Tachyon Mediated Non-Gaussianity. Louis Leblond Texas A&M - PowerPoint PPT Presentation

Tachyon Mediated Non-Gaussianity. Louis Leblond Texas A&M Cosmo 08 University of Wisconsin-Madison Bhaskar Dutta, Jason Kumar, L.L. arXiv:0805.1229 L.L. and Sarah Shandera hep-th/0610321

Non-Gaussianity in the CMB Gaussianity is a consequence of the slow-rolling conditions (from which the inflaton behaves like a free field). Detectable NG can be generated by going beyond the standard single field slow-roll approximation. non-standard kinetic term (e.g. DBI) Silverstein & Tong Multi-fields (this talk, present a string theory motivated D-term inflation with NG from multi-fields) WMAP5 x, t ) = ζ Gauss + 3 5 f NL ( ζ 2 Gauss − ζ 2 ζ ( � Gauss ) − 9 < f N L < 111 Louis Leblond, Cosmo 08, Madison

Tachyon Mediated Non-Gaussianity In Hybrid inflation Curvature T , φ ζ Visible Hidden many string theory models are of this type Louis Leblond, Cosmo 08, Madison

A Quick History In multi-fields inflation, curvature ( )is NOT constant after ζ Bernardeau & Uzan horizon exit and NG can be generated in its evolution. Bernardeau, Kofman, Uzan In general, one needs to integrate these effects over the whole trajectory but in many systems, the effects can all be located at the end simplifying the analysis. Linde & Mukhanov Lyth & Wands Curvaton: a new field starts dominating the energy Moroi & Takahashi density well after the end of inflation. Dvali, Gruzinov & Modulated Reheating: Reheating starts everywhere Zaldarriaga in sync, but the final temperature is modulated. Lyth Modulated End: The onset of reheating is modulated but then proceed everywhere the same. Alabidi & Lyth Louis Leblond, Cosmo 08, Madison

A Quick History In multi-fields inflation, curvature ( )is NOT constant after ζ Bernardeau & Uzan horizon exit and NG can be generated in its evolution. Bernardeau, Kofman, Uzan In general, one needs to integrate these effects over the whole trajectory but in many systems, the effects can all be located at the end simplifying the analysis. Linde & Mukhanov Lyth & Wands Curvaton: a new field starts dominating the energy Moroi & Takahashi density well after the end of inflation. Dvali, Gruzinov & Modulated Reheating: Reheating starts everywhere Zaldarriaga in sync, but the final temperature is modulated. Lyth Modulated End: The onset of reheating is modulated but then proceed everywhere the same. Alabidi & Lyth Louis Leblond, Cosmo 08, Madison

Basic Idea Couple Hybrid inflation (2 fields) to an extra field. (Here Tachyon = Waterfall field) = V inf ( φ ) + V hid ( χ ) + V mess ( φ , χ , T )] V φ There is no direct coupling between and . They couple only through the T χ which is very massive during inflation. Inflation ends at a critical value of the inflaton for which the mass of the tachyon is zero. Horizon exit φ c ( χ ) A B Inflation ends modulated by C t quantum fluctuation of the hidden field Louis Leblond, Cosmo 08, Madison

From field perturbations to curvature. delta N formalism ζ = δ N Sasaki & Stewart The new field only � φ c ( χ ) H change the end N = d φ ˙ φ of inflation φ ∗ * = horizon exit � � ∂ 2 φ c �� ∂φ c δ N = − H + H +1 H δχ 2 − < δχ 2 > � � � � δφ ∂χ δχ + · · · � � � ˙ ˙ ˙ ∂χ 2 2 φ φ φ � � � φ c φ c ∗ Usual Note sign contribution difference � ∂φ c � “transfer function” γ ≡ � ∂χ � φ c Louis Leblond, Cosmo 08, Madison

The 2-pt function � 1 H 2 + γ 2 κ 2 � P ζ ∗ 2 = 8 π 2 M 2 ǫ ∗ ǫ f pl η χ ∼ 0 . 01 κ ∼ e − η χ N e N e ∼ 55 include a “damping” κ ∼ 0 . 6 most models must have γ < 1 In most models, the potential is steeper at the end than at horizon exit (could argue it is unnatural to have it the other way around) Lyth & Riotto In brane inflation, inflation ends with a tachyon. L.L. & Shandera Coulombic potential is too steep while the DBI regime Chen, Gong, Shiu does better. Most recent analysis found no effects. Alabidi and Lyth counter example: hilltop potential which flattens out at the end Louis Leblond, Cosmo 08, Madison

The intrinsic contribution to f NL In most model the contribution to the 2-pt will be negligible but the 3- pt function can be significant. Because, the hidden field is NOT the inflaton, its potential can be steeper and it can be strongly interacting. < δζ 3 > < δχ 3 > � k 3 NL ∼ N e M p γ 3 κ 6 ǫ 2 f int ∗ V , χχχ F ( � k 1 , � k 2 , � k 3 ) ∼ − N e H 2 V , χχχ κ 6 i � k 3 ǫ 3 / 2 H 2 i f Falk, Rangarajan, Srednicki, ’93 Zaldarriaga Lyth, Malik Seery Bernardeau, Brunier T , φ ζ χ Barnaby, Cline Louis Leblond, Cosmo 08, Madison

The Non-linear Contribution From the non-linear piece in the delta N, we will get a non-zero 3-pt curvature even for gaussian χ � � ∂ 2 φ c �� δ N = − H + H ∂φ c H +1 δχ 2 − < δχ 2 > � � � � δφ ∂χ δχ + · · · � � � ˙ ˙ ˙ ∂χ 2 2 φ φ φ � � � φ c φ c ∗ The ratio of these two contributions γ ∼ χ f int � � γ V , χχχ � = 1 β ∼ η χ N e κ 2 NL � � β ≡ H 2 N e κ � � f loc γ , χ 3 � NL This is always smaller than 1 but one can still have a significant fraction of NG in intrinsic Louis Leblond, Cosmo 08, Madison

The Non-linear Contribution From the non-linear piece in the delta N, we will get a non-zero 3-pt curvature even for gaussian χ The ratio of these two contributions γ ∼ χ f int � � γ V , χχχ � = 1 β ∼ η χ N e κ 2 NL � � β ≡ H 2 N e κ � � f loc γ , χ 3 � NL This is always smaller than 1 but one can still have a significant fraction of NG in intrinsic Louis Leblond, Cosmo 08, Madison

The Non-linear Contribution From the non-linear piece in the delta N, we will get a non-zero 3-pt curvature even for gaussian χ ǫ 2 NL ∼ − ∂γ f loc ∂χγ 2 κ 4 M p ∗ ǫ 3 / 2 f The ratio of these two contributions γ ∼ χ f int � � γ V , χχχ � = 1 β ∼ η χ N e κ 2 NL � � β ≡ H 2 N e κ � � f loc γ , χ 3 � NL This is always smaller than 1 but one can still have a significant fraction of NG in intrinsic Louis Leblond, Cosmo 08, Madison

IBM-flation Can realize D-term inflation, using open string between branes (strings are in vector- like rep) φ S Using gauge invariance one can “brane a b engineered” flat direction by forbidding dimension 6 operators for example. � - ϕ 1 � + T and large NG mediated by the tachyon c n s ∼ 1 can get a regime with W = λφ T ϕ 1 + λ NG χ T ϕ 2 cosmic strings Dutta, Kumar, L.L Battye, Garbrecht, Moss Bevis, Hindmarsh, Kunz, Urestilla Louis Leblond, Cosmo 08, Madison

IBM-flation χ Can realize D-term inflation, using open string between branes (strings are in vector- like rep) φ S Using gauge invariance one can “brane a b engineered” flat direction by forbidding ϕ 2 dimension 6 operators for example. � - ϕ 1 � + T and large NG mediated by the tachyon c n s ∼ 1 can get a regime with W = λφ T ϕ 1 + λ NG χ T ϕ 2 cosmic strings Dutta, Kumar, L.L Battye, Garbrecht, Moss Bevis, Hindmarsh, Kunz, Urestilla Louis Leblond, Cosmo 08, Madison

Detailed example The tachyon mass depends on both and φ χ T = − g 2 ξ + λ 2 φ 2 + ( λ 2 m 2 NG − qg 2 2 ) χ 2 so the non-linear contribution dominate γ ≈ χ a point in parameter space f int NL ∼ − 8 , n s ∼ 1 . 002 , Gµ ∼ 7 × 10 − 7 . f loc NL ∼ 45 , Louis Leblond, Cosmo 08, Madison

Conclusion One can generate observable NG at the end of hybrid inflation with a rich structure. Many models fails because the potential is too steep at the end. D-term inflation in the regime of flat spectrum can lead to observable NG. The NG has the local shape and both sign can be obtained. One can write a string theory motivated model with such features. Another, more detailed but similar models will be presented here. L.L. & Shandera Haack, Kallosh, Krause, Huang, Shiu & Underwood Linde, Lust, Zagermann Langlois, Renaux-Patel, Steer, Tanaka A new look into multi-field DBI? Louis Leblond, Cosmo 08, Madison