Outline MSSM inflation Supergravity Conclusions MSSM inflation Sami Nurmi University of Helsinki Cosmo 08 August 26 2008 Sami Nurmi MSSM inflation
Outline MSSM inflation Supergravity Conclusions Outline ◮ Consider flat directions of the MSSM as inflaton candidates ◮ Known gauge couplings! ◮ Low inflationary scale, very flat potential required ◮ Constraints on the underlying supergravity model that determines the potential ◮ Try to find sugra models where the constraints are satisfied Sami Nurmi MSSM inflation
Outline MSSM inflation Supergravity Conclusions Flat directions ◮ Supersymmetric vacuum degenerate, potential vanishes along flat directions ◮ Flatness lifted by susy breaking and non-renormalizable terms in the potential Sami Nurmi MSSM inflation
Outline MSSM inflation Supergravity Conclusions MSSM inflation ◮ d = 6 flat directions LLe and udd candidates for the inflaton 1 ◮ After susy breaking the potential to lowest order becomes V ( φ ) = 1 2 m 2 | φ | 2 − A λ 6 | φ | 6 + λ 2 | φ | 10 ◮ If A 2 = 40 m 2 , saddle point at | φ 0 | ∼ ( m / M P ) 1 / 4 M P = ⇒ Inflation with: � m � 1 / 2 N 2 ζ ∼ ∗ , n s ∼ 1 − 4 / N ∗ M P ◮ Low scale H ∼ 1 GeV , A 2 = 40 m 2 must hold very precisely 1 [Allahverdi, Enqvist, Garcia-Bellido, Mazumdar] Sami Nurmi MSSM inflation
Outline MSSM inflation Supergravity Conclusions What fixes A 2 = 40 m 2 ? G = K + ln | W | 2 ◮ Sugra: V = e G ( G M G M − 3) , ◮ Consider a model with 2 ˆ λ ˆ 6 φ 6 = W + W m ) | φ | 2 + ˆ m ) | φ | 4 + . . . ˆ m ) + ˆ K ( h m , h ∗ Z 2 ( h m , h ∗ Z 4 ( h m , h ∗ K = ◮ V = e G ( G M G M − 3) = 1 2 m 2 | φ | 2 − A λ 6 | φ | 6 + λ 2 | φ | 10 + O ( | φ 0 | 12 ) ◮ A 2 = 40 m 2 reads ( K m = ∂ h m K , K m = ( K m ¯ n ) − 1 K ¯ n ) K m ˆ m ˆ | ˆ K m − 6ˆ Z − 1 K ¯ ˆ m + 3 | 2 Z 2 ¯ 2 K m ˆ K m ˆ = 20( ˆ K m + ˆ n (ˆ Z 2 m ˆ ˆ n − ˆ ˆ K ¯ Z − 2 Z − 1 Z 2¯ Z 2 m ¯ n ) − 2) 2 2 2 [K. Enqvist, L. Mether, SN],[SN] Sami Nurmi MSSM inflation
Outline MSSM inflation Supergravity Conclusions What fixes A 2 = 40 m 2 ? G = K + ln | W | 2 ◮ Sugra: V = e G ( G M G M − 3) , ◮ Consider a model with 2 ˆ λ ˆ 6 φ 6 = W + W m ) | φ | 2 + ˆ m ) | φ | 4 + . . . ˆ m ) + ˆ K ( h m , h ∗ Z 2 ( h m , h ∗ Z 4 ( h m , h ∗ K = ◮ V = e G ( G M G M − 3) = 1 2 m 2 | φ | 2 − A λ 6 | φ | 6 + λ 2 | φ | 10 + O ( | φ 0 | 12 ) ◮ A 2 = 40 m 2 reads ( K m = ∂ h m K , K m = ( K m ¯ n ) − 1 K ¯ n ) K m ˆ m ˆ | ˆ K m − 6ˆ Z − 1 K ¯ ˆ m + 3 | 2 Z 2 ¯ 2 K m ˆ K m ˆ = 20( ˆ K m + ˆ n (ˆ Z 2 m ˆ ˆ n − ˆ ˆ K ¯ Z − 2 Z − 1 Z 2¯ Z 2 m ¯ n ) − 2) 2 2 2 [K. Enqvist, L. Mether, SN],[SN] Sami Nurmi MSSM inflation
Outline MSSM inflation Supergravity Conclusions What fixes A 2 = 40 m 2 ? G = K + ln | W | 2 ◮ Sugra: V = e G ( G M G M − 3) , ◮ Consider a model with 2 ˆ λ ˆ 6 φ 6 = W + W m ) | φ | 2 + ˆ m ) | φ | 4 + . . . ˆ m ) + ˆ K ( h m , h ∗ Z 2 ( h m , h ∗ Z 4 ( h m , h ∗ K = ◮ V = e G ( G M G M − 3) = 1 2 m 2 | φ | 2 − A λ 6 | φ | 6 + λ 2 | φ | 10 + O ( | φ 0 | 12 ) ◮ A 2 = 40 m 2 reads ( K m = ∂ h m K , K m = ( K m ¯ n ) − 1 K ¯ n ) K m ˆ m ˆ | ˆ K m − 6ˆ Z − 1 K ¯ ˆ m + 3 | 2 Z 2 ¯ 2 K m ˆ K m ˆ = 20( ˆ K m + ˆ n (ˆ Z 2 m ˆ ˆ n − ˆ ˆ K ¯ Z − 2 Z − 1 Z 2¯ Z 2 m ¯ n ) − 2) 2 2 2 [K. Enqvist, L. Mether, SN],[SN] Sami Nurmi MSSM inflation
Outline MSSM inflation Supergravity Conclusions ahler potentials that yield A 2 = 40 m 2 K¨ ◮ Solved by: � � m ) α m | φ | 2 + . . . β m ln ( h m + h ∗ ( h m + h ∗ K = m ) + κ m m α = � α m , β = � β m α (36 α + 16 − 12 β ) + ( β + 7) 2 = 0 , ◮ Includes for example the values β = P β m α = P α m − 7 0 − 25 − 7 9 − 1 − 11 9 − 11 − 4 Sami Nurmi MSSM inflation
Outline MSSM inflation Supergravity Conclusions Higher order corrections ◮ Saddle point can be removed by higher order corrections V = 1 2 m 2 | φ | 2 − A λ 6 | φ | 6 + λ 2 | φ | 10 + O ( | φ 0 | ) 12 � �� � Leading order part O ( | φ 0 | 10 ) ◮ Corrections | φ 0 | 12 and | φ 0 | 14 crucial, | φ 0 | 16 affects the spectral index Sami Nurmi MSSM inflation
Outline MSSM inflation Supergravity Conclusions K¨ ahler potentials for the MSSM inflation ◮ Potential flat enough close to | φ 0 | if 3 Z 2 | φ | 2 + µ ˆ 2 | φ | 4 + ν ˆ 2 | φ | 6 + ρ ˆ 2 | φ | 8 + . . . K = ˆ K + ˆ Z 2 Z 3 Z 4 K = � Z 2 = κ � m ) α m and where ˆ m ) , ˆ m β m ln ( h m + h ∗ m ( h m + h ∗ β = P β m α = P α m γ = P α 2 δ = P α 3 m /β 2 m /β m m 1 − 7 0 4 − 3 µ δ 207 µ 2 + 162 − 25 − 46 81 − 22 − 2414 1863 µ − 2804 628 − 7 9 µ 23 ν 9 16767 − 855 µ 2 + 162 − 1 81 − 26 28 69255 − 3736 6556 7695 µ − 12596 − 11 9 µ 19 ν 9 100 µ 2 + 36 − 7 8 − 5 − 339 200 µ − 1371 73 − 11 − 4 2 µ 5 ν 1600 − 3 [Enqvist, Mether, SN],[SN] Sami Nurmi MSSM inflation
Outline MSSM inflation Supergravity Conclusions ◮ An example of the solutions: � � m ) α m − β m | φ | 2 � � m ) − β m − κ ( h m + h ∗ ( h m + h ∗ K = − ln m m with β m = − 1 , α 1 = 1 , α 2 = α 3 = α 4 = α 5 = − 1 4 , α 6 = α 7 = 0 Sami Nurmi MSSM inflation
Outline MSSM inflation Supergravity Conclusions Conclusions ◮ MSSM inflation can be realized ”naturally” in certain supergravity models ◮ Flat inflaton potential not accidental but a direct consequence of the supergravity model ◮ Requires a specific K¨ ahler potential, to some extent motivated by various string theory compactifications ◮ Many open questions: initial conditions 4 , dynamics of the moduli fields 5 , loop corrections... 4 [Allahverdi, Dutta, Mazumdar] 5 [Lalak, Turzynski] Sami Nurmi MSSM inflation
Recommend
More recommend
