Note on the super inflation in loop quantum cosmology

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 $\Gamma$ 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 $H(t_i)\sim0$, then it is possible to solve the flatness problem and horizon problem. As an example, following the method of \cite{Amoros-prd} 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.Comment: 9 pages, 4 figures. Physics Letters B, online publication complete: 13-NOV-201

Observational Constraints on Two-field Warm Inflation

We study the two-field warm inflation models with a double quadratic potential and a linear temperature dependent dissipative coefficient. We derived the evolution equation of all kinds of perturbations without assuming slow-roll approximation, and obtained the curvature power spectrum at the end of inflation with a fully numerical method. Then we compute the scalar spectral index $n_s$, tensor-to-scalar ratio $r$ for several representative potentials, and compare our results with observational data. At last, we use Planck data to constrain the parameters in our models. This work is a natural extension of single-field warm inflation, and the aim of this work is to present some features of multi-field warm inflation using a simple two-field model.Comment: 13 pages, 6 figures. Accepted for publication in Physical Review

Two-field Warm Inflation and Its Scalar Perturbations on Large Scales

We explore the homogeneous background dynamics and the evolution of generated perturbations of cosmological inflation that is driven by multiple scalar fields interacting with a perfect fluid.Then we apply the method to warm inflation driven by two scalar fields and a radiation fluid, and present general results about the evolution of the inflaton and radiation. After decomposing the perturbations into adiabatic and entropy modes, we give the equation of motion of adiabatic and entropy perturbations on large scales. Then, we give numerical results of background and perturbation equations in a concrete model (the dissipative coefficient $\Gamma \propto H$). At last, we use the most recent observational data to constrain our models and give the observationally allowed regions of parameters. This work is a natural extension of warm inflation to multi-field cases.Comment: 10 pages, 4 figure

Primordial non-Gaussianity in noncanonical warm inflation

We study the bispectrum of the primordial curvature perturbation on uniform-density hypersurfaces generated by a kind of the noncanonical warm inflation, wherein the inflation is provided by a noncanonical scalar inflaton field that is coupled to radiation through a thermal dissipation effect. We obtain an analytic form for the nonlinear parameter $f_{NL}$ that describes the non-Gaussianity in first-order cosmological perturbation theory and analyse the magnitude of this nonlinear parameter. We make a comparison between our result and those of the standard inflation and the canonical warm inflation. We also discuss when the contribution to the non-Gaussianity due to the second-order perturbation theory becomes more important and what effect can be observed. We take the Dirac-Born-Infeld (DBI) inflation as a concrete example to find how the sound speed and the thermal dissipation strength to decide the non-Gaussianity and to get a lower bound of the sound speed constrained by PLANCK.Comment: 7 pages, 2 figure

Power spectrum and anisotropy of super inflation in loop quantum cosmology

We investigate the scalar mode of perturbation of super inflation in the version of loop quantum cosmology in which the gauge invariant holonomy corrections are considered. Given a background solution, we calculate the power spectrum of the perturbation in the classical and LQC conditions. Then we compute the anisotropy originated from the perturbation. It is found that in the presence of the gauge invariant holonomy corrections the power spectrum is exponentially blue and the anisotropy also grows exponentially in the epoch of super inflation.Comment: 12 pages,4 figures,Published versio

Warm inflation in loop quantum cosmology: a model with a general dissipative coefficient

A general form of warm inflation with the dissipative coefficient $\Gamma=\Gamma_0(\phi /\phi_0) ^n(T/\tau_0) ^m$ in loop quantum cosmology is studied. In this case, we obtain conditions for the existence of a warm inflationary attractor in the context of loop quantum cosmology by using the method of stability analysis. The two cases when the dissipative coefficient is independent $(m=0)$ and dependent $(m\neq0)$ on temperature are analyzed specifically. In the latter case, we use the new power spectrum which should be used when considering temperature dependence in the dissipative coefficient. We find that the thermal effect is enhanced in the case $m>0$. As in the standard inflation in loop quantum cosmology, we also reach the conclusion that quantum effect leaves a tiny imprint on the cosmic microwave background (CMB) sky.Comment: 12 pages, accepted for publication in Rhys. Rev.

Loop Quantum Cosmology of Bianchi I Model in μˉ\bar{\mu} and μˉ′\bar{\mu}' Schemes with Higher Order Holonomy Corrections

The detailed formulation of loop quantum cosmology with higher order holonomy corrections has been constructed recently in the homogeneous and isotropic spacetime, yet it is important to extend the higher order holonomy corrections to include the effects of anisotropy which typically grow during the collapsing phase. In this paper we investigate the Bianchi I model in $\bar{\mu}'$ scheme which truly captures the regularization of the Hamiltonian constraint. To compare with the earlier works and provide a comparison with the $\bar{\mu}'$ scheme, we also investigate the $\bar{\mu}$ scheme although it has many disadvantages. First we construct the effective dynamics with higher order holonomy corrections in a massless scalar field, then we extend it to the inclusion of arbitrary matter. Besides that, we also analyze the behavior of the anisotropy during the evolution of the universe. We find that in the $\bar{\mu}'$ scheme, the singularity is never approached and the quantum bounce is generic as in the isotropic case, regardless of the order of the holonomy corrections. Some differences in the bouncing phase of the two schemes are also found out. It is also shown that in the two schemes the behavior of the anisotropy is not the same before and after the bounce.Comment: 16 pages, 3 figure

Consistency of the tachyon warm inflationary universe models

This study concerns the consistency of the tachyon warm inflationary models. A linear stability analysis is performed to find the slow-roll conditions, characterized by the potential slow-roll (PSR) parameters, for the existence of a tachyon warm inflationary attractor in the system. The PSR parameters in the tachyon warm inflationary models are redefined. Two cases, an exponential potential and an inverse power-law potential, are studied, when the dissipative coefficient $\Gamma=\Gamma_0$ and $\Gamma=\Gamma(\phi)$, respectively. A crucial condition is obtained for a tachyon warm inflationary model characterized by the Hubble slow-roll (HSR) parameter $\epsilon_{_H}$, and the condition is extendable to some other inflationary models as well. A proper number of e-folds is obtained in both cases of the tachyon warm inflation, in contrast to existing works. It is also found that a constant dissipative coefficient $(\Gamma=\Gamma_0)$ is usually not a suitable assumption for a warm inflationary model.Comment: 10 pages, 0 figures, accepted for publication in Journal of Cosmology and Astroparticle Physics (JCAP

Path Integral of Bianchi I models in Loop Quantum Cosmology

A path integral formulation of the Bianchi I models containing a massless scalar field in loop quantum cosmology is constructed. Following the strategy used in the homogenous and isotropic case, the calculation is extended to the simplest non-isotropic models according to the $\bar{\mu}$ and $\bar{\mu}^{\prime}$ scheme. It is proved from the path integral angle that the quantum dynamic lacks the full invariance with respect to fiducial cell scaling in the $\bar{\mu}$ scheme, but it does not in the $\bar{\mu}^{\prime}$ scheme. The investigation affirms the equivalence of the canonical approach and the path integral approach in loop quantum cosmology.Comment: 11 pages,revised version, accepted for publication in Class. Quantum Gra

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

Assuming that the e-folding number is just determined by the change of the scale factor, the tachyonic inflation theory in LQC has been discussed. Considering the tachyon field with exponential potential and inverse quadratic potential, we find that the evolutionary pictures of super inflation are affected by the potentials and the initial conditions. However it cannot provide enough e-folding number, no matter which condition is chosen. Therefore a slow-rolling inflation is necessary. The e-folding number for slow-rolling inflation depends on the values of the parameter $\alpha$ of the exponential potential and the initial conditions. To get enough e-folding number, $\alpha$ should be small. Based on the slow-rolling inflation happens immediately when the super inflation ends, and the scale factor is continuously growing during the whole inflation stage, we consider an e-folding number provided by the whole inflationary stage, and we find that it is easier to get enough e-folding number when the scale factor increases during all the inflation phase.Comment: 8 pages, 6 figure