Inflation from Axion Monodromy Enrico Pajer Cornell University Stockholm June 2011
Outline 1 Minimal requirements 2 Brane inflation 3 Inflation from axion monodromy 4 Conclusions Enrico Pajer (Cornell) Inflation from Axion Monodromy Stockholm June 2011 2 / 42
Outline 1 Minimal requirements 2 Brane inflation 3 Inflation from axion monodromy 4 Conclusions Enrico Pajer (Cornell) Inflation from Axion Monodromy Stockholm June 2011 3 / 42
Minimal requirements A successful model of inflation in string theory needs: Consistent (4D ?) effective description Something, e.g. V ( φ ), driving more than 60 efoldings of inflation Small, adiabatic, slightly red tilted and Gaussian curvature perturbations. Percent level precision! Graceful exit and reheating into SM fields Enrico Pajer (Cornell) Inflation from Axion Monodromy Stockholm June 2011 4 / 42
Consistent 4D description As long as H ≪ m s we can use SUGRA. Compactification 10 D → 4 D (EFT of warped compactification are poorly understood). Hierarchy: M Pl ≫ m s ∼ g 3 / 4 g s s V 1 / 2 M Pl ≫ m KK ∼ V 2 / 3 M Pl If we see tensors at r = 0 . 01 then H ≃ 5 · 10 − 5 M Pl � No one solves the 10D equations of motion Branes are smeared instead of localized Time dependence of the compact metric is neglected Enrico Pajer (Cornell) Inflation from Axion Monodromy Stockholm June 2011 5 / 42
Driving inflation Dimensional reduction leads to many moduli φ i . The multifield potential slow-roll conditions are ǫ ≡ 1 Pl g ij V i V j 2 M 2 ≪ 1 V 2 Pl g ij V ; ij η ≡ min e-value of M 2 ≪ 1 V where L ⊃ g ij ∂ µ φ i ∂ µ φ j . Inflation is not about finding one flat direction. Each modulus must be at a minimum or have a slow-roll flat potential. Moduli stabilization is essential [see Joe’s discussion] . Enrico Pajer (Cornell) Inflation from Axion Monodromy Stockholm June 2011 6 / 42
Curvature perturbations: data COBE normalization: V = (0 . 027) 4 ǫM 4 Pl Fixed by hand Red tilted: n s = 0 . 968 ± 0 . 024 Gaussian: f NL < O (100). Model dependent Adiabatic: δ cγ adiab < 0 . 02 (anti-correlated isocurvature), where adiab ≡ 2 δρ c /ρ c − 3 δρ γ / (4 ρ γ ) δ cγ δρ c /ρ c + 3 δρ γ / (4 ρ γ ) No tensors: r < 0 . 2 Enrico Pajer (Cornell) Inflation from Axion Monodromy Stockholm June 2011 7 / 42
Curvature perturbations: reproducing the data � Relatively easy to obtain once one has 60 efoldings Scale invariance is a consequence of the quasi de Sitter background The size of scalar and tensor perturbations are easily adjustable by rescaling V Adiabaticity is easily satisfied with slowly curving trajectories Non-Gaussianity can be interestingly large but generally compatible with the data Pre-inflationary remnants behave as in standard scenarios Enrico Pajer (Cornell) Inflation from Axion Monodromy Stockholm June 2011 8 / 42
Reheating � Not very well studied The embedding of the SM is typically not explicit Inflationary sector is often separated from the SM sector in the compact space Bulk propagation induced by KK-mode and massive string modes plays a key role Enrico Pajer (Cornell) Inflation from Axion Monodromy Stockholm June 2011 9 / 42
Summary of minimal requirements A successful model of inflation in string theory needs: Consistent 4D effective description Something, e.g. V ( φ ), driving more than 60 efoldings of inflation Small, adiabatic, slightly red tilted and Gaussian curvature perturbations Graceful exit and reheating into SM fields Enrico Pajer (Cornell) Inflation from Axion Monodromy Stockholm June 2011 10 / 42
What can we learn Questions that can be answered by and explicit UV embedding Is inflation possible and natural in a UV finite theory? (Yes. Probably no) Do the constraints from string theory single out certain characteristic observables? (No) Are there correlated observables? (Yes) Can we improve on the initial condition problem? (Arguably no) Enrico Pajer (Cornell) Inflation from Axion Monodromy Stockholm June 2011 11 / 42
Outline 1 Minimal requirements 2 Brane inflation 3 Inflation from axion monodromy 4 Conclusions Enrico Pajer (Cornell) Inflation from Axion Monodromy Stockholm June 2011 12 / 42
Brane Inflation Consider spacetime filling D3-branes in Type IIB [Dvali & Tye ’98] Six scalars, i.e. the position of the D3-brane. Inflation from open strings DBI like kinetic term Many contributions to the potential: background fluxes, anti-D3-branes, moduli stabilization, . . . Enrico Pajer (Cornell) Inflation from Axion Monodromy Stockholm June 2011 13 / 42
DBI kinetic term The DBI action gives � √− g � 1 − g ij ∂ µ φ i ∂ µ φ j S ⊃ g ij is the (e.g. Kalabi-Yau) metric of the internal space Slow-roll regime: g ij ˙ φ i ˙ φ j ≪ 1 Standard canonical kinetic term � √− g 1 2 g ij ∂ µ φ i ∂ µ φ j S ⊃ DBI regime 1 − g ij ˙ φ i ˙ φ j ≪ 1 Happens only for highly warped metrics g ij ∼ e − 2 A ˜ g ij All (infinitely many) higher derivative terms are important Maximum speed helps for prolonged inflation with steep potentials Enrico Pajer (Cornell) Inflation from Axion Monodromy Stockholm June 2011 14 / 42
Potentials for D3-branes Type IIB flux compactified on a warped Calabi-Yau [Giddings et al. 01] Imaginary self-dual (ISD) fluxes stabilize complex structure and axio-dilaton moduli Generically warped throats are present: locally there is an explicit warped Calabi-Yau metric (essential to specify the kinetic term) Potential can be divided in four parts [Baumann et al.] V ( φ ) = const + V Coulomb + V Bulk + V R V Coulomb attraction to anti D3-branes, if present. Too steep unless warping is introduced [Kachru et al. 03] V Bulk characterizing bulk perturbations to the local solution Enrico Pajer (Cornell) Inflation from Axion Monodromy Stockholm June 2011 15 / 42
Dynamics One can study the whole potential numerically [Agarwal et al. 11] or find particularly simple regimes [Baumann et al., Krause & EP 07] V is generically too steep One can fine tune an inflection point 60 efolds of standard small-field slow-roll inflation Can be compatible with the data Enrico Pajer (Cornell) Inflation from Axion Monodromy Stockholm June 2011 16 / 42
DBI inflation The EFT idea works perfectly but explicity constructions seem to fail: the warp factor does not remain strong enough for a long enough distance in field space [Baumann & McAllister 06] The DBI regime requires strong warping and steep potentials Only part of the 60 efolds can be in the DBI regime [Chen et al. 07, EP 08] Perturbations have a very small speed of sound c s ≪ 1 leading to very distinctive large non-Gaussianity Important UV input: the square root is radiatively stable and valid to all orders in α ′ Enrico Pajer (Cornell) Inflation from Axion Monodromy Stockholm June 2011 17 / 42
Summary of D-brane inflation Consistent 4D description Can give 60 efolds of inflation but needs fine tuning to the percent level Perturbations can easily be compatible with observations Slow-roll regime has no distinctive features DBI regime has characteristic non-Gaussianity. The UV-embedding guaranties the radiative stability and consistency of infinite many derivatives. Brane-anti-brane annihilation has been studied as mechanism for reheating Enrico Pajer (Cornell) Inflation from Axion Monodromy Stockholm June 2011 18 / 42
Outline 1 Minimal requirements 2 Brane inflation 3 Inflation from axion monodromy 4 Conclusions Enrico Pajer (Cornell) Inflation from Axion Monodromy Stockholm June 2011 19 / 42
Tensor modes and the Lyth bound The detection of tensor modes would fix the scale of inflation close to the GUT scale. Measuring tensor modes puts a lower bound on the range of variation of the inflaton [Lyth 98] √ � r dφ = dN 2 ǫ ≃ dN M Pl 8 � r ∆ φ N CMB > M Pl 0 . 01 30 ∆ φ above the cutoff makes the use of EFT suspicious This is the main motivation to consider axion monodromy inflation Enrico Pajer (Cornell) Inflation from Axion Monodromy Stockholm June 2011 20 / 42
Tensor modes and the Lyth bound The detection of tensor modes would fix the scale of inflation close to the GUT scale. Measuring tensor modes puts a lower bound on the range of variation of the inflaton [Lyth 98] √ � r dφ = dN 2 ǫ ≃ dN M Pl 8 � r ∆ φ N CMB > M Pl 0 . 01 30 ∆ φ above the cutoff makes the use of EFT suspicious This is the main motivation to consider axion monodromy inflation Schematically more Tensor High Large ⇒ ⇒ ⇒ UV-sensitive modes scale field Enrico Pajer (Cornell) Inflation from Axion Monodromy Stockholm June 2011 20 / 42
UV-sensitivity EFT approach: learn about higher scales studying UV-sensitive observables. Inflation is a UV-sensitive mechanism. Schematically φ n V ( φ ) = 1 2 m 2 φ 2 + � λ n M n − 4 n Pl Most models suffer from an η -problem We need to invoke a symmetry, e.g. shift symmetry Then we need a fundamental theory (UV-finite) to ask if, how and where the symmetry is broken. Enrico Pajer (Cornell) Inflation from Axion Monodromy Stockholm June 2011 21 / 42
Recommend
More recommend
