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Register a new userWarm bounce in loop quantum cosmology and the prediction for the duration of inflation
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We study and estimate probabilistic predictions for the duration of the preinflationary and slow-roll phases after the bounce in loop quantum cosmology, determining how the presence of radiation in the prebounce phase affects these results. We present our analysis for different classes of inflationary potentials that include the monomial power-law chaotic type of potentials, namely, for the quadratic, quartic and sextic potentials and also for a Higgs-like symmetry breaking potential, considering different values for the vacuum expectation value in the latter case. We obtain the probability density function for the number of inflationary e-folds and for other relevant quantities for each model and produce probabilistic results drawn from these distributions. This study allows us to discuss under which conditions each model could eventually lead to observable signatures on the spectrum of the cosmic microwave background, or, else, be also excluded for not predicting a suffcient amount of accelerated expansion. The effect of radiation on the predictions for each model is explicitly quantified. The obtained results indicate that the number of inflationary e-folds in loop quantum cosmology is not a priori an arbitrary number, but can in principle be a predictable quantity, even though the results are dependent on the model and on the amount of radiation in the Universe prior to the start of the inflationary regime.
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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.
We study the importance of lattice refinement in achieving a successful inflationary era. We solve, in the continuum limit, the second order difference equation governing the quantum evolution in loop quantun cosmology, assuming both a fixed and a dynamically varying lattice in a suitable refinement model. We thus impose a constraint on the potential of a scalar field, so that the continuum approximation is not broken. Considering that such a scalar field could play the role of the inflaton, we obtain a second constraint on the inflationary potential so that there is consistency with the CMB data on large angular scales. For a $m^2phi^2/2$ inflationary model, we combine the two constraints on the inflaton potential to impose an upper limit on $m$, which is severely fine-tuned in the case of a fixed lattice. We thus conclude that lattice refinement is necessary to achieve a natural inflationary model.
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.
In this Essay we investigate the observational signatures of Loop Quantum Cosmology (LQC) in the CMB data. First, we concentrate on the dynamics of LQC and we provide the basic cosmological functions. We then obtain the power spectrum of scalar and tensor perturbations in order to study the performance of LQC against the latest CMB data. We find that LQC provides a robust prediction for the main slow-roll parameters, like the scalar spectral index and the tensor-to-scalar fluctuation ratio, which are in excellent agreement within $1sigma$ with the values recently measured by the Planck collaboration. This result indicates that LQC can be seen as an alternative scenario with respect to that of standard inflation.
Lectures by the author at the 1986 Cargese summer school modestly corrected and uploaded for greater accessibility. Some of the authors views on the quantum mechanics of cosmology have changed from those presented here but may still be of historical interest. The material on the Born-Oppenheimer approximation for solving the Wheeler-DeWitt equation and the work on the classical geometry limit and the approximation of quantum field theory in curved spacetime are still of interest and of use.
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