  The observation of the B-mode in the cosmic microwave background radiation
combined with the so-called Lyth bound suggests the trans-Planckian variation
of the inflaton field during inflation. Such a large variation generates
concerns over inflation models in terms of the effective field theory below the
Planck scale. If the inflaton resides in a Riemann surface and the inflaton
potential is a multivalued function of the inflaton field when it is viewed as
a function on a complex plane, the Lyth bound can be satisfied while keeping
field values in the effective field theory within the Planck scale. We show
that a multivalued inflaton potential can be realized starting from a
single-valued Lagrangian of the effective field theory below the Planck scale.
