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Inflation in supergravity
8.6 The Polonyi problem
This generic problem results from the presence in a theory of a light scalar field
which has only gravitational strength interactions, with the consequence that it
is decoupled during most of the history of the universe and eventually releases
energy stored in its expectation value at a very late time [11]. This release
of energy increases the entropy of the universe at a low temperature thereby
producing a negligible baryon abundance and, worse still, negligible helium and
deuterium abundances. The temperature may then be too low for the required
abundances to be recreated.
A simple example of this problem. from which it derives its name, occurs in
the context of the Polonyi model for supersymmetry breaking in supergravity. We
describe first this mechanism for supersymmetry breaking. The Polonyi model
is an example of a model in which supersymmetry breaking occurs in a 'hidden
sector', by which is meant a sector of the theory which couples to the 'observable
sector' of quarks, leptons, gauge fields, Higgs scalars, and their supersymmetric
partners only through gravitational interactions. The hidden sector of the Polonyi
model employs a single gauge-singlet scalar field j, (not the inflaton) and its
supersymmetric fermionic partner with superpotential
W(j,) = jl2(j, + /3).
(8.87)
(We are using the same notation for the chiral superfield and its scalar field
component.) Minimal kinetic terms are chosen so that G of (2.144) has the form
G = j,*j, + In \W\2.
(8.88)
In (8.87), jl is a real parameter with dimensions of mass and
/3=2--J3
(8.89)
in units where Mp = I. The parameter /3 has been fixed to this value so that the
effective potential of (2.147)
V = jl4e~·~(ll + j,*(j, + /3)1 2 - 31j, + /312)
(8.90)
has its absolute minimum at
j,=-J3-1
(8.91)
with V = 0 and, so, the desirable feature of a vanishing cosmological constant in
the physical vacuum. At this minimum,
a~ + j,*W = -J3jl2 :f:: O.
(8.92)
a~
Consequently, supersymmetry is broken. as discussed after (2.152).
Inflation in supergravity
8.6 The Polonyi problem
This generic problem results from the presence in a theory of a light scalar field
which has only gravitational strength interactions, with the consequence that it
is decoupled during most of the history of the universe and eventually releases
energy stored in its expectation value at a very late time [11]. This release
of energy increases the entropy of the universe at a low temperature thereby
producing a negligible baryon abundance and, worse still, negligible helium and
deuterium abundances. The temperature may then be too low for the required
abundances to be recreated.
A simple example of this problem. from which it derives its name, occurs in
the context of the Polonyi model for supersymmetry breaking in supergravity. We
describe first this mechanism for supersymmetry breaking. The Polonyi model
is an example of a model in which supersymmetry breaking occurs in a 'hidden
sector', by which is meant a sector of the theory which couples to the 'observable
sector' of quarks, leptons, gauge fields, Higgs scalars, and their supersymmetric
partners only through gravitational interactions. The hidden sector of the Polonyi
model employs a single gauge-singlet scalar field j, (not the inflaton) and its
supersymmetric fermionic partner with superpotential
W(j,) = jl2(j, + /3).
(8.87)
(We are using the same notation for the chiral superfield and its scalar field
component.) Minimal kinetic terms are chosen so that G of (2.144) has the form
G = j,*j, + In \W\2.
(8.88)
In (8.87), jl is a real parameter with dimensions of mass and
/3=2--J3
(8.89)
in units where Mp = I. The parameter /3 has been fixed to this value so that the
effective potential of (2.147)
V = jl4e~·~(ll + j,*(j, + /3)1 2 - 31j, + /312)
(8.90)
has its absolute minimum at
j,=-J3-1
(8.91)
with V = 0 and, so, the desirable feature of a vanishing cosmological constant in
the physical vacuum. At this minimum,
a~ + j,*W = -J3jl2 :f:: O.
(8.92)
a~
Consequently, supersymmetry is broken. as discussed after (2.152).