Inter-galactic gravitational field effect on the propagation of light
  Recent observations of the luminosity-redshift in Type Ia supernovae suggest an accelerated inflation of the Universe (open Universe) as well as the observed matter density showed to be less than the critical one, suggesting that a large fraction of the energy density of the Universe is in the form of dark energy with negative pressure (to supply repulsive forces). We present here an alternative mechanism on the basis of the photon energy loss in the inter-galactic gravitational field, and it is close to the Shapiro effect. It is argue that the redshift observed in distant galaxies is a cumulativeprocess, a dominant redshift due to the Doppler effect plus a redshift due to photon energy loss in the intergalactic gravitational field. We show that the last mechanism when interpreted as Doppler effect, supplies a non lineal relationship among the speed of recession of the galaxies and their distances. The effect is very tiny, even so, it increases with the distance and can be the key to explain the anomalous redshift observed in distant supernovae without the accelerated inflation hypothesis 
C. E. Navia, C. R. A. Augusto, D. F. Franceschini and K. H. Tsui