We developed the nonlocal model recently published by Maggiore and Mancarella by introducing a new function [Formula: see text]. This modification allows us to obtain a new analytical solution in the hyperbolic tangent form for the nonlocal distortion function. This model gives rise to an expansion history behaving exactly as [Formula: see text]CDM (Lambda Cold Dark Matter) with the same matter content, but without any need to neither cosmological constant nor dark energy. However, background evolution in our model and [Formula: see text]CDM are the same, but the results may be distinguishable in structure formation investigations or in light of new observations that probably contain additional information more than the background evolution.

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Two eclipsing binary systems UZ Lyr and BR Cyg are the semi-detached types whose secondary component fill its Roche lobe. Although radial velocity and light curves of these systems have already been investigated separately, both radial velocity and light curves of them are analyzed simultaneously for the first time in the present study . Also, the orbital period changes of these systems are studied. Our results show that the mass transfer between components have negligible effects on the orbital period changes of these systems, but two light-time effects are the reasons of the periodic behavior of the O-C curve for UZ Lyr. We could not remark more information about orbital period changes for BR Cyg, but we find a new orbital period for it. By radial velocity and light curves analysis we find a clod spot on the secondary components of BR Cyg. The new geometrical and physical parameters of both systems are obtained and their positions on H-R diagram demonstrated.

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