Related papers: Dynamical dimensional reduction in toy models of 4…
We review a recently discovered continuum limit for the one-matrix model which describes "causal" two-dimensional quantum gravity. The behaviour of the quantum geometry in this limit is different from the quantum geometry of Euclidean…
We review a growing theoretical motivation and evidence that the number of dimensions actually reduces at high energies. This reduction can happen near the Planck scale, or much before, the dimensions that are reduced can be effective,…
One could begin a study like the present one by simply postulating that our universe is four-dimensional. There are ample reasons for doing this. Experience, observation and experiment all point to the fact that we inhabit a…
A profound quantum-gravitational effect of space-time dimension running with respect to the size of space-time region has been discovered a few years ago through the numerical simulations of lattice quantum gravity in the framework of…
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…
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.…
We search for time-dependent solutions for the 5-dimensional system of a scalar field canonically coupled to gravity. Time-independent and time-dependent scalar field configurations with the most general homogeneous and isotropic 4D metric…
We discuss some problems related to dimensional reductions of gravity theories to two-dimensional and one-dimensional dilaton gravity models. We first consider the most general cylindrical reductions of the four-dimensional gravity and…
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…
A number of very different approaches to quantum gravity contain a common thread, a hint that spacetime at very short distances becomes effectively two dimensional. I review this evidence, starting with a discussion of the physical meaning…
We compare the effective action of the scale factor obtained from lattice quantum gravity (in the form of Causal Dynamical Triangulations (CDT)) to the corresponding effective action obtained from the simplest Functional Renormalization…
With toy modelling of conceptual aspects of quantum cosmology and the problem of time in quantum gravity in mind, I study the classical and quantum dynamics of the pure-shape (i.e. scale-free) triangle formed by 3 particles in 2-d. I do so…
A class of cosmological solutions of higher dimensional Einstein field equations with the energy-momentum tensor of a homogeneous, isotropic fluid as the source are considered with an anisotropic metric that includes the direct sum of a…
Scaling relations in four-dimensional simplicial quantum gravity are proposed using the concept of the geodesic distance. Based on the analogy of a loop length distribution in the two-dimensional case, the scaling relations of the boundary…
The statistical properties of dynamically triangulated manifolds (DT mfds) in terms of the geodesic distance have been studied numerically. The string susceptibility exponents for the boundary surfaces in three-dimensional DT mfds were…
Four-dimensional (4D) simplicial quantum gravity coupled to both scalar fields (N_X) and gauge fields (N_A) has been studied using Monte-Carlo simulations. The matter dependence of the string susceptibility exponent gamma^{(4)} is…
Scaling arguments are used to constrain the angular spectrum of distortions on boundaries of macroscopic causal diamonds, produced by Planck-scale vacuum fluctuations of causally-coherent quantum gravity. The small-angle spectrum of…
We performed detailed study of the phase transition region in Four Dimensional Simplicial Quantum Gravity, using the dynamical triangulation approach. The phase transition between the Gravity and Antigravity phases turned out to be…
We study the $N$-dependent behaviour of $\mathrm{2d}$ causal set quantum gravity. This theory is known to exhibit a phase transition as the analytic continuation parameter $\beta$, akin to an inverse temperature, is varied. Using a scaling…
Colored tensor models generalize matrix models in arbitrary dimensions yielding a statistical theory of random higher dimensional topological spaces. They admit a 1/N expansion dominated by graphs of spherical topology. The simplest tensor…