Canonical Structure of Locally Homogeneous Systems on Compact Closed 3-Manifolds of Types E3E^3, Nil and Sol

In this paper we investigate the canonical structure of diffeomorphism invariant phase spaces for spatially locally homogeneous spacetimes with 3-dimensional compact closed spaces. After giving a general algorithm to express the diffeomorphism-invariant phase space and the canonical structure of a locally homogeneous system in terms of those of a homogeneous system on a covering space and a moduli space, we completely determine the canonical structures and the Hamiltonians of locally homogeneous pure gravity systems on orientable compact closed 3-spaces of the Thurston-type $E^3$, \Nil and \Sol for all possible space topologies and invariance groups. We point out that in many cases the canonical structure becomes degenerate in the moduli sectors, which implies that the locally homogeneous systems are not canonically closed in general in the full diffeomorphism-invariant phase space of generic spacetimes with compact closed spaces.Comment: 62 pages, LaTe

PyMieDAP: a Python--Fortran tool to compute fluxes and polarization signals of (exo)planets

PyMieDAP (the Python Mie Doubling-Adding Programme) is a Python--based tool for computing the total, linearly, and circularly polarized fluxes of incident unpolarized sun- or starlight that is reflected by, respectively, Solar System planets or moons, or exoplanets at a range of wavelengths. The radiative transfer computations are based on an adding--doubling Fortran algorithm and fully include polarization for all orders of scattering. The model (exo)planets are described by a model atmosphere composed of a stack of homogeneous layers containing gas and/or aerosol and/or cloud particles bounded below by an isotropically, depolarizing surface (that is optionally black). The reflected light can be computed spatially--resolved and/or disk--integrated. Spatially--resolved signals are mostly representative for observations of Solar System planets (or moons), while disk--integrated signals are mostly representative for exoplanet observations. PyMieDAP is modular and flexible, and allows users to adapt and optimize the code according to their needs. PyMieDAP keeps options open for connections with external programs and for future additions and extensions. In this paper, we describe the radiative transfer algorithm that PyMieDAP is based on and the code's principal functionalities. And we provide benchmark results of PyMieDAP that can be used for testing its installation and for comparison with other codes. PyMieDAP is available online under the GNU GPL license at http://gitlab.com/loic.cg.rossi/pymiedapComment: 15 pages, 7 figures, 4 tables. Accepted for publication in Astronomy and Astrophysic

Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology

We introduce some algebraic geometric models in cosmology related to the "boundaries" of space-time: Big Bang, Mixmaster Universe, Penrose's crossovers between aeons. We suggest to model the kinematics of Big Bang using the algebraic geometric (or analytic) blow up of a point $x$. This creates a boundary which consists of the projective space of tangent directions to $x$ and possibly of the light cone of $x$. We argue that time on the boundary undergoes the Wick rotation and becomes purely imaginary. The Mixmaster (Bianchi IX) model of the early history of the universe is neatly explained in this picture by postulating that the reverse Wick rotation follows a hyperbolic geodesic connecting imaginary time axis to the real one. Penrose's idea to see the Big Bang as a sign of crossover from "the end of previous aeon" of the expanding and cooling Universe to the "beginning of the next aeon" is interpreted as an identification of a natural boundary of Minkowski space at infinity with the Big Bang boundary