Did the Universe Experienced a Pressure non-Crushing Type Cosmological Singularity in the Recent Past?

In the recent literature it has been shown that the $H_0$ tension may be eliminated if an abrupt physics transition changed the Cepheid parameters in the near past of the Universe, nearly $70-150\,$Myrs ago. In this letter we stress the possibility that this abrupt transition was caused by the smooth passage of our Universe through a pressure finite-time cosmological singularity. Being a non-crushing type singularity the pressure singularity can leave its imprints in the Universe, since it occurs globally and literally everywhere. We discuss how this scenario could easily be realized by $F(R)$ gravity, with the strong energy conditions being satisfied without the need for a scalar field or specific matter fluids. We also stress the fact that the pressure singularity can affect the effective gravitational constant of $F(R)$ gravity. Moreover, we stress the fact that pressure singularities can disrupt the trajectories of bound objects in the Universe, which is also pointed out in the literature, even in the context of general relativity. We also show numerically in a general relativistic framework that elliptic trajectories are distorted and changed to different elliptic trajectories when the Universe passes through the pressure singularity. Such a disruption of the trajectories could have tidal effects on the surface of the earth, for example on sea waters and oceans, regarding the distortion of moon's elliptic trajectory. Accordingly, the distortion of earth's trajectory around the sun could have affected climatologically earth $70-150\,$Myrs ago.