Phenomenological Classification of Inflationary Potentials

1. Phenomenological Classification of Inflationary Potentials Katie Mack (Princeton University) with George Efstathiou (Cambridge University) Efstathiou & Mack, JCAP 05, 008 (2005) astro-ph/0503360

2. The Lyth Bound Revisited Katie Mack (Princeton University) with George Efstathiou (Cambridge University) Efstathiou & Mack, JCAP 05, 008 (2005) astro-ph/0503360

3. 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

4. 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?

5. 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?

7. WMAP to the rescue!

9. the good news • Tensor 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

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

11. Seljak et al., 2004 (astro-ph/0407372)

12. B-Mode Polarization

13. Current upper limits r = 0.36

14. 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/0506036)

15. 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

16. 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

17. 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 Δφ, compare with Lyth Bound

18. 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 50-60 e-folds, Δφ could exceed this by an order of magnitude If slow-roll parameter is monotonically increasing, a stronger condition is required:

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

20. Monte Carlo Reconstruction Results (106 models)

22. But in the real world… • Can improve the scatter by comparing with observables • From Seljak et al. 2004, astro-ph/0407372 0.92 < ns < 1.06 -0.04 < nrun < 0.03

23. Remaining models • Now have tighter empirical relationship between r and Δφ Δφ/mPl ~ 6 r1/4 (for r > ~ 10-3)

24. 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

25. 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 < mpl4 But we will need a new way to talk about such models.

26. 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

39. Single-field inflation • Scalar field φrolling down potential V(φ) • Slow rolling of inflaton field causes inflation • Some commonly considered models: • V ~ φ2 • V ~ φ4

40. 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

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

42. acceleration

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

44. WMAP vs. Planck

46. Planck projected B-mode measurement

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

48. Cooray, astro-ph/0503118 Limits on future gravitational wave experiments r = 0.13 r = 5 * 10-4 r = 10-5