Supernova observations fit Einstein-deSitter expansion in 4-sphere
  Recent observations on the redshift and magnitude of distant supernovae have raised fundamental questions of the cosmological structure and the development of space. Interpretation of the observations with the standard cosmology model suggests accelerating expansion of space which requires an assumption of unknown dark energy working against gravitation at cosmological distances. This paper presents an analysis which shows that the observed magnitude redshift relationship is in an excellent agreement with the prediction derived by assuming a zero energy balance of motion and gravitation in an expanding 4-sphere. Such an approach can be regarded as Einstein-deSitter expansion in the fourth dimension, suggesting a decelerating expansion velocity until zero in infinity. 
Tuomo Suntola and Robert Day