shift symmetry and inflation in supergravity ph. brax and j. martin hep/th0504168 to appear in prd
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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…)