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A Randall-Sundrum type brane-cosmological model in which slow-roll inflation on the brane is driven solely by a bulk scalar field was recently proposed by Himemoto and Sasaki. We analyze their model in detail and calculate the quantum…

We formulate a renormalizable quantum gravity in $2+\epsilon$ dimensions by generalizing the nonlinear sigma model approach to string theory. We find that the theory possesses the ultraviolet stable fixed point if the central charge of the…

We present a quantization of unimodular gravity in the connection representation for a homogeneous, isotropic, and spatially flat cosmological model without matter. In this model, the wave function is governed by a Schr\"odinger-type…

The evolution of linear cosmological perturbations in modified theories of gravity is investigated assuming the Palatini formalism. It has been discussed about the stability problem in this model based on the equivalence between f(R)…

I discuss a model for quantized gravitation based on the simplicial lattice discretization. It has been studied in some detail using a comprehensive finite size scaling analysis combined with renormalization group methods. The results are…

An inhomogeneous (1+1)-dimensional model of the quantum gravity is considered. It is found, that this model corresponds to a string propagating against some curved background space. The quantization scheme including the Wheeler-DeWitt…

Dynamical triangulations of four-dimensional Euclidean quantum gravity give rise to an interesting, numerically accessible model of quantum gravity. We give a simple introduction to the model and discuss two particularly important issues.…

The main aim of this article is to investigate a spacetime of quasi-constant sectional curvature. At first, the existence of such a spacetime is established by several examples. We have shown that a spacetime of quasi-constant sectional…

In this essay we offer a comprehensible overview of the gravitational aether scenario. This is a possible extension of Einstein's theory of relativity to the quantum regime via an effective approach. Quantization of gravity usually faces…

In quantum gravity, fields may lose quantum coherence by scattering off vacuum fluctuations in which virtual black hole pairs appear and disappear. Although it is not possible to properly compute the scattering off such fluctuations, we…

We address issues on the origin of gravity and the cosmological constant problem based on a recent understanding about the correspondence between noncommutative field theory and gravity. We suggest that the cosmological constant problem can…

We review and extend the recently proposed model of combinatorial quantum gravity. Contrary to previous discrete approaches, this model is defined on (regular) random graphs and is driven by a purely combinatorial version of Ricci…

We study Lorentzian vacuum transition probabilities between two minima of a scalar field potential within the framework of $f(R)$ gravity. The analysis extends the previously considered WKB expansion of the Wheeler-DeWitt equation to…

A theory of gravitation is proposed, modeled after the notion of a Ricci flow. In addition to the metric an independent volume enters as a fundamental geometric structure. Einstein gravity is included as a limiting case. Despite being a…

We show that a positive cosmological constant is incompatible with the quantum-corpuscular resolution of de Sitter metric in form of a coherent state. The reason is very general and is due to the quantum self-destruction of the coherent…

We discuss how the modifications of the standard Einstein's equations needed to support the cosmological bounce can at the same time lead to vanishing of the well known cosmological constant problem, while also studying the effects of…

We calculate the power spectrum of vacuum fluctuations of a generic scalar field in a quantum cosmological setting that is manifestly singularity-free. The power spectrum is given in terms of the usual scale invariant spectrum plus scale…

We study the dynamics of gauge-invariant scalar perturbations in cosmological scenarios with a modified Friedmann equation, such as quantum gravity bouncing cosmologies. We work within a separate universe approximation which captures…

In the standard inflationary paradigm the inhomogeneities observed in the CMB arise from quantum fluctuations of an initially homogeneous and isotropic vacuum state. This picture suffers from two well-known weaknesses. First, it assumes…

We propose several covariant models which may solve one of the problems in the cosmological constant. One of the model can be regarded as an extension of sequestering model. Other models could be regarded as extensions of the covariant…