Transcript SHIFT SYMMETRY and INFLATION in SUPERGRAVITY

SHIFT SYMMETRY and
INFLATION in SUPERGRAVITY
Ph. Brax and J. Martin
hep/th0504168
to appear in PRD
Outline
The flatness problem in supergravity
Mutated chaotic inflation
Inflation and Supergravity

Inflation requires flat potentials

Almost scale invariant spectrum
requiring

In global susy, easy to obtain chaotic inflation

In supergravity the potential depends on
K Kahler potential, W superpotential
easy to obtain Hybrid inflation, tricky Chaotic inflation
KKLT Stabilisation and Inflation

In string theory

Stabilisation

Inflation

Brane-antibrane potential lifts the potential

Around the stabilised modulus
Moduli (volume of the compactifying manifold)
motion of D3 branes
mass of the inflaton of the Hubble scale
large value of
needs reappraisal
The flatness problem
 In supergravity models of inflation, the scalar potential
 For canonically normalised fields, large mass for the
inflaton
 Generically, scalar index
Shift Symmetry
 Inflaton
flat direction
 Lifted by interactions
 Along the flat direction
shift symmetry
 Natural in string theory
motion of D3/D7
Sugra implementation
Small arguments
Shift 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 inflation

Superpotential for modulus
Leads to AdS susy vacuum
Introduce a lifting term breaking susy

Superpotential for inflation
Chaotic inflation superpotential:
Can be obtained in the condensed phase of
D3/D7 system
COBE normalisation
and
The scalar potential
Curved inflationary trajectory
 Scalar potential
 Curved trajectory
Inflationary valley
 End of inflation
Mutated vs Hybrid
Spectral Index
 Comparison with chaotic inflation
 Mutated chaotic inflation
 Proviso: need to take into account the entropy
perturbations (two field inflation)
Conclusions
 Inflationary model combining modulus
stabilisation and chaotic inflation
 Shift symmetry alleviates the flatness
problem of F-term supergravity inflation
 Curved inflationary trajectory necessitates a
special treatment for perturbations (spectral
index…)