Note on the super-inflation in loop quantum cosmology

Abstract

Phenomenological effect of the super-inflation in loop quantum cosmology (LQC) is discussed. We investigate the case that the Universe is filled with the interacting field between massive scalar field and radiation. Considering the damping coefficient Γ as a constant, the changes of the scale factor during super-inflation with four different initial conditions are discussed, and we find that the changes of the scale factor depends on the initial values of energy density of the scalar field and radiation at the bounce point. But no matter which initial condition is chosen, the radiation always dominated at the late time. Moreover, we investigate whether the super-inflation can provide enough e-folding number. For the super-inflation starts from the quantum bounce point, the initial value of Hubble parameter H(ti) ∼ 0, then it is possible to solve the flatness problem and horizon problem. As an example, following the method of [18] to calculate particle horizon on the condition that the radiation dominated at bounce point, and we find that the Universe has had enough time to be homogeneous and isotopic.

Phenomenology analysis of duration inflation for tachyon field in loop quantum cosmology

“…Although the scale factor a increases very fast when one considers the initial condition that the potential energy dominates at the bounce point, the change rate of a is still less than e 60 . This result is different from [29], in which we found that it is possible to get e-folding number during the super inflation of the interacting scalar field and radiation, i.e., the change rate of scale factor a is bigger than e 60 if the potential energy dominates at the bounce point [29].…”

“…This means the universe will enter an super inflation stage as soon as the bounce begins, and it will last untilḢ = 0, i.e., ρ = 1 2 ρ c . There are lots of studies discuss the properties of super inflation [24][25][26][27][28][29]. As we know, to get enough e-folding number, the scale factor should increase very fast in slow-roll inflation stage to ensure the e-folding number N > 60.…”

“…According to the truth that the e-folding number comes from the changing of the scale factor in slow-roll inflation, some concluded that the e-folding number created during super inflation in LQC is not sufficient [24], but then it was found that the e-folding number during super inflation depends on the initial conditions [36] or the parameter of the potential of scalar field [26]. Noticed that the Hubble parameter H increases during super inflation stage, some argue that the super inflation can provide enough e-folding number for the expression of N corrected as N ≡ [28,29]. In this subsection, we just consider the e-folding number from the change of the scale factor during the super inflation stage.…”

Tachyon warm inflation with the effects of loop quantum cosmology in the light of Planck 2015

“…To this end, the arofementioned analysis points that the (1 − ρ/ρ c ) term, imposes a specific era of inflation 0 < H < H I , where for ρ ρ c the universe enters in the inflationary phase, while the characteristic scale H I presumably connected to a scale which is around to that of the Grand Unified Theory (GUT). Overall, the condition H = 0,Ḣ > 0 implies that the Universe enters in the LQC inflationary era at the bounce point [39] (see also [40]). Unlike nominal (cold) inflation, in which H const., here the key point is to understand that the Hubble parameter varies with time.…”

“…In our model the condition = 1 makes sure that inflation starts at the earliest possible stage [76,80]. As far as the number of e-folds is concerned we have (39) or (40) where for the last equality we used Eq. (24).…”