Finite time future singularities in the interacting dark sector

We construct a piecewise model that gives a physical viable realization of finite-time future singularity for a spatially flat Friedmann-Robertson-Walker universe within the interacting dark matter-dark energy framework, with the latter in the form of a variable vacuum energy. The scale factor solutions provided by the model are accommodated in several branches defined in four regions delimited by the scale factor and the effective energy density. A branch starts from a big bang singularity and describes an expanding matter-ominated universe until the sudden future singularity occurs. Then, an expanding branch emerges from a past singularity, reaches a maximum, reverses its expansion, and possibly collapses into itself while another expanding branch emerges from the latter singularity and has a de Sitter phase which is intrinsically stable. We obtain a different piecewise scale factor which describes a contracting de Sitter universe in the distant past until the finite-time future singularity happens. It emerges and continues in a contracting phase, bounces at the minimum, reverses, and enters into a stable de Sitter phase without a dramatic final. Also, we explore the aforesaid cosmic scenarios by focusing on the leading contributions of some physical quantities near the sudden future singularity and applying the geometric Tiplerand Krlak criteria in order to inspect the behavior of timelike geodesic curves around such singularity.