Distinguishing between inflationary models from cosmic microwave
  background
  In this paper, inflationary cosmology is reviewed, paying particular
attention to its observational signatures associated with large-scale density
perturbations generated from quantum fluctuations. In the most general
scalar-tensor theories with second-order equations of motion, we derive the
scalar spectral index $n_s$, the tensor-to-scalar ratio $r$, and the nonlinear
estimator $f_{\rm NL}$ of primordial non-Gaussianities to confront models with
observations of Cosmic Microwave Background (CMB) temperature anisotropies. Our
analysis includes models such as potential-driven slow-roll inflation,
k-inflation, Starobinsky inflation, and Higgs inflation with
non-minimal/derivative/Galileon couplings. We constrain a host of inflationary
models by using the Planck data combined with other measurements to find models
most favored observationally in the current literature. We also study
anisotropic inflation based on a scalar coupling with a vector (or, two-form)
field and discuss its observational signatures appearing in the two-point and
three-point correlation functions of scalar and tensor perturbations.
