11,537 research outputs found

### Can one determine cosmological parameters from multi-plane strong lens systems?

Strong gravitational lensing of sources with different redshifts has been
used to determine cosmological distance ratios, which in turn depend on the
expansion history. Hence, such systems are viewed as potential tools for
constraining cosmological parameters. Here we show that in lens systems with
two distinct source redshifts, of which the nearest one contributes to the
light deflection towards the more distant one, there exists an invariance
transformation which leaves all strong lensing observables unchanged (except
the product of time delay and Hubble constant), generalizing the well-known
mass-sheet transformation in single plane lens systems. The transformation
preserves the relative distribution of mass and light, so that a
`mass-follows-light' assumption does not fix the MST. All time delays (from
sources on both planes) scale with the same factor -- time-delay ratios are
therefore invariant under the MST. Changing cosmological parameters, and thus
distance ratios, is essentially equivalent to such a mass-sheet transformation.
As an example, we discuss the double source plane system SDSSJ0946+1006, which
has been recently studied by Collett and Auger, and show that variations of
cosmological parameters within reasonable ranges lead to only a small
mass-sheet transformation in both lens planes. Hence, the ability to extract
cosmological information from such systems depends heavily on the ability to
break the mass-sheet degeneracy.Comment: 5 pages, matches the printed versio

### The cosmological lens equation and the equivalent single-plane gravitational lens

The gravitational lens equation resulting from a single (non-linear) mass
concentration (the main lens) plus inhomogeneities of the large-scale structure
is shown to be strictly equivalent to the single-plane gravitational lens
equation without the cosmological perturbations. The deflection potential (and,
by applying the Poisson equation, also the mass distribution) of the equivalent
single-plane lens is derived. If the main lens is described by elliptical
isopotential curves plus a shear term, the equivalent single-plane lens will be
of the same form. Due to the equivalence shown, the determination of the Hubble
constant from time delay measurements is affected by the same mass-sheet
invariance transformation as for the single-plane lens. If the lens strength is
fixed (e.g., by measuring the velocity dispersion of stars in the main lens),
the determination of $H_0$ is affected by inhomogeneous matter between us and
the lens. The orientation of the mass distribution relative to the image
positions is the same for the cosmological lens situation and the single-plane
case. In particular this implies that cosmic shear cannot account for a
misalignment of the observed galaxy orientation relative to the best-fitting
lens model.Comment: TeX, 11 pages, submitted to MNRA

### U(g)-finite locally analytic representations

In this paper we continue the study of locally analytic representations of a
$p$-adic Lie group $G$ in vector spaces over a spherically complete
non-archimedean field $K$, building on the algebraic approach to such
representations introduced in our paper "Locally analytic distributions and
p-adic representation theory, with applications to GL_2." In that paper we
associated to a representation $V$ a module $M$ over the ring $D(G,K)$ of
locally analytic distributions on $G$ and described an admissibility condition
on $V$ in terms of algebraic properties of $M$.
In this paper we determine the relationship between our admissibility
condition on locally analytic modules and the traditional admissibility of
Langlands theory. We then analyze the class of locally analytic representations
with the property that their associated modules are annihilated by an ideal of
finite codimension in the universal enveloping algebra of G, showing under some
hypotheses on G that they are sums of representations of the form $X\otimes Y$,
with X finite dimensional and Y smooth. The irreducible representations of this
type are obtained when X and Y are irreducible.
We conclude by analyzing the reducible members of the locally analytic
principal series of SL_2(\Qp)

### Mass-sheet degeneracy, power-law models and external convergence: Impact on the determination of the Hubble constant from gravitational lensing

The light travel time differences in strong gravitational lensing systems
allows an independent determination of the Hubble constant. This method has
been successfully applied to several lens systems. The formally most precise
measurements are, however, in tension with the recent determination of $H_0$
from the Planck satellite for a spatially flat six-parameters $\Lambda CDM$
cosmology. We reconsider the uncertainties of the method, concerning the mass
profile of the lens galaxies, and show that the formal precision relies on the
assumption that the mass profile is a perfect power law. Simple analytical
arguments and numerical experiments reveal that mass-sheet like transformations
yield significant freedom in choosing the mass profile, even when exquisite
Einstein rings are observed. Furthermore, the characterization of the
environment of the lens does not break that degeneracy which is not physically
linked to extrinsic convergence. We present an illustrative example where the
multiple imaging properties of a composite (baryons + dark matter) lens can be
extremely well reproduced by a power-law model having the same velocity
dispersion, but with predictions for the Hubble constant that deviate by $\sim
20%$. Hence we conclude that the impact of degeneracies between parametrized
models have been underestimated in current $H_0$ measurements from lensing, and
need to be carefully reconsidered.Comment: Accepted for publication in Astronomy and Astrophysics. Discussion
expanded (MSD and velocity dispersion, MSD and free form lens models, MSD and
multiple source redshifts

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