Constraining the Inflationary Gravitational Wave Background: CMB and Direct Detection Nathan Miller Keating Cosmology Lab CASS 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 ParametersDerivatives

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 2 nd 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 (1 o ) 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 ~ cos 2 Θ – Quadrupole Scattering electron Courtesy of Brian Keating

How is the CMB polarized by GW? Gravitational Wavevector e-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-modeB-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 –~ 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 90 o 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 ( times more sensitive)

Big Bang Observer

Deci-hertz Interferometer Gravitational Wave Observatory Frequency [Hz] Strain [Hz - 1/2 ] LISA Terrestrial Detectors (e.g. LCGT) Ga p

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 Ω GW Simplest is extrapolating measured tensor power spectrum to DD scales Can use slow roll to calculate variables at different scales

Extrapolation vs. Numerical Method ExtrapolationNumerical

r vs. ω GW ExtrapolationFrom Slow roll 7

Amplitude as a function of Frequency

Ω GW Comparison 0.99 < n s (k CMB ) < 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 Ω GW 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 Ω GW h 2 <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 n s, α s and large r can have much different ω gw at DD scales –How does this affect the history of H –H is related to V Φ vs. N significantly different depending on r CMB N0N0 (N 0 )

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 -2 r<10 -4

V(Φ) r=0.02r=0.001r<10 -4 Planck CMBPol Foreground Sensitivity Limit

Types of Inflation Each type of inflation can predict observables in allowed range Measurements of P s and n s at CMB/LSS scales along with upper limits to r and α s 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 Law Dotted Magenta: Chaotic Dot-dashed cyan: Symmetry Breaking Dashed Yellow: Hybrid Everything evaluated at CMB scales

Ω GW -n t parameter space Solid-blue: Power Law Dotted Magenta: Chaotic Dot-dashed cyan: Symmetry Breaking Dashed Yellow: Hybrid Everything evaluated at BBO/DECIGO Scales

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, n t from direct detection scales Laser interferometer can measure n t to Connecting n t BBO to n t CMB adds additional uncertainty

Uncertainty of R Uncertainty implied with n s =0.95±0.1

Problems n t (CMB)≠n t (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 Foregrounds Synchrotron 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 n t =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