Inflation model building with an accurate measure of e-folding

摘要

It has become standard practice to take the logarithmic growth of the scalefactor as a measure of the amount of inflation, despite the well-known factthat this is only an approximation for the true amount of inflation required tosolve the horizon and flatness problems. The aim of this work is to show howthis approximation can be completely avoided using an alternative framework forinflation model building. We show that using the inverse Hubble radius as thekey dynamical parameter, the correct number of e-folding arises naturally as ameasure of inflation. As an application, we present an interesting model inwhich the entire inflationary dynamics can be solved analytically and exactly,and, in special cases, reduces to the familiar class of power-law models.