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Register a new userDetecting quantum gravitational effects of loop quantum cosmology in the early universe?
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We derive the primordial power spectra and spectral indexes of the density fluctuations and gravitational waves in the framework of loop quantum cosmology (LQC) with holonomy and inverse-volume corrections, by using the uniform asymptotic approximation method to its third-order, at which the upper error bounds are $lesssim 0.15%$, and accurate enough for the current and forthcoming cosmological observations. Then, using the Planck, BAO and SN data we obtain the tightest constraints on quantum gravitational effects from LQC corrections, and find that such effects could be well within the detection of the current and forthcoming cosmological observations.
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We investigate the gravitational particle production in the bounce phase of Loop Quantum Cosmology (LQC). We perform both analytical and numerical analysis of the particle production process in a LQC scenario with Bunch-Davies vacuum initial condition in the contracting phase. We obtain that if we extend the validity of the dressed metric approach beyond the limit of small backreaction in which it is well justified, this process would lead to a radiation dominated phase in the pre-inflationary phase of LQC. Our results indicate that the test field approximation, which is required in the truncation scheme used in the dressed metric approach, might not be a valid assumption in a LQC scenario with such initial conditions.
We study the tensor modes of linear metric perturbations within an effective framework of loop quantum cosmology. After a review of inverse-volume and holonomy corrections in the background equations of motion, we solve the linearized tensor modes equations and extract their spectrum. Ignoring holonomy corrections, the tensor spectrum is blue tilted in the near-Planckian superinflationary regime and may be observationally disfavoured. However, in this case background dynamics is highly nonperturbative, hence the use of standard perturbative techniques may not be very reliable. On the other hand, in the quasi-classical regime the tensor index receives a small negative quantum correction, slightly enhancing the standard red tilt in slow-roll inflation. We discuss possible interpretations of this correction, which depends on the choice of semiclassical state.
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.
In this work, we revisit the dynamics of pre-inflationary universe with a family of $alpha-$attractor potentials, in the framework of loop quantum cosmology, in which the big bang singularity is generically resolved purely with quantum geometric effects, and replaced by a quantum bounce. At the bounce, the background evolution is divided into two distinct classes, the first is dominated by the kinetic energy of the inflaton field and the second by the potential energy. In both classes, we find the physically viable initial conditions numerically that provide not only the slow-roll inflation, but also sufficient e-folds to be compatible with observations. In the entire range of kinetic energy dominated initial conditions (except some subsets of Models 2 and 4), the background evolution prior to reheating is always split into three different phases: bouncing, transition and slow-roll inflation. In the bouncing phase, the numerical evolution of the scale factor is independent not only of the initial data, but also the inflationary potentials, as long as it is dominated by the kinetic energy, and can be well approximated by an analytical solution, whereas in the potential energy dominated case, such approximated results do not exist. Moreover, we study the phase space analysis for a class of $alpha-$attractor potentials, and discuss the phase space trajectories for physically viable initial conditions of the inflaton field.
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.
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