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We present a rich class of exact solutions which contains radiation-dominated and matter-dominated models for the early and late universe. They include a variable cosmological ``constant'' which is derived from a higher dimension and…

Cosmology and particle physics are deeply interrelated. Among the common problems are dark energy, dark matter and baryon asymmetry of the Universe. We discuss these problems in general terms, and concentrate on several particular…

It is well known that the canonical quantization of the Friedmann-Lema\^itre-Robertson-Walker (FLRW) filled with a perfect fluid leads to nonsingular universes which, for later times, behave as their classical counterpart. This means that…

We show that a number of problems of modern cosmology may be solved in the framework of multidimensional gravity with high-order curvature invariants, without invoking other fields. We use a method employing a slow-change approximation,…

This introductory review is addressed to beginning researchers. Some of the distinguishing features of loop quantum gravity are illustrated through loop quantum cosmology of FRW models. In particular, these examples illustrate: i) how…

Over the years, de Sitter spacetime has been a central focus, in studies involving quantum fields, for its importance in the early and late expansion stages of the universe. While de Sitter spacetime closely mimics characteristics of the…

Despite its great successes in accounting for the current observations, the so called `standard' model of cosmology faces a number of fundamental unresolved questions. Paramount among these are those relating to the nature of the origin of…

We consider the FLRW universe in a loop quantum cosmological model filled with the radiation, baryonic matter (with negligible pressure), dark energy and dark matter. The dark matter sector is supposed to be of Bose-Einstein condensate…

We study gravitational collapse in effective loop quantum gravity, focusing on non-marginally bound configurations in Lema\^itre-Tolman-Bondi spacetimes. In the homogeneous limit we recover the effective dynamics of loop quantum cosmology…

The five-dimensional loop quantum Kaluza-Klein cosmology is constructed based on the symmetric reduction of the connection formulation of the full theory. Through semiclassical analysis, the effective scalar constraint for the cosmological…

Using the reconstruction method, we investigate which $F(R)$ theories, with or without the presence of matter fluids, can produce the matter bounce scenario of holonomy corrected Loop Quantum Cosmology. We focus our study in two limits of…

We study the quantum cosmology of a flat Friedmann-Lema\^{i}tre-Robertson-Walker universe filled with a (free) massless scalar field and a perfect fluid that represents radiation or a cosmological constant whose value is not fixed by the…

We consider a simplified model of quantum gravity using a mini-superspace description of an isotropic and homogeneous universe with dust. We derive the corresponding Friedmann equations for the scale factor, which now contain a dependence…

We show that there exists a choice of scalar field modes, such that the evolution of the quantum field in the zero-mass and large-mass limits is consistent with the Einstein equations for the background geometry. This choice of modes is…

Old and new puzzles of cosmology are reexamined from the point of view of quantum theory of the universe developed here. It is shown that in proposed approach the difficulties of the standard cosmology do not arise. The theory predicts the…

This paper examines two cosmological models of quantum gravity (from string theory and loop quantum gravity) to investigate the foundational and conceptual issues arising from quantum treatments of the big bang. While the classical…

In this work, we investigate the notion of time and unitarity in the vicinity of a bounce in quantum cosmology, that is, a turning point for the scale factor. Because WKB methods drastically fail near a turning point, the scale factor…

In this paper, we study a big bounce universe typified by a non-singular big bounce, as opposed to a singular big bang. This cosmological model can describe radiation dominated early universe and matter dominated late universe in FRW model.…

In loop quantum cosmology, non-perturbative quantum gravity effects lead to the resolution of the big bang singularity by a quantum bounce without introducing any new degrees of freedom. Though fundamentally discrete, the theory admits a…

In this paper we study the creation of super-massive real scalar particles in the framework of a $f(R)=R-\beta/R^n$ modified gravity theory, with parameters constrained by observational data. The analysis is restrict to a homogeneous and…