ChapterS
Inflation in supergravity
8.1 Introduction
In order for new inflation (slow-roll inflation) to produce sufficient e-folds of
inflation, it is necessary for the effective potential for the inflaton to be very
flat near the point where slow roll begins. In general, even if the tree-level
potential has this property, this flatness may be lost once radiative corrections
are included. For this reason, it is advantageous in constructing models of
inflation to employ a supersymmetric theory where cancellations of radiative
corrections are enforced by supersymmetry. If we want a supersymmetric theory
that contains gravity, the natural approach, as discussed in section 2.8, is to
construct a locally supersymmetric theory (supergravity). Once a superpotential
and a Kabler potential have been chosen for the inflaton field, the Lagrangian
terms and the effective potential for the inflaton follow.
As we shall see, viable inflationary theories can be constructed with simple
choices of superpotentials and Kabler potentials. The positive value of the
potential required for inflation may arise either from the first term in (2.156),
the F-term, or from the second term in (2.156), the D-term, in the case that the
inflaton is coupled to fields charged under a U (1) gauge symmetry. Theories of
chaotic inflation and hybrid inflation may also be constructed.
There are two potential problems arising from supergravity models of
inflation which will be addressed in section 8.5 and section 8.6. The first
is that gravitons (whose density was rendered negligible by inflation) may be
produced by reheating after inflation. It is necessary to arrange that the reheating
temperature is such that the gravitons do not have a serious effect on the
abundances of deuterium and of 3He relative to 4He abundance.
The second problem (the so-called 'Polonyi' problem) results from the
presence in supergravity theories of scalar fields with only gravitational strength
interactions, which release the energy stored in their expectation values at very
late times. This can lead to negligibly low helium and deuterium abundances at
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DOl: 10.1201/9780367806637-8
Inflation in supergravity
8.1 Introduction
In order for new inflation (slow-roll inflation) to produce sufficient e-folds of
inflation, it is necessary for the effective potential for the inflaton to be very
flat near the point where slow roll begins. In general, even if the tree-level
potential has this property, this flatness may be lost once radiative corrections
are included. For this reason, it is advantageous in constructing models of
inflation to employ a supersymmetric theory where cancellations of radiative
corrections are enforced by supersymmetry. If we want a supersymmetric theory
that contains gravity, the natural approach, as discussed in section 2.8, is to
construct a locally supersymmetric theory (supergravity). Once a superpotential
and a Kabler potential have been chosen for the inflaton field, the Lagrangian
terms and the effective potential for the inflaton follow.
As we shall see, viable inflationary theories can be constructed with simple
choices of superpotentials and Kabler potentials. The positive value of the
potential required for inflation may arise either from the first term in (2.156),
the F-term, or from the second term in (2.156), the D-term, in the case that the
inflaton is coupled to fields charged under a U (1) gauge symmetry. Theories of
chaotic inflation and hybrid inflation may also be constructed.
There are two potential problems arising from supergravity models of
inflation which will be addressed in section 8.5 and section 8.6. The first
is that gravitons (whose density was rendered negligible by inflation) may be
produced by reheating after inflation. It is necessary to arrange that the reheating
temperature is such that the gravitons do not have a serious effect on the
abundances of deuterium and of 3He relative to 4He abundance.
The second problem (the so-called 'Polonyi' problem) results from the
presence in supergravity theories of scalar fields with only gravitational strength
interactions, which release the energy stored in their expectation values at very
late times. This can lead to negligibly low helium and deuterium abundances at
226
DOl: 10.1201/9780367806637-8