  A scenario with two subsequent periods of inflationary expansion in the very
early universe is examined. The model is based on a potential motivated by
symmetries being found in field theory at high energy. For various parameter
sets of the potential the spectra of scalar and tensor perturbations that are
expected to originate from this scenario are calculated. Also the beginning of
the reheating epoch connecting the second inflation with thermal equilibrium is
studied. Perturbations with wavelengths leaving the horizon around the
transition between the two inflations are special: It is demonstrated that the
power spectrum at such scales deviates significantly from expectations based on
measurements of the cosmic microwave background (CMB). This supports the
conclusion that parameters for which this part of the spectrum leaves
observable traces in the CMB must be excluded. Parameters entailing a very
efficient second inflation correspond to standard small-field inflation and can
meet observational constraints. Particular attention is paid to the case where
the second inflation leads solely to a shift of the observable spectrum from
the first inflation. A viable scenario requires this shift to be small.
