We study the gas distribution in the Milky Way and Andromeda using a constrained cosmological simulation of the Local Group (LG) within the context of the CLUES (Constrained Local UniversE Simulations) project. We analyse the properties of gas in the simulated galaxies at z = 0 for three different phases: 'cold', 'hot' and H i, and compare our results with observations. The amount of material in the hot halo (M hot ≈ 4 − 5 × 10 10 M ⊙ ), and the cold (M cold (r 10 kpc) ≈ 10 8 M ⊙ ) and H i (M HI (r 50 kpc) ≈ 3 − 4 × 10 8 M ⊙ ) components display a reasonable agreement with observations. We also compute the accretion/ejection rates together with the H i (radial and all-sky) covering fractions. The integrated H i accretion rate within r = 50 kpc gives ∼0.2 − 0.3 M ⊙ yr −1 , i.e. close to that obtained from high-velocity clouds in the Milky Way. We find that the global accretion rate is dominated by hot material, although ionized gas with T 10 5 K can contribute significantly too. The net accretion rates of all material at the virial radii are 6 − 8 M ⊙ yr −1 . At z = 0, we find a significant gas excess between the two galaxies, as compared to any other direction, resulting from the overlap of their gaseous haloes. In our simulation, the gas excess first occurs at z ∼ 1, as a consequence of the kinematical evolution of the LG.

Present models describing the interaction of quantum Maxwell and gravitational fields predict a breakdown of Lorentz invariance and a non standard dispersion relation in the semiclassical approximation. Comparison with observational data however, does not support their predictions. In this work we introduce a different set of ab initio assumptions in the canonical approach, namely that the homogeneous Maxwell equations are valid in the semiclassical approximation, and find that the resulting field equations are Lorentz invariant in the semiclassical limit.We also include a phenomenological analysis of possible effects on the propagation of light, and their dependence on energy, in a cosmological context.

We study the electromagnetic field equations on an arbitrary quantum curved background in the semiclassical approximation of Loop Quantum Gravity. The effective interaction hamiltonian for the Maxwell and gravitational fields is obtained and the corresponding field equations, which can be expressed as a modified wave equation for the Maxwell potential, are derived. We use these results to analyze electromagnetic wave propagation on a quantum Robertson-Walker space time and show that Lorentz Invariance is not preserved. The formalism developed can be applied to the case where back reaction effects on the metric due to the electromagnetic field are taken into account, leading to non covariant field equations.

In this article we develop a numerical scheme to deal with interfaces between touching numerical grids when solving the second-order wave equation. We show that it is possible to implement an interface scheme of "penalty" type for the second-order wave equation, similar to the ones used for first-order hyperbolic and parabolic equations, and the second-order scheme used by Mattsson et al. [1]. These schemes, known as SAT schemes for finite difference approximations and penalties for spectral ones, and ours share similar properties but in our case one needs to pass at the interface a smaller amount of data than previously known schemes. This is important for multi-block parallelizations in several dimensions, for it implies that one obtains the same solution quality while sharing among different computational grids only a fraction of the data one would need for a comparable (in accuracy) SAT or Mattsson et al.'s scheme.The semi-discrete approximation used here preserves the norm and uses standard finitedifference operators satisfying summation by parts. For the time integrator we use a semiimplicit IMEX Runge-Kutta method. This is crucial, since the explicit Runge-Kutta method would be impractical given the severe restrictions that arise from the stiff parts of the equations.