Gravitational Wave Background:

CMB and Direct DetectionNathan Miller

Keating Cosmology LabCASS Journal Club

3/13/07

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

Outline

• Introduction

• Comparison Between CMB and Direct Detection

• What can be constrained by measurements

• Foregrounds

13.7 Gyr

380 kyr

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

Inflationary Dynamics

• Inflation occurs when cosmological expansion accelerates

• Driven by a spatially homogeneous scalar field, Φ, the “inflaton”

Slow-Roll Inflation

Rewriting with Φ as “time” variable

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

Slow-Roll Hierarchy and Flow Equations

Definition of Parameters Derivatives

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

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

Results of Slow-Roll Flow Equations

Kinney 2002

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

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

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

How a blackbody becomes polarized (Thomson scattering)

100% polarized

Plane of Polarization

unpolarized

Polarization ~ cos2Θ – Quadrupole Scattering

electron

Courtesy of Brian Keating

How is the CMB polarized by GW?

Gravitational Wavevector

e-

Courtesy of Brian Keating

GW + CMB Plasma

This process leads to….Courtesy of Brian Keating

Gravitational Waves + CMB

Caldwell & Kamionkowski

Temperature and Polarization caused by single wave in +z direction.

Courtesy of Brian Keating

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

WMAP Limits

NO Detection of the B mode

Future CMB Experiments

Measurements of the B-mode power spectrum are the focus of future CMB grounds/balloon/space based experiments

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

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

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

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

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)

Big Bang Observer

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

Current Limits and Projected Sensitivities

Solid Lines are current limits

Dashed Lines are projections

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

Extrapolation vs. Numerical Method

• Extrapolation • Numerical

r vs. ωGW

Extrapolation From Slow roll 7

Amplitude as a function of Frequency

10-17

10-15

ΩGW Comparison

0.99 < ns(kCMB) < 1.01

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

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

Constraints on GWB amplitude from CMB/LSS

CMB Data Sets: WMAP, ACBAR, CBI, VSA, BOOMERanG

Galaxy Power Spectrum Data: 2dF, SDSS, and Lyman-α

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

Current and CMBPol Limits

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)

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

Φ vs. N

r>10-2r<10-4

V(Φ)

r=0.02 r=0.001 r<10-4

Planck CMBPol CMBPol

Foreground Sensitivity Limit

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

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

ΩGW-nt parameter space

Solid-blue: Power LawDotted Magenta: ChaoticDot-dashed cyan: Symmetry BreakingDashed Yellow: Hybrid

Everything evaluated at BBO/DECIGO Scales

Consistency Relation

Consistency Relation

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

Uncertainty of RUncertainty implied with ns=0.95±0.1

Problems

• nt(CMB)≠nt(DD)

• Magnitude is different by an order of magnitude

• R is always less than unity

Friedman, Cooray, Melchiorri 2006

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

CMB ForegroundsSynchrotron

Dust

WMAP 23 GHz

Finkbeiner-Davis-Schlegel Dust Map

Foreground Power Spectrum

Solid: Synchrotron, Dashed: Dust

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

Other Stochastic Gravitational Wave Backgrounds

nt=3

Potentially detectable by LISA and LIGO

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