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.