Review of Small Field Models of Inflation

Transcription

1 Review of Small Field Models of Inflation Ram Brustein אוניברסיטת ב ן -גוריון I. Ben-Dayan in progress I. Ben-Dayan, S. de Alwis Small field models of inflation - Designing small field SUGRA models - Relevance to string theory Predictions for the CMB: Simplest models: n S <1, r 0.01 <<1, α 0.05 <<1 New class: n S, r 0.01, α 0.05 spans allowed values

2 Models of inflation: Background de Sitter phase ρ + p << ρ Η const. Parametrize the deviation from constant H by the value of the field Or by the number of e-folds ε ( ϕ) 2 mp V = 2 V 2 η( ϕ) = mp 2 ξ ( ϕ) = mp 2 4 V V V V V 2 tei tei ei H 1 1 N( ϕ ϕ ϕ ) = d log a( t) = Hdt d d t = t ϕ = ϕ ϕ ϕ 2 m ei ε ( ϕ) ϕ Inflation ends when ε = 1 p

3 Models of inflation:perturbations Spectrum of scalar perturbations P R 2 H 1 ( k) = π m p ε k = ah 2 Spectrum of tensor perturbations 2 H PT ( k) = π m p k = ah 2 Spectral indices Tensor to scalar ratio (many definitions) r is determined by P T /P R α - RUN ( current canonical r =16 ε) CMB observables determined by quantities ~ 60 efolds before the end of inflation

4 φ > m P Large field φ p ε > η > ε Hybrid 1+ φ p 0 < ε <η φ < m P Kinney et al 97 Related to reconstruction φ < m P Small field 1-φ p η < 0, η >ε

5 WMAP5 No evidence for running φ > m P Large field ε > η > ε Hybrid 0 < ε <η φ < m P WMAP n s =.973, σ=.014 r <.24 φ < m P Small field η < 0, η >ε

6 (My) preferred models of modular inflation: small field models Topological inflation : inflation off a flat feature Guendelman 91, Vilenkin 94, Linde 94 2 hep-th/ hep-th/ S. de Alwis, E. Novak φ/m p -1 Enough inflation V /V<1/50 δ wall thickness in space ( /δ) 2 Λ 4 Inflation δ H > 1 > m p H 2 ~1/3 Λ 4 /m 2 p

7 (My) preferred models of modular inflation: small field models hep-th/ S. de Alwis, P. Martens Another version of inflation off a flat feature 2 Recently, Itzhaki φ/m p -1 Enough inflation V /V<1/50

8 Designing flat features for single field modular SUGRA inflation I. Ben-Dayan, S. de Alwis At an extremum with V T 0 > 0

9 A single field with a logarithmic K = Aln ( T + T ) Kaehler potential Cannot design a flat feature! Also: Gomez-Reino and Scrucca, Badziak, Olechowski Covi et al

10 Take the simplest Kahler potential and superpotential in the vicinity of an extremum φ = T T 0 Always a good approximation when expanding in a small region (φ < 1) For the purpose of finding local properties V can be treated as a polynomial

11 Designing flat features for single field SUGRA modular inflation Not a local equation A local equation T a complex scalar field

12 A numerical example: The potential is not sensitive to small changes in coefficients Including adding small higher order terms, inflation is indeed 1/100 of tuning away Need 5 parameters: V (0)=0,V(0)=1,V /V=η D T W(-y), D T W(+y) = b 2 =0, b 4 =0, b 1 =1,b 3 =η/6, b 5 y 4 (y 2 +5) + y 2 +1=0 η =6 b 1 b 3 2(b 0 ) 2 If one wishes to tune the min to be small enough replace D_T W=0 by V_T=0, V=0 (one more condition)

13 Relevance to string theory Small field models, High scale of inflation, central region of moduli space g s < 1, V compact > 1 Relatively small separation of scales m p > M s > Λ Inflation ~ ~ Some hope for stringy physics in anisotropies! ~ ~

14 Small field models, standard lore: No Observable GW tei tei ei H 1 1 N( ϕ ϕ ϕ ) = d log a( t) = Hdt d d t = t ϕ = ϕ ϕ ϕ 2 m ei ε ( ϕ) ϕ r =16 ε If ε ~ const. p Lyth theorem φ 1 r 0.01 > 1 (depending on choice of N CMB ) In practice need φ 10 r 0.01 = (r/0.01) dream sensitivity

15 Small field models, standard lore: Easther+Peiris, : No Observable RUN Simple example: Thus, a definitive observation of a large negative running would imply that any inflationary phase requires multiple fields or the breakdown of slow roll. Alternatively, if single field, slow roll inflation is sources the primordial fluctuations, we can expect the observed running to move much closer to zero as the CMB is measured more accurately at small angular scales. Dodelson, Kolb+Kinney, : I. Ben-Dayan, S. de Alwis This possibility of a blue scalar spectrum (here, blue implies n > 1) is the distinctive feature of hybrid models.

16 Simple example: Hybrid 0 < ε <η ε α CMB η η 2 CMB 2 CMB

17 The minimal model: Quadratic maximum End of inflation determined by higher order terms Results: Suppression of GW φ END =1 Suppression of running

18 Observational consequences Observation of GW signal in the CMB small field models? Observation of RUN in the CMB small field models? single field models?

19 CMB measured parameters relevant to inflation physics Amplitude of temperature fluctuations TT Polarization EE, EB, BB Non-Gaussianity 5 parameters relevant to inflation physics: A s n s r run f NL

20 RUN observations* * A *hard* measurement CBI Wmap5,+CBI,+All Planck wmap3 WMAP n s = 1.076, σ=.065 r <.49, α =.049, σ=.029 wmap5 ACT/SPT+WMAP QUaD

21 New class of small field models 1 V 1 ε + A( φ φmin ) 1 + φ + B( φ φ ) N V N 2 3 min 0

22 New class of small field models 1 V 1 ε + A( φ φmin ) 1 + φ + B( φ φ ) N V N 2 3 min 0 2 initial conditions, 5 equations, 1 non-linear :N = 60 1 non-linear constraint φ END <1

23 New class of models: Predictions

24 New class of models: Predictions

25 New class of models: Predictions

26 New class of small field models: EFT considerations (E/Λ) +ve min( ε, η ) Λ Λ = min( ε, η ) H < E < Λ m λ i i=1,2,3, special. For example (E/Λ) ve, λ 3 <<1 p Small scale-separation

27 λ i i=1,2,3, special. For example Assume λ 3 << 1 to allow the energy range E > H η 1/ r < 1, α > GeV > Λ > 1 10 GeV

28 Non-Gaussianity The running does not scale as 1/(N CMB ) 2 Integrating over the trajectory: HOWEVER: Maldacena 03 single field boundary term (verified explicitly) Need additional fields? (as in SUGRA)

29 Conclusions for models of inflation Small field models of inflation are interesting (in my opinion most relevant to string/sugra) Predictions for the CMB: Simplest models: n S <1, r 0.01 <<1, α 0.05 <<1 New class: n S, r 0.01, α 0.05 spans all allowed values RUN has a strong discriminating power among cosmological models, linked with high r in our models

30 Conclusions for inflation physics Simple Reconstruction = finding the inflaton potential from cosmological observables, is practically impossible Identifying The Inflaton is extremely hard High scale inflation, inflaton an arbitrary direction n field space, moving over a limited range Only window to inflaton dynamics through cosmological observables