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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…
The alternative dynamics of loop quantum cosmology is examined by the path integral formulation. We consider the spatially flat FRW models with a massless scalar field, where the alternative quantization inherit more features from full loop…
The next generation of large scale surveys will not only measure cosmological parameters within the framework of General Relativity, but will also allow for precision tests of the framework itself. At the order of linear perturbations,…
We combine I. background independent Loop Quantum Gravity (LQG) quantization techniques, II. the mathematically rigorous framework of Algebraic Quantum Field Theory (AQFT) and III. the theory of integrable systems resulting in the invariant…
In a remarkable paper, T. Koslowski introduced kinematical representations for loop quantum gravity in which there is a non-degenerate spatial background metric present. He also considered their properties, and showed that Gauss and…
In the loop approach to the quantisation of gravity, one uses a Hilbert space which is too singular for some operators to be realised as derivatives. This is usually addressed by instead using finite difference operators at the Planck…
Quantum cosmology implies corrections to the classical equations of motion which may lead to significant departures from the classical trajectory, especially at high curvature near the big-bang singularity. Corrections could in principle be…
The construction of effective Hamiltonians describing corrections to flat space particle dynamics arising from the granularity of space at very short distances is discussed in the framework of an heuristic approach to the semiclassical…
The standard formulation of the cosmological constant problem is based on one critical assumption---the spacetime is homogeneous and isotropic, which is true only on cosmological scales. However, this problem is caused by extremely small…
We study the cosmological consequences of a recently proposed nonlocal modification of general relativity, obtained by adding a term $m^2R\,\Box^{-2}R$ to the Einstein-Hilbert action. The model has the same number of parameters as…
We investigate the cosmological impacts of the alternative effective mass function of the modified Mukhanov-Sasaki equation in loop quantum cosmology, which is obtained from the polymerization of the classical mass function derived in the…
The primordial spectrum of cosmological tensor perturbations is considered as a possible probe of quantum gravity effects. Together with string theory, loop quantum gravity is one of the most promising frameworks to study quantum effects in…
We employ the techniques of the Functional Renormalization Group in string theory, in order to derive an effective mini-superspace action for cosmological backgrounds to all orders in the string scale $\alpha'$. To this end, T-duality plays…
We apply a hybrid approach which combines loop and Fock quantizations to fully quantize the linearly polarized Gowdy $T^3$ model in the presence of a massless scalar field with the same symmetries as the metric. Like in the absence of…
According to cosmological inflation, the inhomogeneities in our universe are of quantum mechanical origin. This scenario is phenomenologically very appealing as it solves the puzzles of the standard hot big bang model and naturally explains…
We explore the consequences of loop quantum cosmology (inverse-volume corrections) in the spectrum of the gravitational waves using the method of the Bogoliubov coefficients. These corrections are taken into account at the background level…
Scaling solutions for the effective action in dilaton quantum gravity are investigated within the functional renormalization group approach. We find numerical solutions that connect ultraviolet and infrared fixed points as the ratio between…
We explore the extension of quantum cosmology outside the homogeneous approximation, using the formalism of loop quantum gravity. We introduce a model where some of the inhomogeneous degrees of freedom are present, providing a tool for…
Loop Quantum Gravity is a background independent, nonperturbative approach to the quantization of General Relativity. Its application to models of interest in cosmology and astrophysics, known as Loop Quantum Cosmology, has led to new and…
General Relativity receives quantum corrections relevant at macroscopic distance scales and near event horizons. These arise from the conformal scalar degrees of freedom in the extended effective field theory of gravity generated by the…