Phenomenological Classification of Inflationary Potentials Katie Mack (Princeton University) with George Efstathiou (Cambridge University) Efstathiou & Mack, JCAP 05, 008 (2005) astro-ph/

The Lyth Bound Revisited Katie Mack (Princeton University) with George Efstathiou (Cambridge University) Efstathiou & Mack, JCAP 05, 008 (2005) astro-ph/

Outline Current status of inflation What the observations can tell us Linking observations to fundamental theory (Lyth Bound) Phenomenological approach Implications for future theoretical work

The inflationary paradigm today Inflation is successful  offers solution to horizon problem flatness problem  general predictions have been upheld flat universe gaussian and adiabatic metric fluctuations nearly scale-independent spectrum …but which inflation theory are we talking about?

The inflationary paradigm today Inflation is successful  offers solution to horizon problem flatness problem  general predictions have been upheld flat universe gaussian and adiabatic metric fluctuations nearly scale-independent spectrum …but which inflation theory are we talking about?

Tensor modesTensor modes –produced by gravitational waves –no contribution from density perturbations Detection would… –confirm prediction of primordial gravitational waves in inflation –give the energy scale of inflation the good news

“…we cannot yet distinguish between broad classes of inflationary theories that have different physical motivations.” –Peiris et al. (2003) WMAP aloneWMAP+2dF+Lyα the bad news

Seljak et al., 2004 (astro-ph/ )

B-Mode Polarization

Current upper limits r = 0.36

Beyond WMAP Currently proposed experiments (ground and balloon-borne) can reach r=0.01 at ~3σ level Space-based, with improved foreground knowledge, could get to r~10 -3 at ~3σ (Verde, Peiris & Jimenez, astro-ph/ )

You may ask…What about gravitational wave detectors? Of the planned experiments, only Big Bang Observer (next generation after LISA) has any chance of detecting primordial GWs

Linking observation to physics Future experiments may detect primordial gravitational waves, but what would this tell us about inflation itself? Goal: Find a way to link the observables to the fundamental physics without assuming a particular model

Phenomenological Approach Produce a set of inflationary models to be as general as possible Require only: –single field –inflation sustained long enough to solve horizon problem (~ 55 e-foldings) Calculate r and Δ φ, compare with Lyth Bound

The Lyth Bound David Lyth (1996) suggests rough relation: for ΔN ~ 4 (CMB multipoles ~2 to ~100) Considering the full course of inflation, with at least e-folds, Δφ could exceed this by an order of magnitude If slow-roll parameter is monotonically increasing, a stronger condition is required:

The Lyth Bound General expectation: large r => large Δφ High values of r require changes in the field value of order m Pl

Monte Carlo Reconstruction Results (10 6 models)

But in the real world… Can improve the scatter by comparing with observables From Seljak et al. 2004, astro-ph/ < n s < < n run < 0.03

Remaining models Now have tighter empirical relationship between r and Δφ Δφ/m Pl ~ 6 r 1/4 (for r > ~ )

What have we learned? To obtain a large value of r, you need a large variation in the scalar field For r ~ 10 -3, need Δφ of order unity If any conceivable CMB polarization experiment is to detect tensor modes, Δφ must be large

Implications for inflation Large field variations cannot be described by low-energy effective field theory, where the potential is written as: with. This is invalid for. Does that mean we need new physics? Not necessarily… quantum gravity corrections may still be small as long as V < m pl 4 But we will need a new way to talk about such models.

The bottom line Future CMB polarization experiments can only probe high field inflation models (e.g., chaotic inflation) Understanding the physics of such models is important if such experiments are to tell us anything useful about the mechanism behind inflation

Single-field inflation Scalar field φ rolling down potential V(φ) Slow rolling of inflaton field causes inflation Some commonly considered models:  V ~ φ 2  V ~ φ 4

Mechanics of inflation Change in Hubble Parameter depends on change in scalar field (“speed of roll”) In slow-roll inflation, take H ~ constant, slow roll of inflaton

Expand Hubble Parameter in power series Use slow-roll parameters to represent this expansion

acceleration

E mode and B mode polarization E modes (no curl)B modes (no divergence)

WMAP vs. Planck

Planck projected B-mode measurement

Other experiments Clover QUIET None of these experiments likely to probe below r ~10 -2

Cooray, astro- ph/ r = 0.13 r = 5 * r = Limits on future gravitational wave experiments