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Conformal embedding of closed-universe models in a de Sitter backgroundsuggests a quantisation condition on the available conformal time. Thiscondition implies that the universe is closed at no greater than the 10% level.When a massive scalar field is introduced to drive an inflationary phase thisfigure is reduced to closure at nearer the 1% level. In order to enforce theconstraint on the available conformal time we need to consider conditions inthe universe before the onset of inflation. A formal series around the initialsingularity is constructed, which rests on a pair of dimensionless,scale-invariant parameters. For physically-acceptable models we find that bothparameters are of order unity, so no fine tuning is required, except in themass of the scalar field. For typical values of the input parameters we predictthe observed values of the cosmological parameters, including the magnitude ofthe cosmological constant. The model produces a very good fit to the mostrecent CMBR data, predicting a low-l fall-off in the CMB power spectrumconsistent with that observed by WMAP.Comment: 21 pages, 16 figures. To appear in proceedings 'Phi in the Sky',  Porto, 200

Conformal Models of de Sitter Space, Initial Conditions for Inflation and the CMB