The gravitino problem
177
The foregoing analysis shows that the dark matter might well be WIMPs but
there remains the question of what the WIMPs actually are. Since there are no
satisfactory candidates within the standard model. we must investigate plausible
extensions of it. The most favoured. which has been studied in great detail in
recent years, is the MSSM. (See. for example. [11 D. We shall say more about the
MSSM in section 6.4. First we discuss the possibility that dark matter is made of
gravitinos, particles that occur in any locally supersymmetric theory.
6.3 The gravitino problem
In a supersymmetric theory, all particles have an associated superpartner, called a
'sparticle', whose spin differs by ! from that of the original particle. In a (locally
supersymmetric) supergravity theory, the sparticle associated with the (spin-2)
graviton has spin ~ and is called the 'gravitino'. When supersymmetry is broken,
the gravitino acquires a non-zero mass (see chapter 5 of [11], for example)
m3/2 = e Go / 2 mp
(6.29)
where Go is the expectation value of G in the physical vacuum, with G defined in
(2.144), and mp = G"I/2 = 1.22 X 10 19 GeV is the Planck mass. Ifgravitinos
have survived until the present epoch, then their energy density Pl/2.0 could, in
principle, dominate but not exceed [ 12] the present total energy density PO of the
universe. Thus.
03/2 < 00
(6.30)
where 00 is defined in (1.41) and
n
P3/2.0
U3/2= - - .
(6.31)
Pc
As for neutrinos, we can use this to bound m3/2. Since gravitinos interact only
gravitationally, their interaction rate
r3/2.int ..... G~T S ..... ~
(6.32)
m 4 p
just on dimensional grounds. They decouple when
T2
r3/2.int = H ..... m p
(6.33)
which occurs when T ..... m p and while they are still relativistic. After decoupling,
the number of gravitinos per comoving volume is constant so, as in (5.24),
Y3/2.dec = Y3/2.0.
(6.34)
177
The foregoing analysis shows that the dark matter might well be WIMPs but
there remains the question of what the WIMPs actually are. Since there are no
satisfactory candidates within the standard model. we must investigate plausible
extensions of it. The most favoured. which has been studied in great detail in
recent years, is the MSSM. (See. for example. [11 D. We shall say more about the
MSSM in section 6.4. First we discuss the possibility that dark matter is made of
gravitinos, particles that occur in any locally supersymmetric theory.
6.3 The gravitino problem
In a supersymmetric theory, all particles have an associated superpartner, called a
'sparticle', whose spin differs by ! from that of the original particle. In a (locally
supersymmetric) supergravity theory, the sparticle associated with the (spin-2)
graviton has spin ~ and is called the 'gravitino'. When supersymmetry is broken,
the gravitino acquires a non-zero mass (see chapter 5 of [11], for example)
m3/2 = e Go / 2 mp
(6.29)
where Go is the expectation value of G in the physical vacuum, with G defined in
(2.144), and mp = G"I/2 = 1.22 X 10 19 GeV is the Planck mass. Ifgravitinos
have survived until the present epoch, then their energy density Pl/2.0 could, in
principle, dominate but not exceed [ 12] the present total energy density PO of the
universe. Thus.
03/2 < 00
(6.30)
where 00 is defined in (1.41) and
n
P3/2.0
U3/2= - - .
(6.31)
Pc
As for neutrinos, we can use this to bound m3/2. Since gravitinos interact only
gravitationally, their interaction rate
r3/2.int ..... G~T S ..... ~
(6.32)
m 4 p
just on dimensional grounds. They decouple when
T2
r3/2.int = H ..... m p
(6.33)
which occurs when T ..... m p and while they are still relativistic. After decoupling,
the number of gravitinos per comoving volume is constant so, as in (5.24),
Y3/2.dec = Y3/2.0.
(6.34)