Inflatonary model of a single scalar field with primordial potential

V(\phi)=\frac{1}{2}m^2\phi^2+\frac{\lambda}{4}\phi^4 (m^2 >0) non-minimally

coupled to gravity is studied in two-measures theory (TMT) in the Palatini

formalism. In the equations of motion presented in the Einstein frame and

rewritten in terms of the canonically normalized scalar field \varphi, there

arises a TMT effective potential, which differs from the potential of the

T-model in that it has a plateau of finite length: for \varphi greater a

certain value varphi_0 the TMT effective potential becomes exponentially steep.

The length of the plateau, and hence the duration of a quasi-de Sitter

inflation, is controlled by a model parameter. The appearance of this

parameter, as well as the form of the TMT effective potential, are a direct

consequence of the features inherent only in TMT. A detailed analysis shows

that there is a rather narrow interval of initial values of \varphi, bounded

from above by \varphi_0, in which the initial kinetic \rho_{kin,in} and

gradient \rho_{grad,in} energy densities turn out to be less than the potential

energy density; this requires the only additional condition, which is that

\rho_{kin,in}>\rho_{grad,in}. Therefore, in the space-time domain where these

restrictions are satisfied, the initial conditions necessary for inflation are

guaranteed.