The cosmological constant
15
by I, and are characterized by their power spectrum. The multi pole number lpeak
of the first peak in the power spectrum is determined by the total matter content of
the universe. In fact, lpeak '" 22000, where 00 == po/Pc measures the total energy
density PO relative to the critical density. The measured position of the first peak
yields the value (1.42). Thus, for a universe with just matter and a cosmological
constant, we get
Om + OA '" I.
(1.91)
When this result is combined with the supernova and other data, it is found that
Om '" 0.3
OA '" 0.7.
( 1.92)
In Planck units, this means that
Aeff = PvIM: _ n Pc '" 0 8 10-120
2
4 -
UA
4 -
. x
.
( 1.93)
Mp
Mp
Mp
There is currently no known explanation of this extremely small number. It
corresponds to ~t: ~ 10- 3 eV. It is generally believed that the particle physics
vacuum is the minimum of an effective potential in which the electroweak gauge
symmetry SU(2)L x U(I)y is spontaneously broken (see section 2.5). The value
of the effective potential at this minimum (p) has no effect on the particle physics.
By adding a constant Vo to the tree-level potential (2.93), it is easy to arrange that
the potential, including any radiative and temperature-dependent corrections, has
any desired value at the minimum. However, to do so requires the fine tuning of Vo
to ensure that the value (1.93) is obtained and it is this fine tuning that is regarded
as unnatural and for which an explanation is sought. The obvious first approach
to the problem is to seek a symmetry that requires A = 0 and then to explore
mechanisms that break the symmetry only slightly. The only known symmetry
that requires a vanishing cosmological constant is global supersymmetry. The
(fermionic) supersmmetry generator Q satisfies the anticommutation relation
{Q, Q} = 2yl' PI'
( 1.94)
where PI' is the energy-momentum vector. It follows [3] that. for any state 11/1),
(1/II PoI1/l) = (1/IIQaQ: + Q: Qa 11/1) ~ O.
( 1.95)
Thus, the energy of any non-vacuum state is positive and the vanishing of the
vacuum energy defines a unique, supersymmetric vacuum state 10) that satisfies
(OIPoIO) = 0 ~ QaIO) = o.
(1.96)
In a supersymmetric theory. all particles have supersymmetric partners (called
'sparticles') having opposite statistics. That is to say. the sparticle associated with
a fermi on is a hoson and the sparticle associated with a boson is a fermion. The
sparticles associated with the quarks and leptons, called respectively 'squarks'
15
by I, and are characterized by their power spectrum. The multi pole number lpeak
of the first peak in the power spectrum is determined by the total matter content of
the universe. In fact, lpeak '" 22000, where 00 == po/Pc measures the total energy
density PO relative to the critical density. The measured position of the first peak
yields the value (1.42). Thus, for a universe with just matter and a cosmological
constant, we get
Om + OA '" I.
(1.91)
When this result is combined with the supernova and other data, it is found that
Om '" 0.3
OA '" 0.7.
( 1.92)
In Planck units, this means that
Aeff = PvIM: _ n Pc '" 0 8 10-120
2
4 -
UA
4 -
. x
.
( 1.93)
Mp
Mp
Mp
There is currently no known explanation of this extremely small number. It
corresponds to ~t: ~ 10- 3 eV. It is generally believed that the particle physics
vacuum is the minimum of an effective potential in which the electroweak gauge
symmetry SU(2)L x U(I)y is spontaneously broken (see section 2.5). The value
of the effective potential at this minimum (p) has no effect on the particle physics.
By adding a constant Vo to the tree-level potential (2.93), it is easy to arrange that
the potential, including any radiative and temperature-dependent corrections, has
any desired value at the minimum. However, to do so requires the fine tuning of Vo
to ensure that the value (1.93) is obtained and it is this fine tuning that is regarded
as unnatural and for which an explanation is sought. The obvious first approach
to the problem is to seek a symmetry that requires A = 0 and then to explore
mechanisms that break the symmetry only slightly. The only known symmetry
that requires a vanishing cosmological constant is global supersymmetry. The
(fermionic) supersmmetry generator Q satisfies the anticommutation relation
{Q, Q} = 2yl' PI'
( 1.94)
where PI' is the energy-momentum vector. It follows [3] that. for any state 11/1),
(1/II PoI1/l) = (1/IIQaQ: + Q: Qa 11/1) ~ O.
( 1.95)
Thus, the energy of any non-vacuum state is positive and the vanishing of the
vacuum energy defines a unique, supersymmetric vacuum state 10) that satisfies
(OIPoIO) = 0 ~ QaIO) = o.
(1.96)
In a supersymmetric theory. all particles have supersymmetric partners (called
'sparticles') having opposite statistics. That is to say. the sparticle associated with
a fermi on is a hoson and the sparticle associated with a boson is a fermion. The
sparticles associated with the quarks and leptons, called respectively 'squarks'