52 research outputs found
The Self-Organized de Sitter Universe
We propose a theory of quantum gravity which formulates the quantum theory as
a nonperturbative path integral, where each spacetime history appears with a
weight given by the exponentiated Einstein-Hilbert action of the corresponding
causal geometry. The path integral is diffeomorphism-invariant (only geometries
appear) and background-independent. The theory can be investigated by computer
simulations, which show that a de Sitter universe emerges on large scales. This
emergence is of an entropic, self-organizing nature, with the weight of the
Einstein-Hilbert action playing a minor role. Also the quantum fluctuations
around this de Sitter universe can be studied quantitatively and remain small
until one gets close to the Planck scale. The structures found to describe
Planck-scale gravity are reminiscent of certain aspects of condensed-matter
systems.Comment: Article unchanged, one line added to acknowledgmen
A Lorentzian cure for Euclidean troubles
There is strong evidence coming from Lorentzian dynamical triangulations that
the unboundedness of the gravitational action is no obstacle to the
construction of a well-defined non-perturbative path integral. In a continuum
approach, a similar suppression of the conformal divergence comes about as the
result of a non-trivial path-integral measure.Comment: 3 page
A non-perturbative Lorentzian path integral for gravity
A well-defined regularized path integral for Lorentzian quantum gravity in
three and four dimensions is constructed, given in terms of a sum over
dynamically triangulated causal space-times. Each Lorentzian geometry and its
associated action have a unique Wick rotation to the Euclidean sector. All
space-time histories possess a distinguished notion of a discrete proper time.
For finite lattice volume, the associated transfer matrix is self-adjoint and
bounded. The reflection positivity of the model ensures the existence of a
well-defined Hamiltonian. The degenerate geometric phases found previously in
dynamically triangulated Euclidean gravity are not present. The phase structure
of the new Lorentzian quantum gravity model can be readily investigated by both
analytic and numerical methods.Comment: 11 pages, LaTeX, improved discussion of reflection positivity,
conclusions unchanged, references update
Geometry of the quantum universe
A universe much like the (Euclidean) de Sitter space-time appears as
background geometry in the causal dynamical triangulation (CDT) regularization
of quantum gravity. We study the geometry of such universes which appear in the
path integral as a function of the bare coupling constants of the theory.Comment: 19 pages, 7 figures. Typos corrected. Conclusions unchange
Renormalization of 3d quantum gravity from matrix models
Lorentzian simplicial quantum gravity is a non-perturbatively defined theory
of quantum gravity which predicts a positive cosmological constant. Since the
approach is based on a sum over space-time histories, it is perturbatively
non-renormalizable even in three dimensions. By mapping the three-dimensional
theory to a two-matrix model with ABAB interaction we show that both the
cosmological and the (perturbatively) non-renormalizable gravitational coupling
constant undergo additive renormalizations consistent with canonical
quantization.Comment: 14 pages, 3 figure
The Nonperturbative Quantum de Sitter Universe
The dynamical generation of a four-dimensional classical universe from
nothing but fundamental quantum excitations at the Planck scale is a
long-standing challenge to theoretical physicists. A candidate theory of
quantum gravity which achieves this goal without invoking exotic ingredients or
excessive fine-tuning is based on the nonperturbative and
background-independent technique of Causal Dynamical Triangulations. We
demonstrate in detail how in this approach a macroscopic de Sitter universe,
accompanied by small quantum fluctuations, emerges from the full gravitational
path integral, and how the effective action determining its dynamics can be
reconstructed uniquely from Monte Carlo data. We also provide evidence that it
may be possible to penetrate to the sub-Planckian regime, where the Planck
length is large compared to the lattice spacing of the underlying
regularization of geometry.Comment: Article unchanged. Line added in acknowledgmen
Semiclassical Universe from First Principles
Causal Dynamical Triangulations in four dimensions provide a
background-independent definition of the sum over space-time geometries in
nonperturbative quantum gravity. We show that the macroscopic four-dimensional
world which emerges in the Euclidean sector of this theory is a bounce which
satisfies a semiclassical equation. After integrating out all degrees of
freedom except for a global scale factor, we obtain the ground state wave
function of the universe as a function of this scale factor.Comment: 15 pages, 4 figure
A new perspective on matter coupling in 2d quantum gravity
We provide compelling evidence that a previously introduced model of
non-perturbative 2d Lorentzian quantum gravity exhibits (two-dimensional)
flat-space behaviour when coupled to Ising spins. The evidence comes from both
a high-temperature expansion and from Monte Carlo simulations of the combined
gravity-matter system. This weak-coupling behaviour lends further support to
the conclusion that the Lorentzian model is a genuine alternative to Liouville
quantum gravity in two dimensions, with a different, and much `smoother'
critical behaviour.Comment: 24 pages, 7 figures (postscript
CDT meets Horava-Lifshitz gravity
The theory of causal dynamical triangulations (CDT) attempts to define a
nonperturbative theory of quantum gravity as a sum over space-time geometries.
One of the ingredients of the CDT framework is a global time foliation, which
also plays a central role in the quantum gravity theory recently formulated by
Ho\v{r}ava. We show that the phase diagram of CDT bears a striking resemblance
with the generic Lifshitz phase diagram appealed to by Ho\v{r}ava. We argue
that CDT might provide a unifying nonperturbative framework for anisotropic as
well as isotropic theories of quantum gravity.Comment: 17 pages, 3 figures. Typos corrected, a few remarks added
Emergence of a 4D World from Causal Quantum Gravity
Causal Dynamical Triangulations in four dimensions provide a
background-independent definition of the sum over geometries in nonperturbative
quantum gravity, with a positive cosmological constant. We present evidence
that a macroscopic four-dimensional world emerges from this theory dynamically.Comment: 11 pages, 3 figures; some short clarifying comments added; final
version to appear in Phys. Rev. Let
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