Gauge invariant metric perturbations during reheating

The possible amplification of gauge invariant metric fluctuations in the infrared sector are very important during reheating stage of inflation. In this stage the inflaton field oscillates around the minimum of the scalar potential. The evolution for the super Hubble scales gauge invariant metric fluctuations can be studied by means of the Bardeen parameter. For a massive scalar field with potential V (Φc) = m 2 Φ 2 c + Λ with nonzero cosmological constant. I find that (in the reheating regime and for super Hubble scales) the SasakiMukhanov parameter oscillates with amplitude constant such that there is not amplification of Q during reheating. PACS number(s): 98.80.Cq Postulating a period of nearly exponential growth in the primordial universe, inflationary cosmology [1] solved many problems which plagued previous models of the big bang. After inflation, the universe is dominated by the inflation, the scalar field whose evolution controls the dynamics of the inflationary era. The process for which the inflaton energy density is then converted into thermalized matter, is knowed as reheating [2]. The issue of gauge invariance becomes critical when we attempt to analyze how the scalar metric perturbations produced in the very early universe influence of a globally flat isotropic and homogeneous universe [3]. The evolution of gauge invariant metric perturbations during inflation have been well studied [4]. This allows to formulate the problem of the amplitude for the scalar metric perturbations on the evolution of the background Friedmann-RobertsonWalker (FRW) universe in a coordinate independent manner at every moment in time. Parametric resonance instability occurs during a reheating period when the inflaton oscillates around the minimum of the scalar potential [5–7]. Since the gravitational perturbation E-mail address: [email protected] — Cátedra Patrimonial de CONACYT. 1 is coupled to the inflaton field by the Einstein equation, it may also experience parametric amplification during this stage. The parametric resonance instabilities have important consequences for cosmology. They will lead to a reheating temperature which can be much larger than would be obtained by calculating the efficiency of reheating using perturbation theory and could have important implications for grand-unification-scale baryogenesis [8], the production of supermassive dark matter [9] or the formation of topological defects [10]. In this work I study the metric inhomogeneities during reheating for gauge invariant metric perturbations [3] by means of the Sasaki-Mukhanov variable [11] on super Hubble scales for a massive scalar field with potential V (Φc) = m 2 Φc +Λ and nonzero cosmological constant and Φc = + 3MpH0 πm . Since the results do not depend on the gauge, the perturbed globally flat isotropic and homogeneous universe is well described by [3] ds = (1 + 2ψ) dt − a(t)(1− 2Φ) dx, (1) where a is the scale factor of the universe and ψ and Φ the perturbations of the metric. I will consider the particular case where the tensor Tij is diagonal, i.e., for Φ = ψ [12]. Linearizing the Einstein equations in terms of the matter and metric fluctuations φ and Φ, one obtains the system of differential equations for φ and Φ [13]