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.

In the recent paper by Mielczarek et~al. (Ref.~8), an idea of the method which can be used to put some constraint for the reheating phase was proposed. Another method of constraining the reheating temperature has been recently studied by Martin and Ringeval (Ref.~17). Both methods are based on observations of the cosmic microwave background (CMB) radiation. In this paper, we develop the idea introduced in this first article to put constraint on the reheating after the slow-roll inflation. We restrict our considerations to the case of a massive inflaton field. The method can be, however, easily extended to the different inflationary scenarios. As a main result, we derive an expression on the reheating temperature TRH. Surprisingly, the obtained equation is independent on the unknown number of relativistic degrees of freedom g* produced during the reheating. Based on this equation and the WMAP 7 observations, we find TRH=3.5\ifmmode\times\else\texttimes\fi{}106\,\,GeV, which is consistent with the current constraints. The relative uncertainty of the result is, however, very high and equal to $\sigma${}(TRH)/TRH$\approx${}53. As we show, this uncertainty will be significantly reduced with future CMB experiments.

In effective models of loop quantum cosmology, the holonomy corrections are associated with deformations of space-time symmetries. The most evident manifestation of the deformations is the emergence of a Euclidean phase accompanying the nonsingular bouncing dynamics of the scale factor. In this article, we compute the power spectrum of scalar perturbations generated in this model, with a massive scalar field as the matter content. Instantaneous and adiabatic vacuum-type initial conditions for scalar perturbations are imposed in the contracting phase. The evolution through the Euclidean region is calculated based on the extrapolation of the time direction pointed by the vectors normal to the Cauchy hypersurface in the Lorentzian domains. The obtained power spectrum is characterized by a suppression in the IR regime and oscillations in the intermediate energy range. Furthermore, the speculative extension of the analysis in the UV reveals a specific rise of the power leading to results incompatible with the data.

Cosmological models where the standard big bang is replaced by a bounce have been studied for decades. The situation has, however, dramatically changed in the past years for two reasons: first, because new ways to probe the early Universe have emerged, in particular, thanks to the cosmic microwave background, and second, because some well grounded theories—especially loop quantum cosmology—unambiguously predict a bounce, at least for homogeneous models. In this article, we investigate into the details the phenomenological parameters that could be constrained or measured by next-generation $B$-mode cosmic microwave background experiments. We point out that an important observational window could be opened. We then show that those constraints can be converted into very meaningful limits on the fundamental loop quantum cosmology parameters. This establishes the early Universe as an invaluable quantum gravity laboratory. DOI: http://dx.doi.org/10.1103/PhysRevD.82.123520 © 2010 The American Physical Society

In this paper, we consider realistic model of inflation embedded in the framework of loop quantum cosmology. Phase of inflation is preceded here by the phase of a quantum bounce. We show how parameters of inflation depend on the initial conditions established in the contracting, prebounce phase. Our investigations indicate that phase of the bounce easily sets proper initial conditions for the inflation. Subsequently, we study observational effects that might arise due to the quantum gravitational modifications. We perform preliminary observational constraints for the Barbero-Immirzi parameter $\gamma${}, critical density $\rho${}c, and parameter $\lambda${}. In the next step, we study effects on power spectrum of perturbations. We calculate spectrum of perturbations from the bounce and from the joined bounce+inflation phase. Based on these studies, we indicate a possible way to relate quantum cosmological models with the astronomical observations. Using the Sachs-Wolfe approximation, we calculate the spectrum of the superhorizontal CMB anisotropies. We show that quantum cosmological effects can, in the natural way, explain suppression of the low CMB multipoles. We show that fine-tuning is not required here, and the model is consistent with observations. We also analyze other possible probes of the quantum cosmologies and discuss perspectives of their implementation.

Support vector machines (SVMs) are a well-established classifier effectively deployed in an array of classification tasks. In this work, we consider extending classical SVMs with quantum kernels and applying them to satellite data analysis. The design and implementation of SVMs with quantum kernels (hybrid SVMs) are presented. Here, the pixels are mapped to the Hilbert space using a family of parameterized quantum feature maps (related to quantum kernels). The parameters are optimized to maximize the kernel target alignment. The quantum kernels have been selected such that they enabled analysis of numerous relevant properties while being able to simulate them with classical computers on a real-life large-scale dataset. Specifically, we approach the problem of cloud detection in the multispectral satellite imagery, which is one of the pivotal steps in both on-the-ground and on-board satellite image analysis processing chains. The experiments performed over the benchmark Landsat-8 multispectral dataset revealed that the simulated hybrid SVM successfully classifies satellite images with accuracy comparable to the classical SVM with the RBF kernel for large datasets. Interestingly, for large datasets, the high accuracy was also observed for the simple quantum kernels, lacking quantum entanglement.