An up-date on Brane Inflation. Dieter Lüst, LMU (Arnold Sommerfeld Center) and MPI für Physik, München

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1 An up-date on Brane Inflation Dieter Lüst, LMU (Arnold Sommerfeld Center) and MPI für Physik, München Leopoldina Conference, München, 9. October 2008

2 An up-date on Brane Inflation Dieter Lüst, LMU (Arnold Sommerfeld Center) and MPI für Physik, München in collaboration with Gia Dvali: arxiv: Leopoldina Conference, München, 9. October 2008

3 An up-date on Brane Inflation Dieter Lüst, LMU (Arnold Sommerfeld Center) and MPI für Physik, München in collaboration with Gia Dvali: arxiv: and with Michael Haack, Renata Kallosh, Axel Krause, Andrei Linde, Marco Zagermann: arxiv: Leopoldina Conference, München, 9. October 2008

4 Precision cosmology: Concordance and simplicity: Ω = 1, w = -1 Leopoldina Conference, München, 9. October 2008

WMAP 5 CMB-data agree with: almost scale invariant spectrum: small tensor perturbations: n s =0.96 ± 0.

5 WMAP 5 CMB-data agree with: almost scale invariant spectrum: small tensor perturbations: n s =0.96 ± (however without cosmic strings) r 2 T 2 φ, r < 0.30 Expect improvement in these limits from Planck, SPIDER, Clover, QUIET, BICEP, EBEX, PolarBEAR,... Leopoldina Conference, München, 9. October 2008

6 These data can be nicely explained by an epoche of cosmic inflation in the early universe! Leopoldina Conference, München, 9. October 2008

7 These data can be nicely explained by an epoche of cosmic inflation in the early universe! The goal: Use CMB to find/probe fundamental theory Leopoldina Conference, München, 9. October 2008

8 These data can be nicely explained by an epoche of cosmic inflation in the early universe! The goal: Use CMB to find/probe fundamental theory The strategy: Focus on correlated signatures (e.g. n s & cosmic strings,..) Leopoldina Conference, München, 9. October 2008

9 These data can be nicely explained by an epoche of The goal: Use CMB to find/probe fundamental theory The strategy: Focus on correlated signatures (e.g. n s & cosmic strings,..) The method: cosmic inflation in the early universe! Use effective field theories V (φ) φ : inflaton field Leopoldina Conference, München, 9. October 2008

10 These data can be nicely explained by an epoche of cosmic inflation in the early universe! The goal: Use CMB to find/probe fundamental theory The strategy: Focus on correlated signatures (e.g. n s & cosmic strings,..) The method: Use effective field theories V (φ) φ : inflaton field The problem: there exist many effective field theories Leopoldina Conference, München, 9. October 2008

11 These data can be nicely explained by an epoche of cosmic inflation in the early universe! The goal: Use CMB to find/probe fundamental theory The strategy: Focus on correlated signatures (e.g. n s & cosmic strings,..) The method: Use effective field theories V (φ) φ : inflaton field The problem: there exist many effective field theories The theoretical constraint: consistent embedding into quantum gravity & string theory (Swampland approach) Leopoldina Conference, München, 9. October 2008

12 These data can be nicely explained by an epoche of cosmic inflation in the early universe! The goal: Use CMB to find/probe fundamental theory The strategy: Focus on correlated signatures (e.g. n s & cosmic strings,..) The method: Use effective field theories V (φ) φ : inflaton field The problem: there exist many effective field theories The theoretical constraint: consistent embedding into quantum gravity & string theory (Swampland approach) The challenge: obtain flat enough potentials Leopoldina Conference, München, 9. October 2008

13 ɛ = Ḣ H 2 = M P 2 2 η = Conditions for slow roll inflation: ɛ ɛh = M 2 P ( V ) 2 (φ) << 1, V (φ) ( V (φ) V (φ) ) << 1, n s =1 6ɛ +2η Leopoldina Conference, München, 9. October 2008

14 ɛ = Ḣ H 2 = M P 2 2 η = Conditions for slow roll inflation: ɛ ɛh = M 2 P ( V ) 2 (φ) << 1, V (φ) ( V (φ) V (φ) ) This can be achieved by: << 1, n s =1 6ɛ +2η Leopoldina Conference, München, 9. October 2008

15 ɛ = Ḣ H 2 = M P 2 2 η = Conditions for slow roll inflation: ɛ ɛh = M 2 P ( V ) 2 (φ) << 1, V (φ) ( V (φ) V (φ) ) This can be achieved by: << 1, Large field inflation: φ M P e.g. chaotic inflation: V (φ) = 1 2 m2 φ 2 (Linde (1983)) gravitational waves, large r: r =0.01 Observations φ (5 6)M P n s =1 6ɛ +2η ( φ M P ) 2 (Lyth (1996)) Leopoldina Conference, München, 9. October 2008

16 ɛ = Ḣ H 2 = M P 2 2 η = Conditions for slow roll inflation: ɛ ɛh = M 2 P ( V ) 2 (φ) << 1, V (φ) ( V (φ) V (φ) ) This can be achieved by: << 1, Large field inflation: φ M P e.g. chaotic inflation: V (φ) = 1 2 m2 φ 2 (Linde (1983)) gravitational waves, large r: r =0.01 Observations Small field inflation: φ M P Fine tuning of parameters! φ (5 6)M P n s =1 6ɛ +2η ( φ M P ) 2 (Lyth (1996)) Leopoldina Conference, München, 9. October 2008

17 Part I: Bounds from black hole decays: (G. Dvali, arxiv: ) Consider a theory with N species of particles with mass M: N < N max = M 2 P lanck M 2 M: scale of new physics (A quantum black hole can emit at most N max different particles) This bound must be satisfied in every effective string vacuum that is consistently coupled to gravity! E.g. if a scalar field in the effective potential gives mass to N particles via the Higgs effect: M = M(φ) M(φ) 2 < M 2 P lanck N Leopoldina Conference, München, 9. October 2008

18 Cosmological applications of this bound: Leopoldina Conference, München, 9. October 2008

19 Cosmological applications of this bound: De Sitter vacua - inflation: Consider inflaton field φ φ +3H φ + V (φ) =0 φ is coupled to species of mass M: Black hole bound: M(φ) < M P (H 1 (φ)m P ) 1 3 Leopoldina Conference, München, 9. October 2008

20 Cosmological applications of this bound: De Sitter vacua - inflation: Consider inflaton field φ φ +3H φ + V (φ) =0 φ is coupled to species of mass M: Black hole bound: Chaotic inflation: M(φ) < M P (H 1 (φ)m P ) 1 3 V (φ) = 1 2 m2 φ 2 + gφ ψ j ψ j gφ M P ( mφ M 2 P ) 1 3 slow roll condition: φ M P φ cannot be arbitrarily large! Bound forbids essentially large trans-planckian vevs: Leopoldina Conference, München, 9. October 2008

21 Cosmological applications of this bound: De Sitter vacua - inflation: Consider inflaton field φ φ +3H φ + V (φ) =0 φ is coupled to species of mass M: Black hole bound: Chaotic inflation: M(φ) < M P (H 1 (φ)m P ) 1 3 V (φ) = 1 2 m2 φ 2 + gφ ψ j ψ j gφ M P ( mφ M 2 P ) 1 3 slow roll condition: φ M P φ cannot be arbitrarily large! Bound forbids essentially large trans-planckian vevs: Problem to see gravitational waves? Leopoldina Conference, München, 9. October 2008

22 Cosmological applications of this bound: De Sitter vacua - inflation: Consider inflaton field φ φ +3H φ + V (φ) =0 φ is coupled to species of mass M: Black hole bound: Chaotic inflation: M(φ) < M P (H 1 (φ)m P ) 1 3 V (φ) = 1 2 m2 φ 2 + gφ ψ j ψ j gφ M P ( mφ M 2 P ) 1 3 slow roll condition: φ M P φ cannot be arbitrarily large! Bound forbids essentially large trans-planckian vevs: (Silverstein, Westphal: large field range due to monodromy!) (arxiv: ) Leopoldina Conference, München, 9. October 2008

23 Similar bounds can be derived for D-term (hybrid) inflation. (Linde (1993); Binetruy, Dvali (1996))! 4 V (φ)! µ g g φ ln 2 16π Q 2 MP " Black hole bound: g φ (The same bound arise from the interactions of φ with fermions of mass mf gφ.)

24 Part II: String/brane inflation: String theory lives in 10 space-time dimensions! Compactification: M 10 = M 4 M 6 M 4 : 4-dim. expanding FRW universe Internal 6-dimensional compact space: M 6 : e.g. Calabi-Yau space SM HS

25 4d effective potential: stored internal, 6-dimensional energy: V (M) =V (M )+V (M, φ) V 0 +V (φ) Moduli fields Steep potential Stabilization of moduli M Cosmological constant Λ (w = 1) Flat inflaton potential

4d effective potential: stored internal, 6-dimensional energy: V (M) =V (M )+V (M, φ) V 0 +V (φ) Moduli fields Steep potential Stabilization of moduli M Cosmological constant Λ (w = 1) Flat inflaton

26 4d effective potential: stored internal, 6-dimensional energy: V (M) =V (M )+V (M, φ) V 0 +V (φ) Moduli fields Steep potential Stabilization of moduli M Cosmological constant Λ (w = 1) Flat inflaton potential String landscape: string vacua?! V 0 (Lerche, Lüst, Schellekens (1986); Bousso, Polchinski (2000); Kachru, Kallosh, Linde, Trivedi (2003); Susskind (2003); Douglas, Denef (2003))

27 Eternal inflation and string theory landscape Inflationary universe may consist of many parts with different properties depending on the local values of the scalar fields, compactifications, etc.

28 Eternal inflation and string theory landscape Inflationary universe may consist of many parts with different properties depending on the local values of the scalar fields, compactifications, etc.

29 Eternal inflation and string theory landscape Inflationary universe may consist of many parts with different properties depending on the local values of the scalar fields, compactifications, etc. An enormously large number of possible types of compactification which exist e.g. in the theories of superstrings should be considered not as a difficulty but as a virtue of these theories, since it increases the probability of the existence of miniuniverses in which life of our type may appear. (A.Linde (1986))

Eternal inflation and string theory landscape Inflationary universe may consist of many parts with different properties depending on the local values of the scalar fields, compactifications, etc.

30 Eternal inflation and string theory landscape Inflationary universe may consist of many parts with different properties depending on the local values of the scalar fields, compactifications, etc. An enormously large number of possible types of compactification which exist e.g. in the theories of superstrings should be considered not as a difficulty but as a virtue of these theories, since it increases the probability of the existence of miniuniverses in which life of our type may appear. (A.Linde (1986)) Now, Dr. Witten allowed, dark energy might have transformed this from a vice into a virtue, a way to generate universes where you can find any cosmological constant you want. We just live in one where life is possible, just as fish only live in water. June 3, 2008

31 Two scenarios for string inflation:

32 Two scenarios for string inflation: Closed string inflation: inflaton is geometric modulus Effective potential due to force from fluxes! 4 and strings/branes wrapped around cycles: "# $%&'( )*!+,-./ 0*!12-./3

33 Two scenarios for string inflation: Closed string inflation: inflaton is geometric modulus Effective potential due to force from fluxes! 4 and strings/branes wrapped around cycles: Open string inflation: Inflaton is distance between D-branes: Effective potential due to force between branes: (Dvali, Tye (1999)) )*!+,-./ 0*!12-./3 "# $%&'(

34 Two scenarios for string inflation: Closed string inflation: inflaton is geometric modulus Effective potential due to force from fluxes! 4 and strings/branes wrapped around cycles: Open string inflation: Inflaton is distance between D-branes: Effective potential due to force between branes: (Dvali, Tye (1999)) )*!+,-./ 0*!12-./3 "# $%&'( Generic problem: effective supergravity potential is generically non-flat: e.g. K = φ φ V e φ 2 too steep! ] K(φ, φ) V (φ) =e [ DW(φ) 2 3 W (φ) 2

35 Stringy realization of D-term (hybrid) inflation: (Dasgupta, Herdeiro, Hirano Kallosh (2002); Kallosh, Linde (2003); Dasgupta, Hsu, Kallosh, Linde, Zagermann (2003); Haack, Kallosh, Krause, Linde, Lüst, Zagermann, arxiv: ) U(1) shift symmetry: naturally flat inflaton potential Cosmic strings after brane recombination (Dvali, Kallosh, Van Proeyen (2003)) Type IIB orientifold with D3/D7-branes on M 10 = M 4 (K3 T 2 /Z 2 ) Inflaton field: D3-D7 distance on T 2

Stringy realization of D-term (hybrid) inflation: (Dasgupta, Herdeiro, Hirano Kallosh (2002); Kallosh, Linde (2003); Dasgupta, Hsu, Kallosh, Linde, Zagermann (2003); Haack, Kallosh, Krause, Linde,

36 Stringy realization of D-term (hybrid) inflation: (Dasgupta, Herdeiro, Hirano Kallosh (2002); Kallosh, Linde (2003); Dasgupta, Hsu, Kallosh, Linde, Zagermann (2003); Haack, Kallosh, Krause, Linde, Lüst, Zagermann, arxiv: ) U(1) shift symmetry: naturally flat inflaton potential Cosmic strings after brane recombination (Dvali, Kallosh, Van Proeyen (2003)) Type IIB orientifold with D3/D7-branes on #3 M 10 = M 4 (K3 T 2 /Z 2 ) FI D7 #1 #4 #2 mobile D3 volume stabilizing D7s Inflaton field: D3-D7 distance on T 2

37 Classical Kähler potential: [ K = ln 8 (Im(s) Im(t)Im(u) 1 2 Im(s) (Im(yk 7 )) 2 1 ] 2 Im(u) (Im(yr 3)) 2 ) K3 volume Complex structure Dilaton D7 positions D3 positions of T 2 { Moduli fields M Superpotential (from fluxes and gaugino condensation): W = W 0 (t, u, y7)+ae r 8iπ2 s/n W fixes s, t, u, y 7 Landscape of possibilities! K & W do not depend on Re(y 3 ) φ Re(y 3 ) Scalar potential: Good inflaton candidate! Supersymmetry gets broken by F-flux on D7-branes. V (φ) =V D + V CW = g2 ξ 2 FI-parameter (1+ g2 2 4π 2 ln φ ξ )

38 K & W are corrected by stringy quantum corrections: K = ln[ c Im t E(y 3,y 7,t)] ( 8π 2 f D7 (M) ) W = W 0 + A exp c ( ( ) ( ) ) 1 c = W 0 + A ϑ 1 2π(y3 + µ),t ϑ 1 2π(y3 µ),t e 8iπ 2 s/c. Gaugino condensation on D7-branes: one loop threshold corrections to gauge kinetic function: f D7 = is 1 8π 2 ln ϑ 1( 2π(y 3 µ),t) 1 8π 2 ln ϑ 1( 2πy 3 + µ, t)+... (Bachas, Fabre (1996); Lüst, Stieberger (2003); Berg, Haack, Körs (2003)) Additional y 3 dependence to the potential (destroys U(1) shift symmetry) mass term : V (φ) =V D + V CW = g2 ξ 2 2 (1+ g2 4π 2 ln φ ξ ) m2 2 φ2 + O(φ 4 )

39 Non-vanishing moduli dependent mass term : m 2 = m 2 (s, t, u) Inflaton potential: V m 2 =0 Mixed F- and D-term inflation! Φ Ξ One needs sufficiently small (positive) values for fine tuning of parameters s,t and u! Question: can we find points in the landscape, where higher order corrections are suppressed? m 2 Vanishing mass: pure D-term inflation cosmic strings

40 Summary:

41 Summary:

42 Summary: K3 x T2 orientifold : with quantum corrections

43 Summary: K3 x T2 orientifold : with quantum corrections With very small quantum correction: in addition cosmic strings Gµ = ξ (Bevis, Hindmarsh, Kunz, Urrestilla, arxiv:astro-ph/ )

44 Summary: INTERESTING TIMES FOR STRING COSMOLOGY ARE AHEAD OF US. THANK YOU!! K3 x T2 orientifold : with quantum corrections With very small quantum correction: in addition cosmic strings Gµ = ξ (Bevis, Hindmarsh, Kunz, Urrestilla, arxiv:astro-ph/ )

Aspects of Inflationary Theory. Andrei Linde

Aspects of Inflationary Theory Andrei Linde New Inflation 1981-1982 V Chaotic Inflation 1983 Eternal Inflation Hybrid Inflation 1991, 1994 Predictions of Inflation: 1) The universe should be homogeneous,