Natural Inflation and Low Scale Supersymmetry

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 ϕ drives the expansion of the universe • Very flat potential V (ϕ) 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 ϕ V (ϕ) = 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(|X| ) • The scalar potential is (ρ = ρ0 + χ + iϕ)

2 V = 2m4e(ρ0+χ) −a(2ρ0+χ) (cosh(aχ) − cos(aϕ))

• Im(ρ) = ϕ is again the inflaton and there is a log(λ) supersymmetric minimum for X0 = 0 and ρ0 = − a • In the minimum mχ = mϕ 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 ∆ϕ > 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(|Xi | ) 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 (ϕ) without spoiling moduli stabilization

e-folds e-folds 150 100 60 30 10 0 150 100 60 30 10 0

0.05 6 χ φ 4

0 2

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 Planck+ BICEP2+ BAO 68%CL

Planck+ BICEP2+ BAO 95%CL

0.10 Natural Inflation

Flattened Natural Inflation

Tensor-toscalar ratio(r) 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!