Observationally constrainable free parameters of scalar field inflation models

We present an approximate estimate, in the slow ''reheating'' scenario, of the late time power spectrum of adiabatic energy density inhomogeneities generated during an early, scalar field dominated, de Sitter inflation epoch, when the scalar field potential, V(Φ∝V0-λΦα (where V0λ and α are positive parameters). If α is not too large, the power spectrum is fairly sensitive to the value of the Hubble parameter at ''reheating'', expect in the α=4 case (when it only depends logarithmically on the value of this parameter). When α is sufficiently large, the power spectrum is much more sensitive to the value of the Hubble parameter at =reheating'', than it is to the value of the dimensionless coupling constant (λ multiplied by the appropriate power of V0), which is, therefore, not unduly constrained by observational data; also, in this regime, the slow ''reheating'' prescription resembles the rapid ''reheating'' prescription. For a moderately large α (e.g., α=8 or 10), the magnitude of the energy density perturbation is consistent with the late time large-scale observational limit, provided the energy scale of inflation is not too high (for α=8 or 10 it needs to be ≅ 2x1010 or 1011GeV); the dimensionless coupling constant does not have to be small (in both cases it is > or approx.10-2). (orig.)