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# On the constant roll complex scalar field inflationary models

Dec 2022

In this paper we wish to point out the possibility of using a complex scalarfield in a constant roll inflationary model, as needed for observationalviability. We extend the idea of real field inflaton with constant rate of rollto a complex field, showing the feasibility of solving Einstein Klein-Gordonequations constrained by an \emph{appropriate} form of constant rolldefinition. As compared to the well known (two-parametric class of) real fieldmodels, there is one more degree of flexibility in constant roll inflationarysolutions which is represented by an arbitrary function of time, $\gamma(t)$.We work with an arbitrary but constant function $\gamma$ (where $\gamma=0$refers to the corresponding real field model) and find new inflationary classof potentials. In this class of models, the behavior of real and complex fieldmodels are similar in some aspects, for example the solutions with largeconstant roll parameter are not stable and should be considered as early timetransients. These field solutions relax at late time on a dual attractortrajectory. However, complex fields phase space trajectories reach this stableregime after real fields.

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