  We examine observational constraints on single-field inflation in which the
inflaton is a composite field stemming from a four-dimensional strongly
interacting field theory. We confront the predictions with the Planck and very
recent BICEP2 data. In the large non-minimal coupling regions, we discover for
MCI model that the predictions lie well inside the joint $68\%$ CL for the
Planck data, but is in tension with the recent BICEP2 observations. In the case
of the GI model, the predictions satisfy the Planck results. However, this
model can produce a large tensor-to-scalar ratio consistent with the recent
BICEP2 observations if the number of e-foldings is slightly smaller than the
range commonly used. For a super Yang-Mills paradigm, we discover that the
predictions satisfy the Planck data, and surprisingly a large tensor-to-scalar
ratio consistent with the BICEP2 results can also be produced for an acceptable
range of the number of e-foldings and of the confining scale. In the small
non-minimal coupling regions, all of the models can satisfy the BICEP2 results.
However, the predictions of GI and SgbI models cannot satisfy the observational
bound on the amplitude of the curvature perturbation launched by Planck, and
the techni-inflaton self-coupling in the MCI model is constrained to be
extremely small.
