Recent measurements of type Ia supernovae as well as other concordant observations suggest that the expansion of our universe is accelerating .
A dark energy component has usually been invoked as the most feasible mechanism for the acceleration .
However , the effects arising from possible extra dimensions can mimic well the role of a dark energy through a modified Friedmann equation .
In this work , we investigate some observational constraints on a scenario in which this modification is given by H ^ { 2 } = { 8 \pi G \over 3 } ( \rho + C \rho ^ { n } ) .
We mainly focus our attention on the constraints from recent measurements of the dimensionless coordinate distances to type Ia supernovae and Fanaroff-Riley type IIb radio galaxies compiled by Daly and Djorgovski ( 2003 ) and the X-ray gas mass fractions in clusters of galaxies published by Allen et al .
( 2002,2003 ) .
We obtain the confidence region on the power index n of the modificative term and the density parameter \Omega _ { m } of the universe from a combined analysis of these databases .
It is found that n = 0.06 ^ { +0.22 } _ { -0.18 } and \Omega _ { m } = 0.30 ^ { +0.02 } _ { -0.02 } , at the 95.4 % confidence level , which is consistent within the errors with the standard \Lambda CDM model .
These parameter ranges give a universe whose expansion swithes from deceleration to acceleration at a redshift between 0.52 to 0.73 .