content_image/359944.jpg content_image/359949.jpg
<img src='content_image/359944.jpg'>

where z is the redshift defined by z + 1 ≡ a$_{0}$/a . For ΛCDM, the luminosity distance can be written [1]: 

<img src='content_image/359949.jpg'>

where, S ( x ) ≡ sin( x ) and κ = 1 − Ω$_{tot}$ for Ω$_{tot}$ > 1 while S ( x ) ≡ sinh( x ) with κ = 1 − Ω$_{tot}$ for Ω$_{tot}$ < 1 while S ( x ) ≡ x and κ = 1, for Ω$_{tot}$ = 1. For the ΛCDM models we take Ω$_{tot}$ = Ω$_{M}$ + Ω$_{Λ}$. Here we have defined Ω$_{M}$ ≡ ρ$_{M}$/ρ$_{c}$ = 8 πGρ$_{M}$/ 3 H 2 and Ω$_{Λ}$ = Λ / 3 H 2 where ρ$_{c}$ is the critical energy density. The results are that the entropic acceleration models we consider can provide excellent fits to the data as can be seen from Fig. (1). 5 The entropic models move smoothly from a decelerating to an accelerating phase sometime near a redshift of z = . 5, analogous to the ΛCDM models. We suspect a complete model may be further 

