arXiv subjects
Publications and source records attributed to Jan Ambjorn.
We point out that a simple late-time cosmological model where our Universe can absorb "baby universes" explains the exponential expansion of our universe without the need of a cosmological constant and leads to a z-dependence of the parameter w(z) in the equation of state. In this model w(z) is less than -1 for z sufficiently large.
We show how our Universe can emerge from a symmetry breaking of a multicomponent $W_3$ algebra, where the components in addition form a Jordan algebra. We discuss how symmetry breaking related to the Jordan algebras $H_3(C)$ and $H_3(O)$ over the complex and octonion numbers can lead to an extended four-dimensional spacetime, where the expansion of the Universe is governed by a modified Friedmann equation. We finally discuss how this modified Friedmann equation might explain a number of puzzling cosmological observations.
Using numerical data coming from Monte Carlo simulations of four-dimensional Causal Dynamical Triangulations, we study how automated machine learning algorithms can be used to recognize transitions between different phases of quantum geometries observed in lattice quantum gravity. We tested seven supervised and seven unsupervised machine learning models and found that most of them were very successful in that task, even outperforming standard methods based on order parameters.
Causal Dynamical Triangulations (CDT) is a lattice theory of quantum gravity. It is shown how to identify the IR and the UV limits of this lattice theory with similar limits studied using the continuum, functional renormalization group (FRG) approach. The main technical tool in this study will be the so-called two-point function. It will allow us to identify a correlation length not directly related to the propagation of physical degrees of freedom.
If our Universe is allowed to absorb baby universes, one obtains a modified Friedmann equation that can explain the late time acceleration of our Universe and there is no need for a cosmological constant. In addition the modified Friedmann equation favors the value of the Hubble constant obtained by local measurements.
We show that by allowing our Universe to merge with other universes one is lead to modified Friedmann equations that explain the present accelerated expansion of our Universe without the need of a cosmological constant.
This article is an overview of the use of so-called Euclidean Dynamical Triangulations (EDT) and Causal Dynamical Triangulations (CDT) as lattice regularizations of quantum gravity. The lattice regularizations have been very successful in the case of two-dimensional quantum gravity, where the lattice theories indeed provide regularizations of continuum well defined quantum gravity theories. In four-dimensional spacetime the Einstein-Hilbert action leads to a theory of gravity which is not renormalizable as a perturbative quantum theory around flat spacetime. It is discussed how lattice gravity in the form of EDT or CDT can be used to search for a non-perturbative UV fixed point of the lattice renormalization group in the spirit of asymptotic safety. In this way it might be possible to define a quantum theory of gravity also at lengthscales smaller than the Planck length.
We have already shown how a modified Friedmann equation, originating from a model of the Universe built from a certain $W_3$ algebra, is able to explainthe difference between the Hubble constants extracted from CMB data and from local measurements. In this article we show that the same model also describes aspects of the large scale structure of the Universe well.
These Lecture Notes provide an elementary introduction to the quantization of two-dimensional quantum gravity. Nothing beyond undergratuate physics and mathematic is required. Explicit formulas for the partition functions for universes with n boundaries are derived, as well as for the so-called two-point function. The latter shows explicitly that the fractal dimension of a typical two-dimensional quantum universe is four.
We compute the string susceptibility $γ_{str}$ for the regularized Nambu-Goto string in $d$ dimensions and obtain $γ_{str}=1/2 $ in $2<d<26$. This agrees with previous results obtained for lattice strings.
We quantize the two-dimensional projectable Horava-Lifshitz gravity with a bi-local as well as space-like wormhole interaction. The resulting quantum Hamiltonian coincides with the one obtained through summing over all genus in the string field theory for two-dimensional causal dynamical triangulations. This implies that our wormhole interaction can be interpreted as a splitting or joining interaction of one-dimensional strings.
We show that in a two-dimensional model of quantum gravity the summation over all possible wormhole configurations leads to a kind of Coleman mechanism where the cosmological constant plays no role for large universes. Observers who are unable to observe the change in topology will naturally interpret the measurements of the size of the universe as being caused by a fluctuating cosmological constant, rather than fluctuating topology of spacetime.
We propose a model for the universe based on Jordan algebras. The action consists of cubic terms with coefficients being the structure constants of a Jordan algebra. Coupling constants only enter the theory via symmetry breaking which also selects a physical vacuum. "Before" the symmetry breaking the universe is in a pre-geometric state where it makes no sense to talk about space or time, but time comes into existence with the symmetry breaking together with a Hamiltonian which can create space from "nothing" and in some cases can propagate the space to macroscopic size in a finite time. There exists symmetry breaking which results in macroscopic spacetime dimensions 3, 4, 6 and 10, based on the Jordan algebras of Hermitian 3x3 matrices with real, complex, quarternion and octonion entries,respectively.
We investigate the impact of spatial topology in 3+1 dimensional causal dynamical triangulations (CDT) by performing numerical simulations with toroidal spatial topology instead of the previously used spherical topology. In the case of spherical spatial topology we observed in the so-called phase C an average spatial volume distribution n(t) which after a suitable time redefinition could be identified as the spatial volume distribution of the four-sphere. Imposing toroidal spatial topology we find that the average spatial volume distribution n(t) is constant. By measuring the covariance matrix of spatial volume fluctuations we determine the form of the effective action. The difference compared to the spherical case is that the effective potential has changed such that it allows a constant average n(t). This is what we observe and this is what one would expect from a minisuperspace GR action where only the scale factor is kept as dynamical variable. Although no background geometry is put in by hand, the full quantum theory of CDT is also with toroidal spatial toplogy able to identify a classical background geometry around which there are well defined quantum fluctuations.
We search for a continuum limit in the causal dynamical triangulation (CDT) approach to quantum gravity by determining the change in lattice spacing using two independent methods. The two methods yield similar results that may indicate how to tune the relevant couplings in the theory in order to take a continuum limit.
Lattice regularizations of the bosonic string allow no tachyons. This has often been viewed as the reason why these theories have never managed to make any contact to standard continuum string theories when the dimension of spacetime is larger than two. We study the continuum string theory in large spacetime dimensions where simple mean field theory is reliable. By keeping carefully the cutoff we show that precisely the existence of a tachyon makes it possible to take a scaling limit which reproduces the lattice-string results. We compare this scaling limit with another scaling limit which reproduces standard continuum-string results. If the people working with lattice regularizations of string theories are akin to Gulliver they will view the standard string-world as a Lilliputian world no larger than a few lattice spacings.
We review some recent results from the causal dynamical triangulation (CDT) approach to quantum gravity. We review recent observations of dimensional reduction at a number of previously undetermined points in the parameter space of CDT, and discuss their possible relevance to the asymptotic safety scenario. We also present an updated phase diagram of CDT, discussing properties of a newly discovered phase and its possible relation to a signature change of the metric.
We implement a proper-time UV regularisation of the Nambu-Goto string, introducing an independent metric tensor and the corresponding Lagrange multiplier, and treating them in the mean-field approximation justified for long strings and/or when the dimensions of space-time is large. We compute the regularised determinant of the 2d Laplacian for the closed string winding around a compact dimension, obtaining in this way the effective action, whose minimisation determines the energy of the string ground state in the mean-field approximation. We discuss the existence of two scaling limits when the cutoff is taken to infinity. One scaling limit reproduces the results obtained by the hypercubic regularisation of the Nambu-Goto string as well as by the use of the dynamical triangulation regularisation of the Polyakov string. The other scaling limit reproduces the results obtained by canonical quantisation of the Nambu-Goto string.