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The semi-classical approach to the quantum geometrodynamical model is used for the description of the properties of the universe on extremely small spacetime scales. Quantum theory for a homogeneous, isotropic and closed universe is…
Quantum gravity has matured over the last decade to a theory which can tell in a precise and explicit way how cosmological singularities of general relativity are removed. A branch of the universe "before" the classical big bang is obtained…
It has been shown recently by Saad, Shenker and Stanford that the genus expansion of a certain matrix integral generates partition functions of Jackiw-Teitelboim (JT) quantum gravity on Riemann surfaces of arbitrary genus with any fixed…
We measure the fractal structure of four dimensional simplicial quantum gravity by identifying so-called baby universes. This allows an easy determination of the critical exponent $\g$ connected to the entropy of four-dimensional manifolds.
Quantum gravity of a brane-like Universe is formulated, and its Einstein limit is approached. Regge-Teitelboim embedding of Arnowitt-Deser-Misner formalism is carried out. Invoking a novel Lagrange multiplier, accompanying the lapse…
Several lines of evidence hint that quantum gravity at very small distances may be effectively two-dimensional. I summarize the evidence for such ``spontaneous dimensional reduction,'' and suggest an additional argument coming from the…
The properties of the quantum universe on extremely small spacetime scales are studied in the semi-classical approach to the well-defined quantum model. It is shown that near the initial cosmological singularity point quantum gravity…
A transfer matrix formalism applicable to certain reparametrization invariant theories, including quantum gravity, is proposed. In this formulation it is found that every stationary state in quantum gravity satisfies a Wheeler-DeWitt…
Emission of hard microscopic string (graviton) by an excited macroscopic string may be viewed as a model of branching of a $(1+1)$-dimensional baby universe off large parent one. We show that, apart from a trivial factor, the total emission…
The main results for the two-dimensional quantum gravity, conjectured from the matrix model or integrable approach, are presented in the form to be compared with the world-sheet or Liouville approach. In spherical limit the integrable side…
Quantum Action Principle which has been used as a ground for a probabilistic interpretation of one-particle relativistic quantum mechanics \cite{GLL} is applied to quantum cosmology. The quantum creation of matter in a minisuperspace model…
A classical two dimensional theory of gravity which has a number of interesting features (including a Newtonian limit, black holes and gravitational collapse) is quantized using conformal field theoretic techniques. The critical dimension…
A baby-universe model of cosmic inflation is analyzed using quantum Darwinism. In this model cosmic inflation can be approximated as Brownian motion of a quantum field, and quantum Darwinism implies that decoherence is the result of quantum…
We analyse MINBU distribution of 2 dimensional quantum gravity. New data of R$^2$-gravity by the Monte Carlo simulation and its theoretical analysis by the semiclassical approach are presented. The cross-over phenomenon takes place at some…
Despite their diversity, many of the most prominent candidate theories of quantum gravity share the property to be effectively lower-dimensional at small scales. In particular, dimension two plays a fundamental role in the finiteness of…
One of the principal aspects through which the effects of quantum gravity are hoped to manifest is the possible modification of the dispersion relation for electromagnetic (e-m) waves. By combining (i) the symmetry reduced approaches to…
In Loop Quantum Gravity mathematically rigorous models of full quantum gravity were proposed. In this paper we study a cosmological sector of one of the models describing quantum gravity with positive cosmological constant coupled to…
In three spacetime dimensions, general relativity drastically simplifies, becoming a ``topological'' theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are…
Two approaches to quantization of Freedman's closed Universe are compared. In the first approach, the Shrodinger's norm of the wave function of Universe is used, and in the second approach, the Klein-Gordon's norm is used. The second one…
We study a minisuperspace quantum cosmology for a 2+1 dimensional de Sitter universe and find the wave function both exactly and in WKB approximation. Then we extend the model to a canonically quantized field theory for quantum gravity,…