In this paper, we investigate the optical bistability (OB) and optical multistability (OM) phenomena for a quantum dot nanostructure via two different mechanisms. The first process is based on the application of the incoherent pumping field while the second one is due to the ratio between the injection and cavity injection rates. We show that the appearance of OB and OM properties in the system depends strongly on the presence of these mechanisms. It is found that OB appears in the presence of both mechanisms, but OM appears only when both mechanisms are present in the system simultaneously. We also study the linear absorption behaviors for the case when OB and OM are observed in the system. It is shown that for the multistable state, the absorption properties of the system are different from the bistable state, which has a strong dependence on incoherent processes.

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In this work the differential Friedmann-Lemaître-Robertson-Walker model solutions which offer different cosmological parameters. We studied the effect of time and temperature evolution on these cosmological parameters, such as the scale factor R(t) and the deceleration parameter q, across radiation, matter and dark energy eras. The nature of the variations in time and temperature of these quantities are consistent with that obtained from other cosmological models which have taken into account astrophysical observations. Time and temperature variations of these parameters have been shown graphically. These parameters provided strong evidence about the expansion and acceleration of the universe. The scale factor and the deceleration parameter show a linear change with the increase in time during the radiation and matter dominated eras, followed by a rapid expansion during the dark energy era, indicating that the universe has a transition from a phase of decelerated expansion to an accelerated expansion, which is contributed to dark energy. This led to a flat, homogeneous, and isotropic universe.