A static non-singular 10-dimensional closed Friedmann universe of Planck size , filled with a perfect fluid with equation of state p = - \frac { 2 } { 3 } \varepsilon , can arise spontaneously by a quantum fluctuation from nothing in 11-dimensional spacetime .
A quantum transition from this state can initiate the inflationary quantum cosmology outlined in Ref .
2 [ General Relativity and Gravitation 33 , 1415 , 2001 - gr-qc/0103021 ] .
With no fine-tuning , that cosmology predicts about 60 e-folds of inflation and a vacuum energy density depending only on the number of extra space dimensions ( seven ) , G, \hbar,c and the ratio between the strength of gravity and the strength of the strong force .
The fraction of the total energy in the universe represented by this vacuum energy depends on the Hubble constant H _ { 0 } .
Estimates of H _ { 0 } from WMAP , SDSS , the Hubble Key Project , and Sunyaev-Zeldovich and X-ray flux measurements range from 60 to 72 km sec ^ { -1 } Mpc ^ { -1 } .
Using a mid-range value of H _ { 0 } = 65 km sec ^ { -1 } Mpc ^ { -1 } , the model in Ref .
2 predicts \Omega _ { \Lambda } \approx 0.7 .