Observational constraints on cosmological future singularities
  In this work we consider a family of cosmological models featuring future singularities. This type of cosmological evolution is typical of dark energy models with an equation of state violating some of the standard energy conditions (e.g. the null energy condition). Such kind of behavior, widely studied in the literature, may arise in cosmologies with phantom fields, theories of modified gravity or models with interacting dark matter/dark energy. We briefly review the physical consequences of these cosmological evolution regarding geodesic completeness and the divergence of tidal forces in order to emphasize under which circumstances the singularities in some cosmological quantities correspond to actual singular spacetimes. We then introduce several phenomenological parameterizations of the Hubble expansion rate to model different singularities existing in the literature and use SN Ia, BAO and H(z) data to constrain how far in the future the singularity needs to be (under some reasonable assumptions on the behaviour of the Hubble factor). We show that, for our family of parameterizations, the lower bound for the singularity time can not be smaller than about 1.2 times the age of the universe, what roughly speaking means about 2.8 Gyrs from the present time. 
Jose Beltran Jimenez, Ruth Lazkoz, Diego Saez-Gomez and Vincenzo   Salzano
gr-qc astro-ph.CO