We consider the effect of CP violating phases in the MSSM on the relic density of the lightest supersymmetric particle (LSP). In particular, we find that the upper limits on the LSP mass are relaxed ...when phases in the MSSM are allowed to take non-zero values when the LSP is predominantly a gaugino (bino). Previous limits of
m
B
≲ 250
GeV
for
Ωh
2 < 0.25
can be relaxed to
m
B
≲ 650
GeV
. We also consider the additional constraints imposed by the neutron and electron electric dipole moments induced by these phases. Though there is some restriction on the phases, the bino mass may still be as large as ∼ 350 GeV and certain phases can be arbitrarily large.
Assuming that the lightest supersymmetric particle (LSP) is the lightest neutralino
χ
̃
, we present a detailed exploration of neutralino–stau (
χ
̃
−
τ
̃
) coannihilation channels, including ...analytical expressions and numerical results. We also include
χ
̃
coannihilations with the
ẽ and
μ
̃
. We evaluate the implications of coannihilations for the cosmological relic density of the LSP, which is assumed to be stable, in the constrained minimal supersymmetric extension of the Standard Model (CMSSM), in which the soft supersymmetry-breaking parameters are universal at the supergravity GUT scale. We evaluate the changes due to coannihilations in the region of the MSSM parameter space that is consistent with the cosmological upper limit on the relic LSP density. In particular, we find that the upper limit on
m
χ
̃
is increased from about 200 GeV to about 600 GeV in the CMSSM, and estimate a qualitatively similar increase for gauginos in the general MSSM.
We extend previous combinations of LEP and cosmological relic density constraints on the parameter space of the constrained MSSM, with universal input supersymmetry-breaking parameters, to large tan
...β. We take account of the possibility that the lightest Higgs boson might weigh about 115 GeV, but also retain the possibility that it might be heavier. We include the most recent implementation of the
b→
sγ constraint at large tan
β. We refine previous relic density calculations at large tan
β by combining a careful treatment of the direct-channel Higgs poles in annihilation of pairs of neutralinos
χ with a complete treatment of
χ–
τ
̃
coannihilation, and discuss carefully uncertainties associated with the mass of the
b quark. We find that coannihilation and pole annihilations allow the CMSSM to yield an acceptable relic density at large tan
β, but it is consistent with all the constraints only if
m
χ
>140 (180) GeV for
μ>0 (
μ<0) for our default choices
m
b(m
b)
MS
SM
=4.25
GeV,
m
t
=175 GeV, and
A
0=0.
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