Probing Inflation with CMB Polarization Daniel Baumann High Energy - PowerPoint PPT Presentation

Probing Inflation with CMB Polarization Daniel Baumann High Energy Theory Group Harvard University Chicago, July 2009

“How likely is it that B-modes exist at the r=0.01 level?” the organizers Daniel Baumann High Energy Theory Group Harvard University Chicago, July 2009

“I don’t know!” Daniel Baumann High Energy Theory Group Harvard University Chicago, July 2009

“What can we learn from a B-mode detection at the r=0.01 level?” Daniel Baumann High Energy Theory Group Harvard University Chicago, July 2009

Based on CMBPol Mission Concept Study: Probing Inflation with CMB Polarization Daniel Baumann, Mark G. Jackson, Peter Adshead, Alexandre Amblard, Amjad Ashoorioon, Nicola Bartolo, Rachel Bean, Maria Beltran, Francesco de Bernardis, Simeon Bird, Xingang Chen, Daniel J. H. Chung, Loris Colombo, Asantha Cooray, Paolo Creminelli, Scott Dodelson, Joanna Dunkley, Cora Dvorkin, Richard Easther, Fabio Finelli, Raphael Flauger, Mark P. Hertzberg, Katherine Jones-Smith, Shamit Kachru, Kenji Kadota, Justin Khoury, William H. Kinney, Eiichiro Komatsu, Lawrence M. Krauss, Julien Lesgourgues, Andrew Liddle, Michele Liguori, Eugene Lim, Andrei Linde, Sabino Matarrese, Harsh Mathur, Liam McAllister, Alessandro Melchiorri, Alberto Nicolis, Luca Pagano, Hiranya V. Peiris, Marco Peloso, Levon Pogosian, Elena Pierpaoli, Antonio Riotto, Uros Seljak, Leonardo Senatore, Sarah Shandera, Eva Silverstein, Tristan Smith, Pascal Vaudrevange, Licia Verde, Ben Wandelt, David Wands, Scott Watson, Mark Wyman, Amit Yadav, Wessel Valkenburg, and Matias Zaldarriaga White Paper of the Inflation Working Group arXiv: 0811.3919

Outline PART 1: THE PRESENT 1. Classical Dynamics of Inflation 2. Quantum Fluctuations from Inflation 3. Current Observational Evidence PART 2: THE FUTURE 1. B-modes 2. Non-Gaussianity

Part 1: THE PRESENT

Inflation The Quantum Origin of Structure in the Early Universe

Inflation Guth (1980) A period of accelerated expansion a > 0 ¨ ds 2 = dt 2 − a ( t ) 2 d x 2 sourced by a nearly constant energy density � ρ ¨ a a = ( H 2 + ˙ H ) > 0 H = 3 ≈ const . ⇔ and negative pressure ¨ w < − 1 a a = − ρ 6(1 + 3 w ) > 0 ⇔ 3

Inflation Guth (1980) � = 0 A period of accelerated expansion solves the horizon and flatness problems H − 1 horizon i.e. explains why the universe is so large and old! creates a nearly scale-invariant spectrum of primordial fluctuations ‣ stretches microscopic scales to � � = 0 superhorizon sizes ‣ correlates spatial regions over apparently acausal distances time

The Shrinking Hubble Sphere The comoving “horizon” shrinks during inflation and grows after inflation comoving scales ( aH ) − 1 1 ( aH ) − 1 ∝ a 2 (1+3 w ) w < − 1 w > − 1 3 3 today time reheating inflation hot big bang

“Goodbye and Hello-again” large-scale correlations can be set up causally ! comoving scales ( aH ) − 1 horizon exit horizon re-entry super-horizon k − 1 sub-horizon sub-horizon today time reheating inflation hot big bang

Conditions for Inflation negative pressure accelerated expansion d ( aH ) − 1 w < − 1 < 0 a > 0 ¨ ⇔ ⇔ 3 dt shrinking comoving horizon at the heart of the solution of the horizon and flatness problems and crucial for the generation of perturbations

What is the Physics of the Inflationary Expansion?

We don’t know! This is why we are here!

Classical Dynamics Parameterize the decay of the inflationary energy by a scalar field Lagrangian � 2 M 2 � V ′ pl L = 1 ǫ ≡ V 2 2( ∂φ ) 2 − V ( φ ) V ′′ η ≡ M 2 pl V A flat potential drives acceleration slow-roll conditions inflation ǫ , | η | < 1 Linde (1982) Albrecht and Steinhardt (1982) “clock” end of inflation

Quantum Dynamics Quantum fluctuations lead to a local time delay in the end of inflation and density fluctuations after reheating δρ reheating

Zeta in the Sky inflaton fluctuations δφ curvature perturbations ζ on uniform density hypersurfaces reheating density perturbations δρ CMB anisotropies ∆ T

Zeta in the Sky curvature perturbations on uniform density hypersurfaces ds 2 = dt 2 − a 2 ( t ) e 2 ζ ( t, x ) d x 2 • gauge-invariant • freeze on super-horizon scales!

Zeta in the Sky curvature perturbation on uniform density hypersurfaces ds 2 = dt 2 − a 2 ( t ) e 2 ζ ( t, x ) d x 2 two-point correlation function � ζ ( x ) ζ ( x ′ ) � evaluated at horizon crossing power spectrum � ζ k ζ k ′ � = (2 π ) 3 δ ( k + k ′ ) P ζ ( k )

The Inverse Problem comoving scales ( aH ) − 1 k − 1 today time reheating inflation hot big bang DB: TASI Lectures on Inflation (2009)

The Inverse Problem comoving scales ( aH ) − 1 sub-horizon k − 1 ˆ ζ k zero-point fluctuations today time reheating inflation hot big bang DB: TASI Lectures on Inflation (2009)

The Inverse Problem comoving scales ( aH ) − 1 � ζ k ζ k � � sub-horizon k − 1 ˆ ζ k zero-point fluctuations horizon exit today time reheating inflation hot big bang DB: TASI Lectures on Inflation (2009)

The Inverse Problem comoving scales ( aH ) − 1 ˙ ζ ≈ 0 � ζ k ζ k � � super-horzion sub-horizon k − 1 ˆ ζ k zero-point fluctuations horizon exit today time reheating inflation hot big bang DB: TASI Lectures on Inflation (2009)

observed The Inverse Problem comoving scales predicted by inflation ( aH ) − 1 horizon re-entry ˙ ζ ≈ 0 � ζ k ζ k � � C � ∆ T super-horzion sub-horizon projection k − 1 ˆ ζ k transfer function zero-point fluctuations CMB horizon exit recombination today time reheating inflation hot big bang DB: TASI Lectures on Inflation (2009)

observed The Inverse Problem comoving scales predicted by inflation ( aH ) − 1 horizon re-entry ˙ ζ ≈ 0 � ζ k ζ k � � C � ∆ T super-horzion sub-horizon projection k − 1 ˆ ζ k transfer function zero-point fluctuations CMB horizon exit recombination today time reheating inflation hot big bang DB: TASI Lectures on Inflation (2009)

Prediction from Inflation Scalar Fluctuations � H � 2 � H � 2 s ≡ k 3 ∆ 2 2 π 2 P ζ ( k ) = ˙ 2 π φ δφ → ζ δφ conversion de Sitter fluctuations evaluated at horizon crossing k = aH

Prediction from Inflation Scalar Fluctuations � H � 2 � H � 2 s ≡ k 3 ∆ 2 2 π 2 P ζ ( k ) = ˙ 2 π φ how the power is distributed over the scales is determined by the expansion history during inflation H ( t ) scale-dependence e.g. slow-roll inflation ∆ 2 s = A s k n s − 1 n s − 1 = 2 η − 6 ǫ

Prediction from Inflation Scalar Fluctuations � H � 2 � H � 2 s ≡ k 3 ∆ 2 2 π 2 P ζ ( k ) = ˙ 2 π φ Different shapes for the inflationary potential reheating 2 π f 0 lead to slightly different predictions!

Observations

Observational Evidence Flatness Inflation predicts WMAP sees 1 Ω k = 0 ( ± 10 − 5 ) − 0 . 0181 < Ω k < 0 . 0071 1 WMAP 5yrs.+BAO: 95% C.L.

Observational Evidence Scalar Fluctuations Inflation predicts WMAP sees n s = 0 . 963 +0 . 014 percent-level deviations − 0 . 015 from n s = 1 away from n s = 1 2 . 5 σ

Observational Evidence Scalar Fluctuations Inflation predicts WMAP sees Gaussian and Adiabatic Gaussian and Adiabatic Fluctuations Fluctuations

Observational Evidence Scalar Fluctuations Inflation predicts WMAP sees Correlations of Correlations of Superhorizon Superhorizon Fluctuations Fluctuations at Recombination temperature-polarization cross-correlation / 2 π [ µK 2 ] ( ℓ + 1) C T E ℓ θ > 1 ◦ Multipole moment

Fingerprints of the Early Universe We have only just begun to probe the fluctuations created by inflation: Scalar Fluctuations detected density fluctuations • hints of scale-dependence • superhorizon nature confirmed • first constraints on Gaussianity and Adiabaticity Tensor Fluctuations not yet detected gravitational waves The next decade of experiments will be tremendously exciting!

Part 2: THE FUTURE

How can we probe the Physical Origin of Inflation?

How do we constrain the Inflationary Action? “like in all of physics we ultimately want to know the action” ( ∂φ ) 2 , ( ∂ψ ) 2 , � φ , . . . � � L = f − V ( φ , ψ ) • field content • potential, kinetic terms • interactions • symmetries • couplings to gravity • etc.

How do we constrain the Inflationary Action? “like in all of physics we ultimately want to know the action” • minimal models: single-field slow-roll L = 1 2( ∂φ ) 2 − V ( φ ) shape Gaussian fluctuations A s Scalars V ′ , V ′′ , V ′′′ n s V V V all information in α s power spectra scale! Tensors A t V

How do we constrain the Inflationary Action? “like in all of physics we ultimately want to know the action” • minimal models: single-field slow-roll • non-minimal models: - non-minimal coupling to gravity - multiple fields - higher-derivative interactions fluctuations can be non-Gaussian and non-adiabatic information beyond the bispectrum, trispectum, etc. power spectra