UNIVERSAL BEHAVIOUR OF NON- MINIMAL MODELS OF INFLATION

Transcription

1 UNIVERSAL BEHAVIOUR OF NON- MINIMAL MODELS OF INFLATION Jan Pieter van der Schaar Delta Institute for Theoretical Physics University of Amsterdam CP3 Origins seminars, Oct , Odense arxiv: [he-th] with Benjamin Mosk

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3 Oortunities:! Postdocs and Fellows! PhD students! Mini-workshos! Extended visitors! Triangle meetings! Education & Outreach!! Contact information:! Science Park Amsterdam! DeltaITP.nl

4 PLAN General introduction to inflation and non-minimal models Strong couling Starobinsky attractors Weak couling chaotic attractors Summary

5 GENERAL INTRO The case for inflation A short history of non-minimal models Non-minimal models and ure gravity Motivation for another look

6 P s = A s k k ns 1 P t = A t k k nt n s 1=2 6 r = A t A s = 16

7 P t = A t k k nt r = A t A s = 16 NOT BICEP BITES THE DUST

8 SINGLE FIELD SLOW-ROLL MINIMALLY COUPLED OCCAM s razor BUT: UV consistency Observations: multile fields/ non-minimal couling Organising rincile(s) m 2 H 2

9 NON-MINIMAL HISTORY Sontaneous symmetry breaking inducing mpl, ameliorate fine-tuning issues Relation to Starobinsky s R+R 2 Higgs inflation Phys.Rev.D31 (1985) 3046 Accetta, Zoller and Turner Phys.Rev.D31 (1990) 1783 Fakir and Unruh astro-h/ Kaiser Phys.Lett.B 91, 99 (1980) Starobinsky Phys.Lett.B 145, 176 (1984) Whitt ArXiv: [he-th] Bezrukov and Shaoshnikov L = g ale 1 2 ( )R 1 2 (@ )2 U( )

10 PURE GRAVITY n s 1= 2 N ; r = 12 N 2 BUT: order 1 higher curvature correction

11 RENEWED INTEREST 3 Higgs inflation Suergravity embedding. The non-minimal couling can be embedded in suergravity. We follow the setu of [13], which introduces two chiral multilets with scalar fields and S. The former will contain the inflaton while the latter is resonsible for SUSY breaking. We thus take the sgoldstini to be orthogonal to the inflaton, allowing for an arbitrary scalar otential and avoiding the restrictions of [14]. While the original roosal has a secific Ka hler otential and an arbitrary function in the suerotential, we take the Ka hler otential to deend on ( 2 ) which will be related to the scalar otential. Our final exressions are: )2 K = 3 log[ 12 ( ( 2 ) + ( 2 )) 13 S S + 16 ( (S S )2 + ], W = Sf ( 2 ), (19) ( 2 ) + ( 2 ) where ( 2 ) = 1 + f ( 2 ) and f ( 2 ) is a real holomorhic function. This leads exactly to thebosonic model discussed above uon identifying = / 2 while S = 0. It can easily be seen that this is a consistent truncation. The suerconformal version of this model exlains the simlicity of the Jordan frame otential in these models: in a gauge where the conformon is fixed, the suerconformal otential is given by W = Sf ( 2 ) (in the notation of [15, 16]). This imlies that the Jordan frame otential at S = 0, = / 2, is given by 3 2 The PLANCK sweetsot 1/N exansion Universal (strong couling) attractor 4 and, which can always be satisfied by suitable choice of. For the secific case of the 4 theory this was discussed in detail in [5]. Embedding in suer(conformal) 2 = 2f 2( ). This model generalizes the suersymmetric embedding VJ = Figure from0.960 Kallosh, Linde and0.975 Roest0.980 arxiv: [he-th] Kallosh and Linde arxiv: [he-th] Kallosh, Linde and Roest arxiv: [he-th] Roest arxiv: [he-th] Giudice and Lee and more

12 STRONG COUPLING ATTRACTOR L = ( vac )=1; U( vac )=0 g! ale 1 L = 2 ( )R 1 2 (@ )2 U( ) g R ! 0 2 (@ ) 2! U 2 stee V ( )= 1 e 2 3 2

13 Large couling limits ( ) = 1 + f ( ) ; ( ) = f ( ) universal attractor f( ) = n induced (Note: fvac different!) 3 n=2: Higgs universal attractor 4 and, which can always be satisfied by suitable choice of. For the secific case of the 4 theory this was discussed in detail in [5]. Suergravity embedding. The non-minimal couling can be embedded in suergravity. We follow the setu of [13], which introduces two chiral multilets with scalar fields and S. The former will contain the inflaton while the latter is resonsible for SUSY breaking. We thus take the sgoldstini to be orthogonal to the inflaton, allowing for an arbitrary scalar otential and avoiding the restrictions of [14]. While the original roosal has a secific Ka hler otential and an arbitrary function in the suerotential, we take the Ka hler otential to deend on ( 2 ) which will be related to the scalar otential. Our final exressions are: )2 K = 3 log[ 12 ( ( 2 ) + ( 2 )) 13 S S + 16 ( (S S )2 + ], W = Sf ( 2 ), (19) ( 2 ) + ( 2 ) where ( 2 ) = 1 + f ( 2 ) and f ( 2 ) is a real holomorhic function. This leads exactly to thebosonic model discussed above uon identifying = / 2 while S = 0. It can easily be seen that this is a consistent truncation. The suerconformal version of this model exlains the simlicity of the Jordan frame otential in these models: 3 n>1: universal attractor models violate erturbative unitarity before hitting the Planck scale, as oosed to induced models Universal inflationary behaviour due to large stretching Figure from0.960 Kallosh, Linde and0.975 Roest0.980 arxiv: [he-th] Kallosh, Linde and Roest arxiv: [he-th] Giudice and Lee

14 WEAK COUPLING LIMIT flat Small derivatives around vacuum field value Non-vanishing first derivative: quadratic chaotic inflation Higher order owers small due to flat conformal factor Chaotic redictions for ns and r are universal Scale is deendent on the derivative (as comared to stee limit)

15 Small couling limits ( )= f( ) f( )= m See also: arxiv: [he-th] Kallosh, Linde and Roest

16 Generalisations stee flat order 2n chaotic weak

17 SUMMARY Derived general criteria for existence of a chaotic attractor Induced (ower law) models feature a chaotic attractor Scale of inflation distinguishes secifics of the conformal factor Universal aroach Did not discuss suer(conformal) gravity or string embedding Fine-tuning (EFT)? arxiv: [he-th] van der Schaar, Mosk arxiv: [he-th] Kallosh, Linde and Roest Thanks for your attention!