Effect of Massive Fields on Inflation

Effects caused by an additional massive scalar field interacting with an inflaton field are analyzed. Inflation is shown to have two stages, the first of which is dominant and characterized by ultraslow dynamics of the inflaton field. Constraints on the model parameters are obtained. The occurrence of inflationary era in the universe evolution seems to be inevitable because it allows the explanation of a great number of observed facts [1, 2]. Early inflation mechanisms [3, 4] were based on the consistent equations of scalar and gravitational fields. Nevertheless, the simplest inflation models could not explain the totality of observed data. In particular, the predictions of the chaotic inflation model [5, 6] about temperature fluctuations in cosmic background radiation do not contradict observations only for a rather unnatural form of the inflaton field potential (see also [7]). At the same time, the interaction of a large number of various fields existing in nature should give rise to new phenomena in inflation scenario. Further development of the theory has led to the emergence of inflation models involving additional fields, among which are the models of hybrid inflation [5] and inflation on the pseudo Nambu Goldstone field [6]. The interaction of the classical inflaton field with other particles produced by it is one of the basic elements of some inflation models. This effect provides a basis for the warm inflation scenario [7], which, however, is not free from flaws [8]; back reaction of the produced particles on the dynamics of inflaton field was considered in [9] [10]. The purpose of this work is to study the back reaction of an additional field on the classical motion of the basic inflaton field. It is assumed that the additional field is massive enough for it to be at the minimum of its effective potential during inflation. Nevertheless, it is shown below that its influence can noticeably decelerate the system motion. In what follows, the simplest form of interaction is considered allowing the analytical results to be obtained. Namely, we introduce, apart from the inflaton field φ, an additional scalar field χ and write the action in the form S = ∫ dx √ −g [ 1 2 φ,μφ ,μ − V (φ) + 1 2 χ,μχ ,μ − 1 2 mχ − κχu(φ) ] . (1) where u(φ) is a polynomial of degree no higher than three for the renormalizable theories. Below, u(φ) = φ is taken for definiteness. The first power of the field χ in the interaction is necessary in order to obtain compact analytical results valid for an arbitrary coupling constant κ, rather than the expansion in powers of this constant. The interaction of this type arises in supersymmetric theories and is considered in hybrid inflation scenarios [11]. Dolgov and Hansen [9] used this type of interaction in studying the back reaction of produced particles on the motion of classical field. The set of the classical equations for both fields is written as 1 √ −g∂μ ( √ −g∂χ) +mχχ+ κφ = 0, 1 √ −g∂μ ( √ −g∂φ) + V ′(φ) + 2κφχ = 0. (2) Let us consider the case of heavy χ particles. In the inflationary era, this means that