Inflationary Cosmology and Particle Physics

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1 Inflationary Cosmology and Particle Physics Qaisar Shafi Bartol Research Institute Department of Physics and Astronomy University of Delaware Cambridge August, /67

2 Outline Introduction Standard Model Inflation Non-Supersymmetric GUTs and Inflation Supersymmetry, Supergravity and Inflation Radiative Corrections and Precision Cosmology Conclusions 2 /67

3 Hot Big Bang Cosmology (SM+GR) Standard Model (SM) + General Relativity (GR) gives rise to highly successful Hot Big Bang Cosmology Redshift of distant galaxies Cosmic Microwave Background (CMB) Primordial nucleosynthesis 3 /67

4 Hot Big Bang Cosmology (SM+GR) But Hot Big Bang Cosmology cannot explain: High degree of CMB isotropy Origin of δt T Flatness n B /s (baryon asymmetry) Cold Dark Matter (CDM) WMAP Collaboration /67

5 Hot Big Bang Cosmology (SM+GR) In recent years ΛCDM has become the leading candidate for the description of the universe. WMAP Collaboration 2008 Where does ΛCDM come from? 5 /67

6 Inflationary Cosmology [Guth, Linde, Albrecht & Steinhardt, Starobinsky, Mukhanov, Hawking,... ] Successful Primordial Inflation should: Explain flatness, isotropy; Provide origin of δt T ; Offer testable predictions for n s, r, dn s /dln k; Recover Hot Big Bang Cosmology; Explain the observed baryon asymmetry; Offer plausible CDM candidate Physics Beyond the SM? 6 /67

7 Physics Beyond the SM Solar and atmospheric neutrino oscillation experiments require new physics beyond the SM Simplest Extensions 1 Just add 2-3 SM singlet ( right handed ) neutrinos and use seesaw mechanism to understand why m ν m charged matter 2 Gauge U(1) B L global symmetry of SM requires 3 RH-ν s to cancel anomalies Will discuss these two possible extensions of the SM in the context of inflation Gauge hierarchy problem (M W M P ) Electric charge quantization Strong CP problem (axions) 7 /67

8 Beyond the SM Supersymmetry (Gauge hierarchy problem, LSP dark matter) Grand Unification (Charge quantization, proton decay, gauge coupling unification) Technicolor (Complicated models) Large Extra Dimensions (Black holes at LHC?) Warped Extra Dimensions (TeV scale KK excitations) Universal Extra Dimensions (KK dark matter candidate) 8 /67

9 Slow-roll Inflation The slow-roll parameters may be defined as ( ) ǫ = m2 p V 2, ( ) ( 2 V η = m 2 V p V, ξ 2 = m 4 V V P ). V 2 Assuming slow-roll approximation (i.e. (ǫ, η,ξ 2 ) 1), the spectral index n s, the tensor to scalar ratio r and the running of the spectral index dn s /dln k are given by n s 1 6ǫ + 2η, r 16ǫ, dn s dln k 16ǫη 24ǫ2 2ξ 2. The number of e-folds after the comoving scale l 0 = 2π/k 0 has crossed the horizon is given by N 0 = 1 φ0 ( V ) m 2 p φ e V dφ. Inflation ends when ǫ(φ e ) 1 or η(φ e ) 1. The amplitude of the curvature perturbation is given by ( 1 R = 2 V 3/2 3πm 3 V = p )φ=φ 5 (WMAP5 normalization) 0 9 /67

10 Standard Model Inflation? [Bezrukov, Magnin and Shaposhnikov; De Simone, Hertzberg and Wilczek.] [Barvinsky, Kamenshchik, Kiefer, Starobinsky and Steinwachs.] Consider the following action with non-minimal coupling: S J = dx 4 ) 2 g{ H 2 + λ( H H v m2 P R ξh H R} In the Einstein frame the potential turns out to be: λ G 4 φ4 V E (φ) (1+ ξφ2 m 2 ) 2; G(t) = exp[ 4 t 0 dt γ(t )/(1 + γ(t ))] P where H T = 1 2 (0,v + φ), t = log[ φ M t ] and γ(t) is the anomalous dimension of the Higgs field. For large φ values, V E (φ) gives rise to inflation. 10 /67

11 Standard Model Inflation? Mt 175 GeV, Ξ 2893, m h GeV Λ t G t t log Φ Mt Mt GeV, Ξ 6379, m h GeV Λ t G t t log Φ Mt λ(t) G(t) vs. t, between pivot-scale t 0 = log[ φ 0 M t ] and inflation end scale t e = log[ φe M t ] The spectral index is with n s 1 2 N e R λ G ξ 2 Ne 2 72π 2 ( ) ψ0 (λ G) (λ G) ; ψ 0 ξ φ0 m P ( ) N λg ξ e 6 2 π 10 4 (!) R 11 /67

12 Standard Model Inflation? Mt 169 GeV Mt 171 GeV Mt GeV Mt 173 GeV 0.05 ns Mt 175 GeV Λ Φ 0 Mt 169 GeV Mt 171 GeV Mt GeV mh GeV mh GeV 0.03 Mt 173 GeV Mt 175 GeV Green curve is the tree level result (independent of Higgs mass). Blue and red include quantum corrections. 12 /67

13 Challenges for SM inflation [Burgess, Lee and Trott; Barbon and Espinosa, 09] Consider g µν = η µν + hµν m P, so that the term ξ φ 2 R yields ξ m P φ 2 η µν 2 h µν + This suggests an effective cut-off scale Λ m P ξ m P. The energy scale of inflation is estimated to be E i V 1/4 0 = λ1/4 m P 4 1/4 ξ Λ = m P ξ. Thus it is not clear how reliable are the calculations. 13 /67

14 Non-Supersymmetric GUTs and Inflation [Q. Shafi and A. Vilenkin, 1984] Consider Coleman-Weinberg (CW) and Higgs Potentials for inflation in Non-Supersymmetric GUTs V (φ) = A φ 4 [ln( φ M V (φ) = V 0 [1 ) 1 4 ] + A M4 4 (CW Potential) ( φ M ) 2 ] 2 (Higgs Potential) Here φ is a gauge singlet field. Coleman Weinberg Potential V Φ V Φ Higgs Potential M Φ [Rehman, Shafi and Wickman, 08] [Kallosh and Linde, 07] M Φ 14 /67

15 Non-Supersymmetric GUTs and Inflation [V. N. Senoguz, Q. Shafi, 2007] 1 ns Log 10 V GeV Below vev inflation 15 /67

16 Non-Supersymmetric GUTs and Inflation ns Log 10 V Φ 0 Below vev inflation 16 /67

17 Predictions for CW and Higgs Potentials [M. Rehman, Q. Shafi and J. Wickman, 2008] r CW Potential BV CW Potential AV Higgs Potential BV Higgs Potential AV Φ Φ Φ 2 1 Φ n s 17 /67

18 Proton Decay and WMAP CW Potential BV CW Potential AV Higgs Potential BV Higgs Potential AV Φ 2 ns 0.94 Φ Φ 4 1 Φ log 10 V Φ GeV M X 2-4V 1/ GeV (CWP) V 1/4 0 (GeV) V (φ 0 ) 1/4 (GeV) n s r τ p years (proton lifetime) 18 /67

19 Magnetic Monopoles and Inflation [Q. Shafi and A. Vilenkin, 1984; G. Lazarides, Q. Shafi, 1984] Consider the breaking G SO(10) H SM where H SU(4) SU(2) SU(2). First breaking produces superheavy monopoles carrying one unit of Dirac charge; these will be inflated away. π 2 (G/H) = Z 2 ; The second breaking at scale M c produces monopoles which carry two units of Dirac magnetic charge. These are intermediate mass monopoles and they may survive inflation. 19 /67

20 Magnetic Monopoles and Inflation Consider the quartic coupling cφ 2 χ χ, with c (M c /M) 2. Here χ vev breaks to and φ is the inflaton. Monopole formation occurs when cφ 2 H 2 H(t t χ ) η 3c/λ. Initial monopole number density H 3, which gets diluted by inflation down to H 3 exp( 3η); thus, r M = n M /TR 3 (H/T R) 3 exp( 3η) Roughly e-folds can yield a flux close to or below the Parker bound. 20 /67

21 Why Supersymmetry? Resolution of the gauge hierarchy problem Unification of the SM gauge couplings at M GUT GeV Cold dark matter candidate (LSP) Other good reasons: Radiative electroweak breaking String theory requires susy Leading candidate is the MSSM (Minimal Supersymmetric Standard Model) 21 /67

22 Why Supersymmetry? Α 1 1 MSSM Αi Α 2 1 Α Log 10 GeV 22 /67

23 MSSM Inflation Numerous flat dimensions exist in MSSM. Utilize UDD and LLE. [Allahverdi, Enqvist, Garcia-Bellido, Mazumdar] By suitable tuning of soft susy breaking parameters A and m φ, an inflationary scenario may be realized. Flat directions lifted by higher dimensional operators W = λ Φn, Φ is flat direction superfield. m n 3 P V = 1 2 m2 φ φ2 + Acos(nθ + θ A ) λn φn nm n 3 P + λ2 n φ2(n 1) m 2(n 3) P For A 2 8(n 1)m 2 φ, there is a secondary minimum at φ = φ 0 (m φ m n 3 P ) 1 (n 2) m p, with V m 2 φ φ2 0 m2 φ (m φm n 3 P ) 2 n 2 (this can drive inflation) 23 /67

24 MSSM Inflation H inf (m φφ 0 ) m P m φ ( m φ m P ) 1 (n 2) m φ To implement realistic inflation, one wants both the first and second derivatives of V to vanish at φ 0 : Thus V (φ) V (φ 0 ) + 1 3! V (φ 0 )(φ φ 0 ) 3 + Using slow roll approximations (take n = 6, φ GeV, m φ 1 10 TeV) n s 1 4 N 0.92 dn s dlnk 4 N r H m P /67

25 CMSSM and Inflation CMSSM is a special case of MSSM in which we assume that SUSY is spontaneously broken in some hidden sector and this information is transmitted to our (visible) sector via gravity One employs universal soft SUSY breaking terms (say at M GUT ); these include scalar masses, gaugino masses, trilinear couplings, etc In our discussion of SUSY hybrid inflation we will follow this minimal SUGRA scenario for the soft terms 25 /67

26 Susy Hybrid Inflation [Dvali, Shafi, Schaefer; Copeland, Liddle, Lyth, Stewart, Wands 94] Attractive scenario in which inflation can be associated with symmetry breaking G H SUSY hybrid inflation is defined by the superpotential inflaton (singlet) = S, R-symmetry W = κs (Φ Φ M 2 ) waterfall field = (Φ,Φ) G Φ Φ Φ Φ, S e iα S, W e iα W W is unique renormalizable superpotential Some examples of gauge groups: G = U(1) B L, (Supersymmetric superconductor) G = 3 c 2 L 2 R 1 B L, (Φ, Φ) = ((1, 1, 2, +1),(1, 1, 2, 1)) G = 4 c 2 L 2 R, (Φ, Φ) = ((4, 1, 2),(4, 1, 2)) G = SO(10), (Φ, Φ) = (16, 16) 26 /67

27 Susy Hybrid Inflation SUSY vacua Φ = Φ = M, S = 0 Potential V F = κ 2 (M 2 Φ 2 ) 2 + 2κ 2 S 2 Φ 2 S M V Κ 2 M M 1 27 /67

28 Susy Hybrid Inflation Mass splitting in Φ Φ m 2 ± = κ2 S 2 ± κ 2 M 2, m 2 F = κ2 S 2 One-loop radiative corrections V 1loop = 1 64π 2 Str[M 4 (S)(ln M2 (S) Q )] In the inflationary valley (Φ = 0) ) V κ 2 M (1 4 + κ2 N 8π F(x) 2 where x = S /M and ( (x F(x) = ) ) 1) ln (x4 x + 2x 2 ln x x ln κ2 M 2 x 2 Q /67

29 Susy Hybrid Inflation Tree Level plus radiative corrections: ns log 10 Κ log 10 r ns n s 1 ( m p ) ( ) 2 κ 2 N M F (x 8π 2 0 ) r 4(1 n s ) F (x 0 ) F (x 0 ) x N /67

30 Minimal Sugra Hybrid Inflation The minimal Kähler potential can be expanded as K = S 2 + Φ 2 + Φ 2 The SUGRA scalar potential is given by V F = e K/m2 p where we have defined ( K 1 ij D z i WD z j W 3m 2 p W 2) D zi W W z i + m 2 p K z i W; K ij and z i {Φ,Φ,S,...} 2 K z i z j 30 /67

31 Minimal Sugra Hybrid Inflation Take into account SUGRA corrections, radiative corrections and soft SUSY breaking terms, the potential is given by V κ 2 M 4 (1 + ( M mp ) 4 x κ2 N 8π 2 F(x) + a ( ) m3/2 x κm + ( ) ) m3/2 x 2 κm where a = 2 2 A cos[arg S + arg(2 A)] and S m P. Note: No η problem with minimal Kähler potential [V. N. Senoguz, Q. Shafi 04; A. D. Linde, A. Riotto 97] 31 /67

32 Minimal Sugra Hybrid Inflation V Κ 2 M a 1, x x l a 0, x x l a 1, x x l Hybrid vs. Hilltop Solutions (κ = ) [L. Boubekeur and D. H. Lyth, 2005] 32 /67

33 Minimal Sugra Hybrid Inflation [M. Rehman, Q. Shafi, J. Wickman, in preparation.] a 1 a 1 ns a log 10 Κ ( ) 2 n s M mp x ( [ m P ) 2 M κ2 N 8π F (x 2 0 ) + 2 ( ) ] m3/2 2 κ M 33 /67

34 Minimal Sugra Hybrid Inflation 1.02 a 1 ns a 0 a log 10 Κ ) 2 n s 1 + 6( M m P x ( [ m P ) ( ) ] 2 M κ2 N F m3/2 2 (x 8π 2 0 ) + 2 κ M 34 /67

35 Minimal Sugra Hybrid Inflation log 10 M GeV a 1 a 1 log 10 M GeV a a log 10 Κ 15.0 a 0 a log 10 Κ 35 /67

36 Minimal Sugra Hybrid Inflation a 1 log M GeV a 1 a 1 log M GeV a 1 a ns ns 36 /67

37 Minimal Sugra Hybrid Inflation 4 6 log 10 r a 1 a r 4 ( [ m P ) ( ) 2 4 ( ) ] M 2 M mp x κ2 N F (x 8π 2 0 ) + am 3/2 κm + 2 m3/2 2 2 κm x0 n s 37 /67

38 Minimal Sugra Hybrid Inflation log 10 r a 1 a r 4 ( [ m P ) ( ) 2 4 ( ) ] M 2 M mp x κ2 N F (x 8π 2 0 ) + am 3/2 κm + 2 m3/2 2 2 κm x0 n s 38 /67

39 Minimal Sugra Hybrid Inflation 3 log 10 dns dlnk a 1 a n s dn s dln k ǫ 39 /67

40 Minimal Sugra Hybrid Inflation 2 3 log 10 dns dlnk a a n s dn s dln k ǫ 40 /67

41 WMAP and Cosmic Strings [Battye, Bjorn, Adam] ns Κ n s vs. κ for N = 1 susy hybrid inflation with string contribution included. The contours represent the 68% and 95% confidence levels for a 7 parameter fit to the WMAP5+ACBAR data [arxiv:astro-ph/ ]. δt T = (δt T ) 2 inf + ( δt T ) 2 cs, ( δt T ) cs Gµ = 2π ( M M P ) ln(2/κ 2 ) 41 /67

42 Reheat Temperature and Non-Thermal Leptogenesis log 10 Tr GeV a 1 a 0 a 1 log 10 M GeV a 0 a 1 a log 10 Κ log 10 m inf GeV ( ) 1/2 T r GeV GeV ( ) ( ) m inf 3/4 1/ ev M GeV m ν3 42 /67

43 Reheat Temperature and Non-Thermal Leptogenesis log 10 Tr GeV a 1 a 1 a 1 log 10 M GeV a 1 a 1 a log 10 Κ log 10 m inf GeV ( ) 1/2 T r GeV GeV ( ) ( ) m inf 3/4 1/ ev M GeV m ν3 43 /67

44 Non-Minimal Sugra Hybrid Inflation [M. Bastero-Gil, S. F. King, Q. Shafi; M. Rehman, V. N. Senoguz, Q. Shafi 06] The Kähler potential including non-minimal terms can be expanded as K = S 2 + Φ 2 + Φ 2 S +κ 4 S S + κ 2 Φ 2 S 4m 2 Sφ + κ 2 Φ 2 S p m 2 p Sφ + κ 6 m 2 SS +. p 6m 4 p The potential is of the following form ( ( ) 2 ( ) 4 V κ 2 M 4 1 κ M S m p x 2 + γ M x 4 S m p ( ) ( ) ) m3/2 x m3/2 x 2 +a κm + κm, where γ S = 1 7κ S 2 + 2κ 2 S. 2 + κ2 N 8π 2 F(x) 44 /67

45 Non-Minimal Sugra Hybrid Inflation n s s = 0 s = s = s = 0.01 s = ( ) 2 n S 1 2κ S + 6γ M S m p x 2 0 ( m p ) ( ) 2 κ 2 N M 8π F (x 2 0 ) 45 /67

46 MSSM µ Problem In MSSM, the term µh u H d is both supersymmetric and also gauge invariant, and we require that µ GeV in order to implement radiative EW breaking µ, in principle, could be of order M GUT /M P? In SUSY hybrid inflation models, the R-symmetry forbids the bare µ term. However, λh u H d S is allowed, λ a dimensionless coefficient. After SUSY breaking, S m 3/2 /κ, so that µ m 3/2 λ/κ. 46 /67

47 Shifted Hybrid Inflation Useful for inflating away troublesome objects. [R. Jeannerot, S. Khalil, G. Lazarides, Q. Shafi 2000] Shifted hybrid inflation is defined by the superpotential Potential W = κs (Φ Φ M 2 ) S (Φ Φ)2 M 2 S V F = κ 2 (M 2 Φ 2 + ξ Φ 4 ) 2 + 2κ 2 S 2 Φ 2 (M 2 2ξ Φ 2 ) 2 where ξ = M 2 /κm 2 S Inflationary trajectories Φ = 0 and Φ = 1/2ξ M with S > M 47 /67

48 Shifted Hybrid Inflation Monopoles produced in the shifted directions get inflated away 3 4 S M V Κ 2 M M /67

49 Shifted Hybrid Inflation Including 1-loop radiative corrections in the shifted direction ( Φ = 1/2ξ M) V κ 2 M 4 ξ ( ) 1 + κ2 N F(x 8π 2 ξ ) where x ξ = S /M ξ and M ξ = M 1/4ξ 1 Same results/predictions are obtained as that of regular SUSY/SUGRA inflation M ξ M 49 /67

50 r Chaotic Inflation (Linde) 0.4 Driven by potentials m 2 φ 2 or λφ 4 Where does φ come from? One promising candidate is right handed sneutrino: m2 Φ 2 ΛΦ ns W N mñ2 V m 2 N 2 ; m GeV Komatsu et al, WMAP Collaboration 2008 Challenge: Does this survive SUGRA corrections? (since N > M P during inflation) Answer: With N > M P during inflation, SUGRA corrections overwhelm this scenario: W = mφ 2 large vev of W during inflation potential negative/no inflation 50 /67

51 Chaotic Inflation Shift symmetry imposed on the inflaton (removes the nasty expotential factor in the inflaton potential) K(Φ,Φ ) invariant for Φ Φ + icm, so K is a function of Φ + Φ, i.e., K(Φ + Φ ) However, with W = m Φ 2, chaotic inflation will not take place due to the large vev of W. To cure this introduce a field X with W = m X Φ. During inflation, X is assumed to be stablized at the origin, so that W vanishes. (Kawasaki, Yamaguchi, Yanagida) Why is W = m X Φ the only relevant term? 51 /67

52 Chaotic Inflation Gravitino Problem If Φ transforms under a shift symmetry, the following term is allowed: K = c(φ + Φ ), with c O(1) in Planck units The inflaton Φ decays into susy breaking sector as well as the MSSM sector, leading to thermal and non-thermal gravitino overproduction. One possible solution: Introduce a discrete symmetry which suppresses/eliminates the linear term. 52 /67

53 Chaotic Inflation If Φ is RH sneutrino, it is charged under the shift symmetry. It does not have a Majorana mass, so it is not clear how leptogenesis/ν oscillations work out. 53 /67

54 Radiative Corrections and Precision Cosmology Chaotic: potential is quadratic (V m 2 φ 2 ) or quartic (V λφ 4 ) Simplest (renormalizable) potential Predicts significant primordial gravity waves Hybrid: inflation driven by φ field, vacuum energy provided by second scalar field χ ( ) 2 V (φ,χ) = κ 2 M 2 χ2 4 + m 2 φ λ2 χ 2 φ 2 4 Compelling and robust Translates well to SUSY Non-SUSY model results in n s > 1 (unless in chaotic-like regime) SUSY case has n s < 1 54 /67

55 Tree Level Inflation Models vs. WMAP ΛΦ Φ 0 1 Φ 0 1 r m2 Φ 2 r Not Allowed Flat Potential Φ n s n s Komatsu et. al. (WMAP Collaboration), /67

56 Radiative Corrections in Chaotic Inflation Quadratic: V (φ) = 1 2 m2 φ 2 ± Aφ 4 ln φ2 µ 2 Quartic: V (φ) = λφ 4 ± Aφ 4 ln φ2 µ 2 Fermion-dominated corrections ( ) (say from right handed neutrinos) V Φ Φ 56 /67

57 Radiative Corrections in Chaotic Inflation Results [V. N. Senoguz and Q. Shafi, 2008] ΛΦ 4 r m2 Φ n s 57 /67

58 Radiative Corrections in Hybrid Inflation [M. Rehman, Q. Shafi and J. Wickman, 2009] ( ) 2 V (φ,χ) = κ 2 M 2 χ2 + m2 φ 2 + λ2 χ 2 φ 2 ( ) φ ± Aφ 4 ln, φ c where φ inflaton field, χ waterfall field (χ = 0 during inflation) 1 log 10 r 2 3 Φ P 2.5 Φ P 1 4 Φ P n s 58 /67

59 Radiative Corrections & Precision Cosmology Radiatively-corrected inflation models; Chaotic Inflation Permits low values of r (e.g. 0 r 0.2 to agree with WMAP5 2σ bound) Hybrid Inflation Red spectrum (n s < 1) can be produced for Planckian or sub-planckian values of the inflaton Better agreement with WMAP5 Generically 2 solutions of n s for each A 59 /67

60 Brane Inflation In the simplest brane inflation models the inflaton φ is a field which parametrizes the distance r between two brane worlds embedded in the extra dimensions. If the distance between these two branes is much bigger than the string scale, the potential between them is essentially governed by the infrared bulk supergravity. Assuming the effects of higher string excitations are decoupled, the potential is expected to be V M 4 s ( a b (M sr) N 2 ), where M s is the string scale, and a, b are constants. 60 /67

61 Brane Inflation Thus, in this picture inflation in four dimensions is driven by brane motion in the extra-dimensional space. Positive powers of φ are absent because the inter-brane interaction falls off with the distance. For a D 3 brane - anti D 3 brane system, assuming the extra dimensions have been suitably compactified (say T 6 ) and remain frozen during inflation, ) V (φ) Ms (1 4 αφ, φ = T 4 3 r, α = T π 2 (contributions from dilaton, graviton and RR field) In this case δt T M c/m P, M c GeV (intermediate compactification scale), n s 1 2 N NOTE: No very compelling/realistic model so far!! 61 /67

62 D-brane Inflation Brane-Antibrane Dvali & Tye; Dvali,Shafi,Solganik; Burgess,Majumdar,Nolte,Quevedo,Rajesh,Zhang; Alexander;. Branes at Angles Garcia-Bellido, Rabadan, Zamora; Blumenhagen, Körs, Lüst, Ott; Dutta, Kumar, Leblond. D3-D7 Dasgupta,Herdeiro,Hirano, Kallosh; Hsu,Kallosh, Prokushkin; Hsu & Kallosh; Aspinwall & Kallosh; Haack, Kallosh, Krause, Linde, Lüst, Zagermann. warped brane-antibrane Kachru,Kallosh,Linde,Maldacena,L.M.,Trivedi; Firouzjahi & Tye; Burgess,Cline,Stoica,Quevedo; Iizuka & Trivedi,... DBI Silverstein & Tong; Alishahiha,Silverstein,Tong; Chen; Chen; Shiu & Underwood; Leblond & Shandera,... Monodromy Silverstein & Westphal. Adapted from McAllister, /67

63 D-brane Inflation Closed string inflation models, e.g.: Racetrack Blanco-Pillado, Burgess, Cline, Escoda, Gomez-Reino, Kallosh, Linde, Quevedo. Kähler moduli Conlon & Quevedo. N-flation Dimopoulos, Kachru, McGreevy, Wacker; Easther & L.M. Adapted from McAllister, /67

64 Chaotic inflation in string theory [Silverstein, Westphal, 2008] 64 /67

65 Brane Inflation and Cosmic Strings Prior to brane annihilation the associated gauge symmetry is U(1) U(1). One linear combination gives rise to D-strings, while the orthogonal combination is associated with F (fundamental)-strings. It has been argued that a substantial fraction of energy of the annihilating branes is used up in the production of a network of cosmic D and F strings. If one assumes that brane inflation gives rise to the observed inhomogeneities, estimates suggest that Gµ With some(?) luck it may be possible to observe these primordial strings with LIGO/LISA. 65 /67

66 Conclusions One of the most important challenges in our field is to find a Standard Model of Inflationary Cosmology. A large class of realistic inflation models, based on grand unification and/or low scale supersymmetry are consistent with the data currently available from WMAP and other observations. Non-supersymmetric GUT inflation models typically predict an observable value for the tensor to scalar ratio r. Supersymmetric hybrid inflation, on the other hand, predicts a tiny r value ( 10 4 ), even though the symmetry breaking scale associated with inflation is comparable to M GUT. 66 /67

67 Conclusions Hopefully, the PLANCK Satellite will soon shed light on this fundamental parameter r. In addition, we expect the LHC to provide answers to the following long-standing and very basic questions: Is there a SM Higgs boson and what is its mass? Is there low scale supersymmetry? Is the LSP stable? Mass? To achieve truly significant progress in particle physics and cosmology we need both the LHC and the PLANCK Satellite. They hold the key to future developments in these fields. 67 /67