240 The cosmic microwave background
- , the ratio of the total energy density to the critical densityρcr= 8 π/ 3 H^2.
This parameter determines the spatial curvature of the universe:= 1
is a flat universe with critical density. Smaller values ofcorrespond
to a negative spatial curvature, while larger values correspond to positive
curvature. Current microwave background measurements constrainto be
roughly within the range 0.8–1.2, consistent with a critical-density universe. - b, the ratio of the baryon density to the critical density. Observations of
the abundance of deuterium in high redshift gas clouds and comparison with
predictions from primordial nucleosynthesis place strong constraints on this
parameter (Tytleret al2000). - m, the ratio of the DM density to the critical density. Dynamical
constraints, gravitational lensing, cluster abundances and numerous other
lines of evidence all point to a total matter density in the neighbourhood
of 0 =m+b= 0 .3. - , the ratio of vacuum energy densityto the critical density. This is the
notorious cosmological constant. Several years ago, almost no cosmologist
advocated a cosmological constant; now almost every cosmologist accepts
its existence. The shift was precipitated by the Type Ia supernova Hubble
diagram (Perlmutteret al1999, Riesset al1998) which shows an apparent
acceleration in the expansion of the universe. Combined with strong
constraints on, a cosmological constant now seems unavoidable, although
high-energy theorists have a difficult time accepting it. Strong gravitational
lensing of quasars places upper limits on(Falcoet al1998). - The present Hubble parameterh, in units of 100 km s−^1 /Mpc−^1. Distance
ladder measurements (Mouldet al2000) and supernova Ia measurements
(Riesset al1998) give consistent estimates forhof around 0.70, with
systematic errors on the order of 10%. - Optionally, further parameters describing additional contributions to the
energy density of the universe; for example, the ‘quintessence’ models
(Caldwellet al1998) which add one or more scalar fields to the universe.
Parameters describing the initial conditions are:
- The amplitude of fluctuationsQ, often defined at the quadrupole scale.
COBE fixed this amplitude to high accuracy (Bennettet al1996). - The power law indexnof initial adiabatic density fluctuations. The scale-
invariant Harrison–Zeldovich spectrum isn=1. Comparison of microwave
background and large-scale structure measurements shows thatnis close to
unity. - The relative contribution of tensor and scalar perturbationsr, usually defined
as the ratio of the power atl=2 from each type of perturbation. The fact
that prominent features are seen in the power spectrum (presumably arising
from scalar density perturbations) limits the power spectrum contribution of
tensor perturbations to roughly 20% of the scalar amplitude. - The power law indexnTof tensor perturbations. Unfortunately, tensor power