Type V singularities with inhomogeneous equations of state

Interest in cosmological singularities has remarkably grown in recent times, particularly on future singularities with the discovery of late-time acceleration of the universe and dark energy. Recent work has seen a proper classification of such singularities into strong and weak based on their strength, with weak singularities being the likes of sudden, w and big freeze singularities and strong singularities like the big rip. This has led to a classification of such singularities in various types like Big rip is Type 1, w-singularity is type V etc. While singularities of type I-type IV have been discussed vividly by taking into account inhomogeneous equations of state (EOS), the same has not been attempted for type V singularities. So in this work we have discussed in detail about the formation of type V singularities in various cosmologies after considering inhomogeneous equations of state. We consider two inhomogeneous forms of the EOS in the context of four different cosmological backgrounds ; standard general relativistic cosmology, an asymptotically safe cosmology, a cosmology inspired by modified area-entropy relations, generalized uncertainty principles, holographic renormalization and Chern-Simons gravity( all of which can be coincidentally described by the same form of the modified Friedmann equation) and an f® gravity cosmology. We show in detail that one sees some very big differences in the occurence conditions of type V singularities when one makes such considerations. In the particular case of the f® gravity cosmology, we see that the type V singularities get completely removed. This work goes to show that the creation and formation of type V singularities is influenced most strongly by the form of the equation of state that one considers, way more so than what background cosmology one chooses.