If cosmological inflation is due to a slowly rolling single inflation
field taking trans-Planckian values as suggested by the BICEP2
measurement of primordial tensor modes in CMB, embedding inflation
into the Standard Model challenges standard paradigm of effective
field theories. Together with an apparent absence of Planck scale
contributions to the Higgs mass and to the cosmological constant,
BICEP2 provides further experimental evidence for the absence of large
$M_{\rm P}$ induced operators. We show that classical scale
invariance, the paradigm that all fundamental scales in Nature are
induced by quantum effects, solves the problem and allows for a
remarkably simple scale-free inflaton models without extending the
gauge group. Due to trans-Planckian inflaton values and vevs, a
dynamically induced Coleman-Weinberg-type inflaton potential of the
model can predict tensor-to-scalar ratio $r$ in a large range,
converging around the prediction of chaotic $m^2\phi^2$ inflation for
a large trans-Planckian value of the inflaton vev. We propose two
models: one in which the Planck scale is given by hand and one in
which also the Planck scale is generated by quantum effects. Precise
determination of $r$ in future experiments will single out a unique
scale-free inflation potential, allowing to test the proposed
field-theoretic framework.