SHIFT SYMMETRY and SHIFT SYMMETRY and INFLATION in SUPERGRAVITYINFLATION in SUPERGRAVITY

Ph. Brax and J. MartinPh. Brax and J. Martinhep/th0504168hep/th0504168

to appear in PRDto appear in PRD

OutlineOutline

The flatness problem in supergravityThe flatness problem in supergravity

Mutated chaotic inflationMutated chaotic inflation

Inflation and SupergravityInflation and Supergravity Inflation requires Inflation requires flat potentialsflat potentials

Almost scale invariant spectrum Almost scale invariant spectrum

requiring requiring

In global susy, easy to obtain In global susy, easy to obtain chaotic inflationchaotic inflation

In supergravity the potential depends onIn supergravity the potential depends on

K K Kahler potential,Kahler potential, W superpotential W superpotential

easy to obtain easy to obtain Hybrid inflation, Hybrid inflation, tricky tricky Chaotic inflationChaotic inflation

KKLT Stabilisation and InflationKKLT Stabilisation and Inflation In string theory In string theory Moduli Moduli (volume of the compactifying manifold)(volume of the compactifying manifold)

StabilisationStabilisation

Inflation motion of D3 branesInflation motion of D3 branes

Brane-antibrane potential lifts the potentialBrane-antibrane potential lifts the potential

Around the stabilised modulusAround the stabilised modulus

mass of the inflaton of the Hubble scalemass of the inflaton of the Hubble scale

large value of large value of

needs reappraisalneeds reappraisal

The flatness problemThe flatness problem

In supergravity models of inflation, the scalar potentialIn supergravity models of inflation, the scalar potential

For canonically normalised fields, large mass for the For canonically normalised fields, large mass for the inflatoninflaton

Generically, scalar index Generically, scalar index

Shift SymmetryShift Symmetry

Inflaton flat direction Inflaton flat direction Lifted by interactionsLifted by interactions Along the flat direction shift symmetryAlong the flat direction shift symmetry

Natural in string theory motion of D3/D7Natural in string theory motion of D3/D7

Sugra implementationSugra implementation

Small argumentsSmall arguments

Shift symmetryShift symmetry

Special form of the superpotential

After a Kahler transformation

Inflation obtained by breaking shift symmetry in the superpotential

Does not generate large values of the mass

Mutated chaotic inflationMutated chaotic inflation Superpotential for modulusSuperpotential for modulus

Leads to AdS susy vacuum Leads to AdS susy vacuum

Introduce a lifting term breaking susy and Introduce a lifting term breaking susy and

Superpotential for inflationSuperpotential for inflation

Chaotic inflation superpotential: Chaotic inflation superpotential:

Can be obtained in the condensed phase of Can be obtained in the condensed phase of D3/D7 systemD3/D7 system

COBE normalisation COBE normalisation

The scalar potentialThe scalar potential

Curved inflationary trajectoryCurved inflationary trajectory

Scalar potentialScalar potential

Curved trajectoryCurved trajectory

Inflationary valleyInflationary valley

End of inflation End of inflation

Mutated vs HybridMutated vs Hybrid

Spectral IndexSpectral Index

Comparison with chaotic inflationComparison with chaotic inflation

Mutated chaotic inflationMutated chaotic inflation

Proviso: need to take into account the entropy Proviso: need to take into account the entropy perturbations (two field inflation)perturbations (two field inflation)

ConclusionsConclusions

Inflationary model combiningInflationary model combining modulus modulus stabilisation stabilisation and and chaotic inflationchaotic inflation

Shift symmetry alleviates the flatness Shift symmetry alleviates the flatness problem of F-term supergravity inflationproblem of F-term supergravity inflation

Curved inflationary trajectory necessitates a Curved inflationary trajectory necessitates a special treatment for perturbations (spectral special treatment for perturbations (spectral index…)index…)