PRICE OF WMAP INFLATION IN SUPERGRAVITY

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1 PRICE OF WMAP INFLATION IN SUPERGRAVITY Zygmunt Lalak Planck 06 with J. Ellis, S. Pokorski and K. Turzyński

2 Outline - Inflation and WMAP3 data - Embedding inflation in supergravity - Moduli stabilisation - Inflation from matter-like fields with (i) F-type stabilisation or (ii) D-type stabilisation Summary and Conclusions

3 References D.N. Spergel et al., astro-ph/ U. Seljak et al., astro-ph/ J. Ellis, D. Nanopoulos, K. Olive, K. Tamvakis; G. Coughlan, R. Holman, P. Ramond, G.G. Ross E. Cremmer, S. Ferrara, C. Kounnas, D. Nanopoulos, J. Ellis, A. Lahanas E. Witten, J. Derendinger, L. Ibanez, H.-P. Nilles J. Ellis, K. Enqvist, D. Nanopoulos, K. Olive, M. Srednicki S. Giddings, S. Kachru, J. Polchinski S. Kachru, R. Kallosh, A. Linde, S. Trivedi P. Binetruy, G. Dvali, R. Kallosh, A. Van Proeyen E. Dudas, S. Vempati G. Villadoro, F. Zwirner Z. Lalak, G.G. Ross, S. Sarkar WMAP3 supergravity inflation flux stabilisation D-term stabilisation no-scale inflation consistent D-terms no-scale structure

4 Observables chaotic new, or symmetry-breaking Simple potentials consistent with WMAP3

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7 Can any of these potentials be embedded in supergravity? In 4d N=1 SUGRA For canonically normalized fields and So typically slow-roll rather difficult to achieve

8 Ways out? - Pseudo-goldstone inflation, for instance with the phase of - D-term inflation - Modification (softening) of the Kaehler potential -Particulary well motivated is the no-scale structure of the Kaehler potential: (i) it appears in string theory compactifications (ii) leads to models which are very close to globally supersymmetric models (iii) in particular it gives a semi-positive scalar potential

9 simple no-scale Kaehler potential kinetic terms positiive definite scalar potential resembles globally supersymmetric case for any form of the superpotential W (if independent of T)

10 Hence, any inflation spoiled by curvature along the direction of T One needs to stabilize T Concentrate of 4d SUGRA 2 options: (i) stabilise (ii) stabilise

11 Assume T frozen and take quadratic superpotential Inflation impossible But with Symmetry-breaking inflation if No chaotic inflation

12 Then with the quadratic superpotential Simple quadratic inflation allowed by WMAP3

13 More details of the evolution Kinetic energy of (imaginary part of T) and of redshifts away

14 In microscopic models T must be stabilised dynamically Try F-type stabilisation need to lift the vacuum energy add a constant one may add brane-antibrane potential, but this doesn t work

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17 Brane-antibrane potential minimum at However, has a large negative eigenvalue along T Inflation spoiled by curvature of the potential along T

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19 Gauging a U(1) symmetry Supersymmetry breaking after inflation

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26 Conclusions and Outlook Simple inflation consistent with WMAP3 possible in no-scale supergravities Moduluis stabilised by a separate mechanism (higher-scale dynamics) Tuning between the inflationary sector and stabilisation sector necessary D-term stabilisation offers least finely-tuned models and allows for a separation of mass scales both chaotic and symmetry-breaking inflation possible in this case With F-stabilisation and brane-antibrane potential, inflation spoiled by curvature along modulus direction For simple models inflation severely constrains post-inflationary vacuum Analysis of fluctuations rather complex when scales merge