A Study of the Early Cosmic Dynamics in a Multifield Model of Inflation and Curvature Perturbations

In this work, we study the cosmological dynamics of the early universe by employing a small field potential in the context of multifield inflation. By investigating analytically the cosmological observables, such as the number of e-folds $N$, potential slow-roll parameters ${ϵ}_V$, ${\eta }_V$, and spectral index $n_s$ which carry significant information, we show that they impact the inflationary universe considerably. The tensor-to-scalar ratio concerning the curvature perturbation is worked out for the potential under consideration which is another significant observable and comes out to be nonnegative. In multifield models of inflation, both types of curvature and isocurvature perturbations exist, while, in the present work, during the slow-roll, isocurvature perturbations are suppressed and therefore can be neglected. The surviving perturbations which are due to the curvature only can be tackled suitably by a mechanism developed by Sasaki and Stewart known as Sasaki–Stewart formalism. The effect of augmenting the number of e-folds on the power spectrum through the spectral index and its impact on the observable parameters of the slow-roll inflationary phase is observed by carrying out the analysis. It is observed analytically that the spectrum of multifield inflation is effectively different than its corresponding single-field inflation. The field values and their masses affect the results profoundly at the time of horizon-crossing.