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.

A hybrid framework of spin hydrodynamics is proposed that combines the results of kinetic theory for particles with spin 1 / 2 with the Israel-Stewart method of introducing nonequilibrium dynamics. The framework of kinetic theory is used to define the perfect-fluid description that conserves baryon number, energy, linear momentum and spin part of angular momentum. This leads to the entropy conservation although, in the presence of spin degrees of freedom, the perfect-fluid formalism includes extra terms whose structure is usually attributed to dissipation. The genuine dissipative terms appear from the condition of positive entropy production in nonequilibrium processes. They are responsible for the transfer between the spin and orbital parts of angular momentum, with the total angular momentum being conserved. Published by the American Physical Society 2024

Lattice formulations of gravity can be used to study non-perturbative aspects of quantum gravity. Causal Dynamical Triangulations (CDT) is a lattice model of gravity that has been used in this way. It has a built-in time foliation but is coordinate-independent in the spatial directions. The higher-order phase transitions observed in the model may be used to define a continuum limit of the lattice theory. Some aspects of the transitions are better studied when the topology of space is toroidal rather than spherical. In addition, a toroidal spatial topology allows us to understand more easily the nature of typical quantum fluctuations of the geometry. In particular, this topology makes it possible to use massless scalar fields that are solutions to Laplace’s equation with special boundary conditions as coordinates that capture the fractal structure of the quantum geometry. When such scalar fields are included as dynamical fields in the path integral, they can have a dramatic effect on the geometry.

A typical geometry extracted from the path integral of a quantum theory of gravity may be quite complicated in the UV region. Even if a single configuration is not physical, its properties may be of interest to understand the details of its nature, since some universal features can be important for the physics of the model. If the formalism describing the geometry is coordinate independent, which is the case in the model studied here, such understanding may be facilitated by the use of suitable coordinate systems. In this article we use scalar fields that solve Laplace’s equation to introduce coordinates on geometries with a toroidal topology. Using these coordinates we observe what we identify as the cosmic voids and filaments structure, even if matter is only a tool to visualize the geometry. We also show that if the scalar fields we used as coordinates are dynamically coupled to geometry, they can change it in a dramatic way, leading to a modification of the spatial topology.

Using Monte Carlo computer simulations, we study the impact of matter fields on the geometry of a typical quantum universe in the causal dynamical triangulations (cdt) model of lattice quantum gravity. The quantum universe has the size of a few Planck lengths and the spatial topology of a three-torus. The matter fields are multicomponent scalar fields taking values in a torus with circumference $\delta$ in each spatial direction, which acts as a new parameter in the cdt model. Changing $\delta$, we observe a phase transition caused by the scalar field. This discovery may have important consequences for quantum universes with nontrivial topology, since the phase transition can change the topology to a simply connected one.

A recently formulated extension of perfect spin hydrodynamics, which includes second-order corrections in the spin polarization tensor to the energy-momentum tensor and baryon current, is studied in the case of a one-dimensional boost-invariant expansion. The presence of second-order corrections introduces feedback from spin dynamics on the hydrodynamic background, constraining possible spin polarization configurations. However, as long as the magnitude of the spin polarization tensor remains small (below unity in natural units), the permitted spin dynamics differs very little from that found in the case without the second-order corrections. Published by the American Physical Society 2025