Naturalness in Inflation

1. Naturalness in Inflation Katherine Freese Michigan Center for Theoretical Physics University of Michigan Ann Arbor, MI

2. Outline • Brief review of inflation • Naturalness in rolling models: • flat potential required, i.e., two disparate mass scales, natural inflation uses shift symmetries, new twists in new contexts • New paradigm for tunneling models: Chain Inflation Nice features: no fine-tuning, single mass scale for potential can be 10 MeV-GUT scale, graceful exit is successful

3. Old Inflation(Guth 1981) Enough inflation requires the scale factor to grow at least 60 e-foldings.

4. Inflation Resolves Cosmological Problems • Horizon Problem (homogeneity and isotropy): small causally connected region inflates to large region containing our universe • Flatness Problem • Monopole Problem: tightest bounds on GUT monopoles from neutron stars (Freese, Schramm, and Turner 1983); monopoles inflated away (outside our horizon) • BONUS: Density Perturbations that give rise to large scale structure are generated by inflation

5. Shortcomings of Inflationary Models • Tunneling Fields Inflation Fails: no graceful exit except through a time-dependent nucleation rate (double-field) . F. Adams and K. Freese 1991; A. Linde 1991 • Rolling Field Inflation: Linde 1981; Albrecht and Steinhardt 1981 Fine-Tuned Except natural inflation (shift symmetry) . Freese, Frieman, and Olinto 1991

6. What’s new in inflation? • Observational Tests: spectral index, tensor modes • New physical setup: extra dimensions, braneworlds • New solutions to old problems, new ideas naturalness in rolling models graceful exit in tunneling models new paradigm: chain inflation

7. I. Fine Tuning in Rolling Models • The potential must be very flat: (Adams, Freese, and Guth 1990) But particle physics typically gives this ratio = 1!

8. Need small ratio of mass scales • Two attitudes: 1) We know there is a heirarchy problem, wait until it’s explained 2) Two ways to get small masses in particles physics: (i) supersymmetry (ii) Goldstone bosons (shift symmetries)

9. Natural Inflation: Shift Symmetries • Shift (axionic) symmetries protect flatness of inflaton potential (inflaton is Goldstone boson) • Additional explicit breaking allows field to roll. • This mechanism, known as natural inflation, was first proposed in Freese, Frieman, and Olinto 1990;Adams, Bond, Freese, Frieman and Olinto 1993

10. e.g., mimic the physics of the axion (Weinberg; Wilczek)

11. Natural Inflation(Freese, Frieman, and Olinto 1990; Adams, Bond, Freese, Frieman and Olinto 1993) • Two different mass scales: • Width f is the scale of SSB of some global symmetry • Height is the scale at which some gauge group becomes strong

12. Two Mass Scales Provide required heirarchy • For QCD axion, • For inflation, need Enough inflation requires width = f ≈ mpl, Amplitude of density fluctuations requires height =

13. Density Fluctuations and Tensor Modes can determine which model is right Density Fluctuations and Tensor Modes • Density Fluctuations: WMAP data: Slight indication of running of spectral index • Tensor Modes gravitational wave modes, detectable in upcoming experiments

14. Density Fluctuations in Natural Inflation • Power Spectrum: • WMAP data: implies (Freese and Kinney 2004)

15. Tensor Modes in Natural Inflation(original model)(Freese and Kinney 2004) Two predictions, testable in next decade: 1) Tensor modes, while smaller than in other models, must be found. 2) There is very little running of n in natural inflation. n.b. not much running of n Sensitivity of PLANCK: error bars +/- 0.05 on r and 0.01 on n. Next generation expts (3 times more sensitive) must see it.

16. Implementations of natural inflation’s shift symmetry • Natural chaotic inflation in SUGRA using shift symmetry in Kahler potential (Gaillard, Murayama, Olive 1995; Kawasaki, Yamaguchi, Yanagida 2000) • In context of extra dimensions: Wilson line with (Arkani-Hamed et al 2003) but Banks et al (2003) showed it fails in string theory. • “Little” field models (Kaplan and Weiner 2004) • In brane Inflation ideas (Firouzjahi and Tye 2004) • Gaugino condensation in SU(N) SU(M): Adams, Bond, Freese, Frieman, Olinto 1993; Blanco-Pillado et al 2004 (Racetrack inflation)

17. Legitimacy of large axion scale? Natural Inflation needs Is such a high value compatible with an effective field theory description? Do quantum gravity effects break the global axion symmetry? Kinney and Mahantappa 1995: symmetries suppress the mass term and is OK. Arkani-Hamed et al (2003):axion direction from Wilson line of U(1) field along compactified extra dimension provides However, Banks et al (2003) showed it does not work in string theory.

18. A large effective axion scale(Kim, Nilles, Peloso 2004) • Two or more axions with low PQ scale can provide large • Two axions • Mass eigenstates are linear combinations of • Effective axion scale can be large,

19. Natural Inflation (again): Shift Symmetries • Inflationary Potentials in rolling models must be flat I.e. have two disparate mass scales • Shift (axionic) symmetries protect flatness of inflaton potential (inflaton is Goldstone boson) • Original model of natural inflation is testable in CMB in next decade • New implementation in extra dimensions and with multiple fields allows f≈mpl

20. II) New Framework for Inflation: Chain Inflation • No fine-tuning even with only one mass scale in the potential • Large Range of Energy Scales for Potential: • Saves Old Inflation Graceful Exit: each stage of phase transition occurs very quickly • E.g. can inflate with QCD axion or in stringy landscape Freese and Spolyar hep-ph/0412145; Freese, Liu, and Spolyar hep-ph/0502177

21. Inflation Requires Two Basic Ingredients • 1. Sufficient e-foldings of inflation • 2. The universe must thermalize and reheat • Old inflation, wih a single tunneling event, failed to do both. • Here, MULTIPLE TUNNELING events, each responsible for a fraction of an e-fold (adds to enough). Graceful exit is obtained: phase transition completes at each tunneling event.

22. Basic Scenario: Inflation with the QCD axion or in the Stringy Landscape V (a) = V0[1− cos (Na /v)] − η cos(a/v +γ) Chain Inflate: Tunnel from higher to lower minimum in stages, with a fraction of an efold at each stage Freese, Liu, and Spolyar (2005)

23. Chain Inflation: Basic Setup • The universe transitions from an initially high vacuum down towards zero, through a series of tunneling events. • The picture to consider: tilted cosine • Solves old inflation problem: Graceful Exit requires that the number of e-folds per stage < 1/3 • Sufficient Inflation requires a total number of e-folds > 60, hence there are many tunneling events

24. Topics • Why Old Inflation Fails • What’s Needed: Time Dependent • This model: Multiple tunneling events each with less than one e-fold provide graceful exit

25. Old Inflation(Guth 1981) Universe goes from false vacuum to true vacuum. Bubbles of true vacuum nucleate in a sea of false vacuum (first order phase transition).

26. Swiss Cheese Problem of Old Inflation: no graceful exit PROBLEM: Bubbles never percolate and thermalize: REHEATING FAILS; we don’t live in a vacuum Bubbles of true vacuum nucleate in a sea of false vacuum.

27. What is needed for tunneling inflation to work? • Probability of a point remaining in false vacuum phase: • is the nucleation rate of T bubbles and H is the expansion rate of the universe • Theories with constant fail (e.g. old inflation) • Small : slow phase transition, inflation but no reheating • Large : fast phase transition, not enough inflation, yes there is reheating • Need time-dependent ,first small then large

28. Graceful Exit Achieved

30. For large

31. Two Requirements for Inflation • Lifetime of field in metastable state: • Number of e-folds from single tunneling event: • Sufficient Inflation: • Reheating:

32. How to achieve both criteria: • Sufficient inflation: • Reheating: • With single tunneling event: • “Double Field Inflation” (Adams + Freese 91; Linde 91) : time-dependent nucleation rate, couple two scalar fields • With multiple tunneling events: CHAIN INFLATION get a fraction of an e-fold at each stage, adds to more than 60 in the end

33. Double Field Inflation (Adams and Freese 1991) • Time dependent nucleation rate • Couple 2 scalar fields • Once the roller reaches its min, • grows, tunneling rate increases. The tunneling rate is zero for at top of potential, large as approaches min (then, nucleation)

34. Required time dependence Need small initially to inflate. Then, suddenly, gets larger so that all of universe goes from false to true vacuum at once. All bubbles of same size, get percolation and thermalization. No Swiss Cheese!

35. Asymmetric Well • is energy d difference between vacua Nucleation rate of true vacuum: (thin wall) (Callan and Coleman; Voloshin, Okun, and Obzarev))

36. Sensitivity of nucleation rate to parameters in the potential • Sufficient inflation: number of e-folds= • Followed by rapid nucleation: • Both achieved by small change in e.g. consider TeV, 100 fields: N=1000 for N=0.01 for To go from enough inflation to percolation, need this ratio to change by less that 2%

38. How to achieve both criteria: • Sufficient inflation: • Reheating: • With single tunneling event: • “Double Field Inflation” (Adams + Freese 91; Linde 91) : time-dependent nucleation rate, couple two scalar fields • With multiple tunneling events: CHAIN INFLATION get a fraction of an e-fold at each stage, adds to more than 60 in the end

39. Inflating with the QCD axion

42. Invisible Axion (DFSZ) • Axion is identified as phase of a complex SU(2) U(1) singlet scalar s below PQ symmetry breaking scale s=v/√2 • Soft breaking: Phase shift

50. REHEATING: radiation is produced in last few stages PROBLEM: Get stuck in last minimum before the bottom (tunneling becomes too slow), How stop inflating?