Preheating in Generalized Einstein Theories

One of the most important epochs in the history of inflationary Universe is the transition from almost De Sitter expansion to the radiation dominated universe. Until few years ago proper understanding of this phenomena was not well established. Recent development in the theory of resonant particle creation of bosons [1] as well as fermions [2] due to coherent oscillations of the Bose-condensate inflatons may explain satisfactorily the emergence of radiation era from the ultra cold inflationary universe [1]. Although such phenomena are hard to reproduce in a laboratory they are the simplest manifestation of a slowly varying scalar field which rolls down the potential and oscillates as a coherent source at each and every space time region. Apart from reheating the universe to the temperature ambient for the production of light nuclei this phenomena has multifaceted consequences. It is also a well known mechanism to create non-equilibrium environment which can be exploited for the generation of net baryon antibaryon asymmetry required for the baryogenesis [3]. If there exist general chiral fields, then, in particular, breaking of parity invariance could also lead to different production of left and right fermions. If the rotational invariance is broken explicitly by an axial background then there would be anisotropic distribution of fermions [4]. The same phenomena is also responsible for the generation of primordial magnetic field [5,6] in the context of string cosmology, where the dynamical dilaton field plays the role of an oscillating background. The preheating scenario has been studied so far in the context of general theory of relativity. It has been well established from the present observations that this theory of gravitation is the correct description of space-time geometry at scales larger than 1 cm. There exists a class of deviant theories which are scalar-tensor gravity theories, known as Generalized Einstein Theories (GET) of which the Jordan–Brans–Dicke (JBD) theory [7,8] is the simplest and best-studied generalization of general relativity. This theory leads to variations in the Newtonian gravitation ”constant” G, and introduces a new coupling constant ω, with general relativity recovered in the limit 1/ω → 0. The constraint on ω based on timing experiments using the Viking space probe suggests that it must exceed 500 [9]. The JBD theory also mimics the effective lagrangian derived from low energy scale of the string theory where the Brans-Dicke (BD) field is called Dilaton and the coupling constant ω takes the negative value of −1 [10]. It also represents the (4 + D) dimensional Kaluza–Klein theories with an inflaton field which has mainly two subclasses out of which we shall consider the one where the inflaton is introduced in an effective four dimensional theory. In this case the BD/dilaton field plays the role of homogeneous scalar field in 4 dimensions and is related to the size of the compactification. Most of these models are conformally equivalent and can be recast in the form of Einstein gravity theory [12]. The only difference is that the scaling of the fields and their corresponding couplings will be different for different interpretations of BD/dilaton field. In this paper we shall consider the general relativity limit of the JBD theory as well as other variant theories such as string and Kaluza–Klein and for the sake of consistency we just use one representative of the coupling constant, γ, which takes different values accordingly. We must say that there is an obvious advantage in all these theories that they are well constrained at the present day and the evolution of the BD/dilaton field is roughly constant after a period of 60 e-foldings of inflation. Here