16
The standard model of cosmology
and 'sleptons', are (spin-O) scalar particles and, in a supersymmetric theory, they
must have the same mass and quantum numbers as the original particles. This
has the important consequence that the vanishing cosmological constant result is
unaffected by quantum effects, because supersymmetry ensures that any quantum
corrections arising from fermion loops, say, are cancelled by those that arise
from the bosonic loops of the associated sparticle. It has yet to be demonstrated
experimentally that supersymmetry has anything to do with reality. None of the
sparticles associated with the known particles has ever be seen. (It is hoped that
they will be discovered at the Large Hadron Collider (LHC).) Supersymmetry
(susy), if present at all, is therefore a broken symmetry. It then follows from
(1.95) that the vacuum energy is positive definite. The experimental limits on the
sparticle masses require that
msusy ~ 100 GeV.
(1.97)
If something like this bound were to set the scale for Pv8l:' then
~ '" 10- 68 •
(1.98)
Mp
Although small compared with the 0(1) expected in a generic quantum theory
of gravity, this is still very much larger than the value (1.93) derived from the
supernovae and Wilkinson Microwave Anisotropy Probe (WMAP) data. Thus,
if this were the only contribution to the vacuum energy density, we should be
confronted with an unmitigated disaster.
However, including gravity in any supersymmetric theory inevitably leads
to a supergravity theory, in which supersymmetry is a local, rather than a global,
symmetry. This is because in GR the momentum generator Pp. becomes a local
field generating diffeomorphisms of spacetime. Then, in a supersymmetric theory
incorporating GR, the supersymmetry generators too become local fields: this is
why supergravity emerges as the low-energy limit of string theory. The form
of the potential in a supergravity theory is given in section 2.8. The main
point to note is that, as in the case of global supersymmetry, supersymmetric
vacua are generally stationary points of this potential but that at such points the
vacuum energy density is now generally negative. Non-supersymmetric (scalar)
field configurations in which the energy density is zero do exist but (without
fine tuning) these are not generally stationary points of the potential. Thus,
supergravity does not solve the cosmological constant problem but it is no worse
than in non-supersymmetric theories.
In the absence of any theoretical insight into the origin of the smallness of the
cosmological constant, it is of interest to see whether 'anthropic' considerations
can shed any light on the issue. Using the 'weak anthropic principle', we seek
to determine which era or which part of the universe could support human life,
so that physicists exist to pose such questions. A large positive cosmological
constant leads to an exponentially expanding (de Sitter) universe, see (1.55).
The standard model of cosmology
and 'sleptons', are (spin-O) scalar particles and, in a supersymmetric theory, they
must have the same mass and quantum numbers as the original particles. This
has the important consequence that the vanishing cosmological constant result is
unaffected by quantum effects, because supersymmetry ensures that any quantum
corrections arising from fermion loops, say, are cancelled by those that arise
from the bosonic loops of the associated sparticle. It has yet to be demonstrated
experimentally that supersymmetry has anything to do with reality. None of the
sparticles associated with the known particles has ever be seen. (It is hoped that
they will be discovered at the Large Hadron Collider (LHC).) Supersymmetry
(susy), if present at all, is therefore a broken symmetry. It then follows from
(1.95) that the vacuum energy is positive definite. The experimental limits on the
sparticle masses require that
msusy ~ 100 GeV.
(1.97)
If something like this bound were to set the scale for Pv8l:' then
~ '" 10- 68 •
(1.98)
Mp
Although small compared with the 0(1) expected in a generic quantum theory
of gravity, this is still very much larger than the value (1.93) derived from the
supernovae and Wilkinson Microwave Anisotropy Probe (WMAP) data. Thus,
if this were the only contribution to the vacuum energy density, we should be
confronted with an unmitigated disaster.
However, including gravity in any supersymmetric theory inevitably leads
to a supergravity theory, in which supersymmetry is a local, rather than a global,
symmetry. This is because in GR the momentum generator Pp. becomes a local
field generating diffeomorphisms of spacetime. Then, in a supersymmetric theory
incorporating GR, the supersymmetry generators too become local fields: this is
why supergravity emerges as the low-energy limit of string theory. The form
of the potential in a supergravity theory is given in section 2.8. The main
point to note is that, as in the case of global supersymmetry, supersymmetric
vacua are generally stationary points of this potential but that at such points the
vacuum energy density is now generally negative. Non-supersymmetric (scalar)
field configurations in which the energy density is zero do exist but (without
fine tuning) these are not generally stationary points of the potential. Thus,
supergravity does not solve the cosmological constant problem but it is no worse
than in non-supersymmetric theories.
In the absence of any theoretical insight into the origin of the smallness of the
cosmological constant, it is of interest to see whether 'anthropic' considerations
can shed any light on the issue. Using the 'weak anthropic principle', we seek
to determine which era or which part of the universe could support human life,
so that physicists exist to pose such questions. A large positive cosmological
constant leads to an exponentially expanding (de Sitter) universe, see (1.55).