Motivation Natural Inflation And Supersymmetry Embedding In String Theory Conclusions Natural Inflation And Low Scale Supersymmetry Rolf Kappl Bethe Center for Theoretical Physics & Physikalisches Institut der Universität Bonn based on RK, Hans Peter Nilles and Martin Wolfgang Winkler arXiv:1503.01777, Phys.Lett. B746 (2015) 15-21 DESY THEORY WORKSHOP 2015 Hamburg, October 1st 2015 Motivation Natural Inflation And Supersymmetry Embedding In String Theory Conclusions Outline Motivation Natural Inflation And Supersymmetry Embedding In String Theory Conclusions Motivation Natural Inflation And Supersymmetry Embedding In String Theory Conclusions Motivation • Inflation is a very successful paradigm for the history of the early universe • Scalar field ' drives the expansion of the universe • Very flat potential V (') is required • Connection to particle physics and string theory is challenging How can we find a natural and working model for inflation? Motivation Natural Inflation And Supersymmetry Embedding In String Theory Conclusions Connection To LHC And String Theory • Assumption 1: LHC will find low scale supersymmetry ) m3=2 ≈ O(1 ::: 100)TeV • Such a low Gravitino mass results in a small superpotential −10 in the minimum ) hW i = W0 ≈ 10 • Assumption 2: A large scalar-to-tensor ratio r = O(0:01) will be discovered • This results in a large Hubble scale during inflation ) H ≈ 10−4 • A large Hubble scale would favor a model like natural or chaotic inflation How can we find a string-inspired model with small W0 and large H? Motivation Natural Inflation And Supersymmetry Embedding In String Theory Conclusions Natural Inflation For Large r And Large H • Natural inflation [Freese, Frieman, Olinto, 1990] is inflation with one axion • Axion has a continous shift symmetry • Non-perturbative effects break the shift symmetry to a discrete symmetry • Small breaking induces a flat potential sufficient for inflation • Flatness is controlled by the symmetry breaking Axion is a natural inflaton candidate with potential ' V (') = Λ4 1 − cos f Motivation Natural Inflation And Supersymmetry Embedding In String Theory Conclusions Inflation And High Scale Supersymmetry Breaking • −aρ 1 2 Simple model with W = W0 + Ae and K = 4 (ρ +ρ ¯) • The non-perturbative term in W breaks the shift symmetry and Im(ρ) can be used as inflaton • Without large W0 this model results not in the correct scalar potential for natural inflation −aρ • If W0 Ae we can integrate out the stabilized saxion Re(ρ) and get the correct potential after an uplift with 2 Vup ∼ O(W0 ) • The large constant W0 needed for the uplift results in high scale supersymmetry breaking If the LHC will find supersymmetry this class of models is ruled out! Motivation Natural Inflation And Supersymmetry Embedding In String Theory Conclusions Natural Inflation And Preserved Supersymmetry • 2 −aρ 1 2 2 W = m X(e − λ) and K = 4 (ρ +ρ ¯) + k(jXj ) • The scalar potential is (ρ = ρ0 + χ + i') 2 V = 2m4e(ρ0+χ) −a(2ρ0+χ) (cosh(aχ) − cos(a')) • Im(ρ) = ' is again the inflaton and there is a log(λ) supersymmetric minimum for X0 = 0 and ρ0 = − a • In the minimum mχ = m' due to supersymmetry, but the saxion is trapped through the exponential eK in V . • This potential realizes natural inflation (large r and H) with unbroken supersymmetry at the end of inflation If the LHC will find supersymmetry and r is large this class of models is very good Motivation Natural Inflation And Supersymmetry Embedding In String Theory Conclusions Problems Within String Theory • N = 60 e-folds require trans-Planckian field ranges ∆' > MPlanck • This implies also a trans-Planckian axion decay constant f > MPlanck • This is problematic for an effective field theory description as well as for a string theory embedding Motivation Natural Inflation And Supersymmetry Embedding In String Theory Conclusions Moduli Stabilization Problems Within String Theory • Kähler potential in string theory more likely K = − log(ρ +ρ ¯) • Saxion stabilization is much more difficult because of the runaway direction Motivation Natural Inflation And Supersymmetry Embedding In String Theory Conclusions Solution With Aligned Natural Inflation • A second axion solves the problem with the trans-Planckian decay constant as well as the problem with the saxion stabilization • Inflation along a trajectory of two misaligned axions results in an effective trans-Planckian decay constant [Kim, Nilles, Peloso, 2004] sufficient for natural inflation • We consider a two axion (ρi ) model with matter fields (Xi ) 2 X 2 −ai ρ1−bi ρ2 W = mi Xi (e − λi ) i=1 2 X 2 K = − log(ρi +ρ ¯i ) + k(jXi j ) i=1 Motivation Natural Inflation And Supersymmetry Embedding In String Theory Conclusions Stabilized Saxion And Successful Inflation • The light saxion combination (χ) is stabilized because the Kähler metric has two poles between which the saxion is trapped • Inflation happens along the light axion direction (') without spoiling moduli stabilization e-folds e-folds 150 100 60 30 10 0 150 100 60 30 10 0 8 0.05 6 χ φ 4 0 2 0 0 5·106 107 0 5·106 107 t t Motivation Natural Inflation And Supersymmetry Embedding In String Theory Conclusions Natural Parameters For Natural Inflation a1 b1 a2 b2 m1 m2 λ1 λ2 7π 8π 6π 7π −4 −3 6 7 7 8 0:45 0:55 2:6 · 10 2:0 · 10 Motivation Natural Inflation And Supersymmetry Embedding In String Theory Conclusions Link String Theory With Observations • Natural inflation is at the edge of the measured data • Flattening helps to find better agreement • What about other string theory corrections to the potential? ) Will help a lot! Results appear soon... 0.20 0.15 ) r ( Planck+ BICEP2+ BAO 68%CL Planck+ BICEP2+ BAO 95%CL scalar ratio 0.10 Natural Inflation - to - Flattened Natural Inflation Tensor 0.05 0.00 0.94 0.95 0.96 0.97 0.98 0.99 Spectral index(n s ) Motivation Natural Inflation And Supersymmetry Embedding In String Theory Conclusions Conclusions • Low scale supersymmetry together with high scale inflation is possible • Aligned natural inflation with matter fields leads to low scale supersymmetry with successful moduli stabilization Thank you for your attention!.