A quantitative analysis of singular inflation with scalar-tensor and
  modified gravity
  We provide a detailed quantitative description of singular inflation. Its
close analogy with finite-time future singularity which is associated to dark
energy era is described. Calling and classifying the singularities of such
inflation as finite-time cosmological singularities we investigate their
occurrence, with special emphasis on the Type IV singularity. The study is
performed in the context of a general non-canonical scalar-tensor theory. In
addition, the impact of finite time singularities on the slow-roll parameters
is also investigated. Particularly, we study three cases, in which the
singularity occurs during the inflationary era, at the end, and also we study
the case that the singularity occurs much more later than inflation ends. Using
the obtained slow-roll parameters, for each case, we calculate explicitly the
spectral index of primordial curvature perturbations $n_s$, the associated
running of the spectral index $a_s$ and of the scalar-to-tensor ratio $r$ and
compare the resulting values to the Planck and BICEP2 data. As we demonstrate,
in some cases corresponding to the Type IV singularity, there might be the
possibility of agreement with the observational data, when the singularity
occurs at the end, or after inflation. However, absolute concordance of all
observational indices is not achieved. On the contrary, if the singularity
occurs during the inflationary era, this is catastrophic for the theory, since
the observational indices become divergent. We also show how a Type IV
singularity may be consistently accommodated in the Universe's late time
evolution.
