Inflation In Loop Quantum Cosmology Research Articles

Pre-inflation dynamical behavior of warm inflation in loop quantum cosmology

Considering a constant dissipative coefficient [Formula: see text], the pre-inflation dynamical behaviors of warm inflation in the loop quantum cosmology scenario are discussed. We consider three sets of initial conditions. The evolution of the background can always be divided into three phases, namely super-inflation, damping, and slow-roll inflation phases, with the duration of each phase depending on the initial conditions. As an example, we compare the background evolution between [Formula: see text] and [Formula: see text] under special initial conditions and find that there is no slow-roll inflation phase for [Formula: see text] while the number of e-folds is about 60.209 for [Formula: see text].

Tachyonic inflation in loop quantum cosmology

A tachyon field might be responsible for cosmological inflation at an early time and contribute to cosmological dark matter at a later time. We investigate tachyonic inflation by analyzing a tachyon field with different potentials in the framework of loop quantum cosmology. No matter which tachyon field energy dominates at the bounce, the evolution of the background can be divided into three phases: super-inflation, damping, and slow-roll inflation. The duration of each phase depends on the initial condition. During the slow-roll inflation, when the initial condition is V(T_mathrm{B})/rho _mathrm{c}ge 10^{-6}, the number of e-folds is very high (Ngg 60) for Vpropto T^{-n} with n=1 and 1 / 2. For an exponential potential, to get enough e-folds, V(T_mathrm{B})/rho _mathrm{c} should be greater than 7.802times 10^{-4}. Furthermore, the probability of slow-roll inflation is obtained. We find that the probability of obtaining slow-roll inflation with 60 or more e-folds is very close to 1.

The evolutionary pictures for phantom field in loop quantum cosmology

The evolutionary pictures for phantom field in loop quantum cosmology are discussed in this paper. Comparing the dynamical behaviors of the phantom field with one of the canonical scalar fields in loop quantum cosmology scenario, we found that the [Formula: see text] phase trajectories are the same, but the [Formula: see text] phase-spaces are very different, and the phantom field with considering potentials can drive neither super inflation nor slow-roll inflation in loop quantum cosmology (LQC) scenario. While the universe is filled with multiple dark fluids, to ensure that the condition [Formula: see text] does not violate, the energy density of dark matter [Formula: see text] and the equation-of-state of phantom field [Formula: see text] should satisfy the condition [Formula: see text] at the bounce point. If this constraint condition holds, the universe can enter an inflationary stage, and it is possible to unify the description of phantom field, dark matter and inflation. We introduced a toy model which has the same form of the general Chaplygin gas to unify the dark energy, dark matter and slow-roll inflation, and the slow-roll inflation of the toy model has also been discussed.

Observational constraints on warm inflation in loop quantum cosmology

By incorporating quantum aspects of gravity, Loop Quantum Cosmology (LQC) provides a self-consistent extension of the inflationary scenario, allowing for modifications in the primordial inflationary power spectrum with respect to the standard General Relativity one. We investigate such modifications and explore the constraints imposed by the Cosmic Microwave Background (CMB) Planck Collaboration data on the Warm Inflation (WI) scenario in the LQC context. We obtain useful relations between the dissipative parameter of WI and the bounce scale parameter of LQC. We also find that the number of required e-folds of expansion from the bounce instant till the moment the observable scales crossed the Hubble radius during inflation can be smaller in WI than in CI. In particular, we find that this depends on how large is the dissipation in WI, with the amount of required e-folds decreasing with the increasing of the dissipation value. {}Furthermore, by performing a Monte Carlo Markov Chain analysis for the considered WI models, we find good agreement of the model with the data. This shows that the WI models studied here can explain the current observations also in the context of LQC.

Inflation in loop quantum cosmology

We develop a consistent analytic approach to determine the conditions under which slow roll inflation can arise when the inflaton is the same scalar field that is responsible for the bounce in Loop Quantum Cosmology (LQC). We find that the requirement that the energy density of the field is fixed at the bounce having to match a critical density has important consequences for its future evolution. For a generic potential with a minimum, we find different scenarios depending on the initial velocity of the field and whether it begins life in a kinetic or potential energy dominated regime. For chaotic potentials that start in a kinetic dominated regime, we find an initial phase of superinflation independent of the shape of the potential followed by a damping phase which slows the inflaton down, forcing it to turnaround and naturally enter a phase of slow-roll inflation. If we begin in a potential energy dominated regime, then the field undergoes a period where the corrections present in LQC damp its evolution once again forcing it to turnaround and enter a phase of slow roll inflation. On the other hand we show for the Starobinsky potential that inflation never occurs when we begin in a potential dominated regime. In fact traditional Starobinsky inflation has to start in a kinetic energy dominated regime, with corresponding tighter constraints on the initial value of the field for successful inflation than in the conventional case. Comparing our analytic results to published numerical ones, we find remarkable agreement especially when we consider the different epochs that are involved. In particular the values of key observables obtained from the two approaches are in excellent agreement, opening up the possibility of obtaining analytic results for the evolution of the density perturbations in these models.

Probability of inflation in loop quantum cosmology

We discuss how initial conditions for cosmological evolution can be defined in Loop Quantum Cosmology with massive scalar field and how the presence of the bounce influences the probability of inflation in this theory, compared with General Relativity. The main finding of the paper is existence of an attractor in the contracting phase of the universe, which results in special conditions at the bounce, quite independent on the measure of initial conditions in the remote past, and hence very specific duration of inflationary stage with the number of e-foldings about $140$.

Probability of warm inflation in loop quantum cosmology

Warm inflation is analyzed in the context of Loop Quantum Cosmology (LQC). The bounce in LQC provides a mean through which a Liouville measure can be defined, which has been used previously to characterize the a priori probability for inflation in LQC. Here we take advantage of the tools provided by LQC to study instead the a priori probability for warm inflation dynamics in the context of a monomial quartic inflaton potential. We study not only the question of how a general warm inflation dynamics can be realized in LQC with an appropriate number of e-folds, but also how such dynamics is constrained to be in agreement with the latest cosmic microwave background radiation from Planck. The fraction of warm inflation trajectories in LQC that gives both the required minimum amount e-folds of expansion and also passes through the observational window of allowed values for the tensor-to-scalar ratio and the spectral tilt is explicitly obtained. We find that the probability of warm inflation with a monomial quartic potential in LQC is higher than that of cold inflation in the same context. Furthermore, we also obtain that the a priori probability gets higher as the inherent dissipation of the warm inflation dynamics increases.

Some clarifications on the duration of inflation in loop quantum cosmology

The prediction of a phase of inflation whose number of e-folds is constrained is an important feature of loop quantum cosmology. This work aims at giving some elementary clarifications on the role of the different hypotheses leading to this conclusion. We show that the duration of inflation does not depend significantly on the modified background dynamics in the quantum regime.

Detailed investigation of the duration of inflation in loop quantum cosmology for a Bianchi I universe with different inflaton potentials and initial conditions

There is a wide consensus on the correct dynamics of the background in loop quantum cosmology. In this article we make a systematic investigation of the duration of inflation by varying what we think to be the most important "unknowns" of the model: the way to set initial conditions, the amount of shear at the bounce and the shape of the inflaton potential.

Slow-roll inflation in loop quantum cosmology of scalar–tensor theories of gravity

The slow-roll inflation of scalar–tensor theories (STTs) of gravity in the context of loop quantum cosmology (LQC) is investigated in this paper. After deriving the effective Hamiltonian, we obtain the semiclassical equations of motion for the background variables in both Jordan frame and Einstein frame of STTs. Then we apply these equations in the slow-roll limit and derive the LQC corrections to the scalar spectral index [Formula: see text] and the tensor-to-scalar ratio [Formula: see text] in the two frames of STTs. Finally, we take two special sectors of STTs as specific examples, namely the Starobinsky model and the non-minimally coupled scalar field model (with the coupling function [Formula: see text] and the potential [Formula: see text]). We derive the detailed expressions of the LQC corrections to [Formula: see text] and [Formula: see text] in terms of the [Formula: see text]-folding number for these two models in both frames.

General dissipative coefficient in warm intermediate inflation in Loop Quantum Cosmology in light of Planck and BICEP2

In this paper, we study a warm intermediate inflationary model with a general form for the dissipative coefficient Γ(T, ϕ) = CϕTm/ϕm-1 in the context of Loop Quantum Cosmology (LQC). We examine this model in the weak and strong dissipative regimes. In general, we discuss in great detail the characteristics of this model in the slow-roll approximation. Also, we assume that the modifications to perturbation equations result exclusively from Hubble rate. In this approach, we use recent astronomical observations from Planck and BICEP2 experiments to restrict the parameters in our model.

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.

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.

Nonsingular power-law and assisted inflation in loop quantum cosmology

We investigate the dynamics of single and multiple scalar fields with exponential potentials, leading to power-law and assisted inflation, in loop quantum cosmology. Unlike in the classical theory, dynamical trajectories in loop quantum cosmology are generically nonsingular, with a big bounce replacing classical big bang in the Planck regime. Post-bounce, after a phase of superinflation, dynamical trajectories evolve towards the classical attractor in the inflationary scenarios. Depending on the initial conditions, bounce is shown to occur in kinetic as well as potential dominated regimes. We analyze the number of e-foldings resulting from the phase of superinflation and find the dependence of the maximum possible number of e-foldings on the equation of state at the bounce and on the steepness of the potential. We find that if the potential is not steep, this phase can lead to a large number of e-foldings in power-law inflation. For the assisted inflation scenario, an increase in the number of fields can yield a significant increase in the number of e-foldings during superinflation.

Observational test of inflation in loop quantum cosmology

We study in detail the power spectra of scalar and tensor perturbations generated during inflation in loop quantum cosmology (LQC). After clarifying in a novel quantitative way how inverse-volume corrections arise in inhomogeneous settings, we show that they can generate large running spectral indices, which generally lead to an enhancement of power at large scales. We provide explicit formulæ for the scalar/tensor power spectra under the slow-roll approximation, by taking into account corrections of order higher than the runnings. Via a standard analysis, we place observational bounds on the inverse-volume quantum correction δ∝a−σ (σ > 0, a is the scale factor) and the slow-roll parameter ϵV for power-law potentials as well as exponential potentials by using the data of WMAP 7yr combined with other observations. We derive the constraints on δ for two pivot wavenumbers k0 for several values of δ. The quadratic potential can be compatible with the data even in the presence of the LQC corrections, but the quartic potential is in tension with observations. We also find that the upper bounds on δ(k0) for given σ and k0 are insensitive to the choice of the inflaton potentials.

Probability of inflation in loop quantum cosmology

Inflationary models of the early universe provide a natural mechanism for the formation of large scale structure. This success brings to forefront the question of naturalness: Does a sufficiently long slow roll inflation occur generically or does it require a careful fine tuning of initial parameters? In recent years there has been considerable controversy on this issue. In particular, for a quadratic potential, Kofman, Linde and Mukhanov have argued that the probability of inflation with at least 65 e-foldings is close to one, while Gibbons and Turok have argued that this probability is suppressed by a factor of ~ $\10^{-85}$. We first clarify that such dramatically different predictions can arise because the required measure on the space of solutions is intrinsically ambiguous in general relativity. We then show that this ambiguity can be naturally resolved in loop quantum cosmology (LQC) because the big bang is replaced by a big bounce and the bounce surface can be used to introduce the structure necessary to specify a satisfactory measure. The second goal of the paper is to present a detailed analysis of the inflationary dynamics of LQC using analytical and numerical methods. By combining this information with the measure on the space of solutions, we address a sharper question than those investigated in the literature: What is the probability of a sufficiently long slow roll inflation WHICH IS COMPATIBLE WITH THE SEVEN YEAR WMAP DATA? We show that the probability is very close to 1. The material is so organized that cosmologists who may be more interested in the inflationary dynamics in LQC than in the subtleties associated with measures can skip that material without loss of continuity.

A phenomenology analysis of the tachyon warm inflation in loop quantum cosmology

We investigate the warm inflation condition in loop quantum cosmology. In our consideration, the system is described by a tachyon field interacted with radiation. The exponential potential function, V(ϕ)=V0e−αϕ, with the same order parameters V0 and α, is taken as an example of this tachyon warm inflation model. We find that, for the strong dissipative regime, the total number of e-folds is less than the one in the classical scenario, and for the weak dissipative regime, the beginning time of the warm inflation will be later than the tachyon (cool) inflation.

Inflation in loop quantum cosmology: Dynamics and spectrum of gravitational waves

Loop quantum cosmology provides an efficient framework to study the evolution of the Universe beyond the classical Big Bang paradigm. Because of holonomy corrections, the singularity is replaced by a "bounce". The dynamics of the background is investigated into the details, as a function of the parameters of the model. In particular, the conditions required for inflation to occur are carefully considered and are shown to be generically met. The propagation of gravitational waves is then investigated in this framework. By both numerical and analytical approaches, the primordial tensor power spectrum is computed for a wide range of parameters. Several interesting features could be observationally probed.

Inverse volume corrections to emergent tachyonic inflation in loop quantum cosmology

The emergent model in the context of loop quantumcosmology with a tachyon scalar field is studied. We find that thereis a center equilibrium point in the semiclassical region and asaddle point in the classical region. If the potential of thetachyon field satisfies some conditions, the universe can stay atthe center equilibrium point past-eternally and then oscillateinfinitely around this point with the tachyon climbing up itspotential. Once the potential reaches a critical value, these twoequilibrium points coincide with each other and the oscillationphase is broken by an emergent inflation. In order to obtain asuccessful emergent tachyon inflation, a constraint onϕ̇2 of tachyon is required.

Onset of inflation in loop quantum cosmology

Using a Liouville measure, similar to the one proposed recently by Gibbons and Turok, we investigate the probability that single-field inflation with a polynomial potential can last long enough to solve the shortcomings of the standard hot big bang model, within the semiclassical regime of loop quantum cosmology. We conclude that, for such a class of inflationary models and for natural values of the loop quantum cosmology parameters, a successful inflationary scenario is highly improbable.