2,511,842 research outputs found
Anisotropically Inflating Universes
We show that in theories of gravity that add quadratic curvature invariants
to the Einstein-Hilbert action there exist expanding vacuum cosmologies with
positive cosmological constant which do not approach the de Sitter universe.
Exact solutions are found which inflate anisotropically. This behaviour is
driven by the Ricci curvature invariant and has no counterpart in the general
relativistic limit. These examples show that the cosmic no-hair theorem does
not hold in these higher-order extensions of general relativity and raises new
questions about the ubiquity of inflation in the very early universe and the
thermodynamics of gravitational fields.Comment: 5 pages, further discussion and references adde
Unambiguous probabilities in an eternally inflating universe
``Constants of Nature'' and cosmological parameters may in fact be variables
related to some slowly-varying fields. In models of eternal inflation, such
fields will take different values in different parts of the universe. Here I
show how one can assign probabilities to values of the ``constants'' measured
by a typical observer. This method does not suffer from ambiguities previously
discussed in the literature.Comment: 7 pages, Final version (minor changes), to appear in Phys. Rev. Let
Parameters for Twisted Representations
The study of Hermitian forms on a real reductive group gives rise, in the
unequal rank case, to a new class of Kazhdan-Lusztig-Vogan polynomials. These
are associated with an outer automorphism of , and are related to
representations of the extended group . These polynomials were
defined geometrically by Lusztig and Vogan in "Quasisplit Hecke Algebras and
Symmetric Spaces", Duke Math. J. 163 (2014), 983--1034. In order to use their
results to compute the polynomials, one needs to describe explicitly the
extension of representations to the extended group. This paper analyzes these
extensions, and thereby gives a complete algorithm for computing the
polynomials. This algorithm is being implemented in the Atlas of Lie Groups and
Representations software
Relaxing in foam
We investigate the mechanical response of an aqueous foam, and its relation
to the microscopic rearrangement dynamics of the bubble-packing structure. At
rest, even though the foam is coarsening, the rheology is demonstrated to be
linear. Under flow, shear-induced rearrangements compete with
coarsening-induced rearrangements. The macroscopic consequences are captured by
a novel rheological method in which a step-strain is superposed on an otherwise
steady flow
The Number of Group Homomorphisms from into
Counting homomorphisms between cyclic groups is a common exercise in a first
course in abstract algebra. A similar problem, accessible at the same level, is
to count the number of group homomorphisms from a dihedral group of order
into a dihedral group of order . While the solution requires only
elementary group theory, the result does not appear in the literature or in the
usual texts. As the solution may be of interest, particularly to those teaching
undergraduate abstract algebra, it is provided in this note
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