15 research outputs found
Finding a Spherically Symmetric Cosmology from Observations in Observational Coordinates -- Advantages and Challenges
One of the continuing challenges in cosmology has been to determine the
large-scale space-time metric from observations with a minimum of assumptions
-- without, for instance, assuming that the universe is almost
Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW). If we are lucky enough this
would be a way of demonstrating that our universe is FLRW, instead of
presupposing it or simply showing that the observations are consistent with
FLRW. Showing how to do this within the more general spherically symmetric,
inhomogeneous space-time framework takes us a long way towards fulfilling this
goal. In recent work researchers have shown how this can be done both in the
traditional Lema\^{i}tre-Tolman-Bondi (LTB) 3 + 1 coordinate framework, and in
the observational coordinate (OC) framework. In this paper we investigate the
stability of solutions, and the use of data in the OC field equations including
their time evolution and compare both approaches with respect to the
singularity problem at the maximum of the angular-diameter distance, the
stability of solutions, and the use of data in the field equations. This allows
a more detailed account and assessment of the OC integration procedure, and
enables a comparison of the relative advantages of the two equivalent solution
frameworks. Both formulations and integration procedures should, in principle,
lead to the same results. However, as we show in this paper, the OC procedure
manifests certain advantages, particularly in the avoidance of coordinate
singularities at the maximum of the angular-diameter distance, and in the
stability of the solutions obtained. This particular feature is what allows us
to do the best fitting of the data to smooth data functions and the possibility
of constructing analytic solutions to the field equations.Comment: 31 page
Supernovae data and perturbative deviation from homogeneity
We show that a spherically symmetric perturbation of a dust dominated
FRW universe in the Newtonian gauge can lead to an apparent
acceleration of standard candles and provide a fit to the magnitude-redshift
relation inferred from the supernovae data, while the perturbation in the
gravitational potential remains small at all scales. We also demonstrate that
the supernovae data does not necessarily imply the presence of some additional
non-perturbative contribution by showing that any Lemaitre-Tolman-Bondi model
fitting the supernovae data (with appropriate initial conditions) will be
equivalent to a perturbed FRW spacetime along the past light cone.Comment: 8 pages, 3 figures; v2: 1 figure added, references added/updated,
minor modifications and clarifications, matches published versio
Light-cone averaging in cosmology: formalism and applications
We present a general gauge invariant formalism for defining cosmological
averages that are relevant for observations based on light-like signals. Such
averages involve either null hypersurfaces corresponding to a family of past
light-cones or compact surfaces given by their intersection with timelike
hypersurfaces. Generalized Buchert-Ehlers commutation rules for derivatives of
these light-cone averages are given. After introducing some adapted "geodesic
light-cone" coordinates, we give explicit expressions for averaging the
redshift to luminosity-distance relation and the so-called "redshift drift" in
a generic inhomogeneous Universe.Comment: 20 pages, 2 figures. Comments and references added, typos corrected.
Version accepted for publication in JCA
Strong Gravitational Lensing and Dark Energy Complementarity
In the search for the nature of dark energy most cosmological probes measure
simple functions of the expansion rate. While powerful, these all involve
roughly the same dependence on the dark energy equation of state parameters,
with anticorrelation between its present value w_0 and time variation w_a.
Quantities that have instead positive correlation and so a sensitivity
direction largely orthogonal to, e.g., distance probes offer the hope of
achieving tight constraints through complementarity. Such quantities are found
in strong gravitational lensing observations of image separations and time
delays. While degeneracy between cosmological parameters prevents full
complementarity, strong lensing measurements to 1% accuracy can improve
equation of state characterization by 15-50%. Next generation surveys should
provide data on roughly 10^5 lens systems, though systematic errors will remain
challenging.Comment: 7 pages, 5 figure
Backreaction on the luminosity-redshift relation from gauge invariant light-cone averaging
Using a recently proposed gauge invariant formulation of light-cone
averaging, together with adapted "geodesic light-cone" coordinates, we show how
an "induced backreaction" effect emerges, in general, from correlated
fluctuations in the luminosity distance and covariant integration measure.
Considering a realistic stochastic spectrum of inhomogeneities of primordial
(inflationary) origin we find that both the induced backreaction on the
luminosity-redshift relation and the dispersion are larger than naively
expected. On the other hand the former, at least to leading order and in the
linear perturbative regime, cannot account by itself for the observed effects
of dark energy at large-redshifts. A full second-order calculation, or even
better a reliable estimate of contributions from the non-linear regime, appears
to be necessary before firm conclusions on the correct interpretation of the
data can be drawn.Comment: 22 pages, 4 figures. Comments and references added, Fig. 1 modified.
Version accepted for publication in JCA
Constraints on the CMB temperature redshift dependence from SZ and distance measurements
The relation between redshift and the CMB temperature,
is a key prediction of standard cosmology, but is violated in many non-standard
models. Constraining possible deviations to this law is an effective way to
test the CDM paradigm and search for hints of new physics. We present
state-of-the-art constraints, using both direct and indirect measurements. In
particular, we point out that in models where photons can be created or
destroyed, not only does the temperature-redshift relation change, but so does
the distance duality relation, and these departures from the standard behaviour
are related, providing us with an opportunity to improve constraints. We show
that current datasets limit possible deviations of the form
to be up to a redshift
. We also discuss how, with the next generation of space and
ground-based experiments, these constraints can be improved by more than one
order of magnitude.Comment: 27 pages, 11 figure
Dark energy as a mirage
Motivated by the observed cosmic matter distribution, we present the
following conjecture: due to the formation of voids and opaque structures, the
average matter density on the path of the light from the well-observed objects
changes from Omega_M ~ 1 in the homogeneous early universe to Omega_M ~ 0 in
the clumpy late universe, so that the average expansion rate increases along
our line of sight from EdS expansion Ht ~ 2/3 at high redshifts to free
expansion Ht ~ 1 at low redshifts. To calculate the modified observable
distance-redshift relations, we introduce a generalized Dyer-Roeder method that
allows for two crucial physical properties of the universe: inhomogeneities in
the expansion rate and the growth of the nonlinear structures. By treating the
transition redshift to the void-dominated era as a free parameter, we find a
phenomenological fit to the observations from the CMB anisotropy, the position
of the baryon oscillation peak, the magnitude-redshift relations of type Ia
supernovae, the local Hubble flow and the nucleosynthesis, resulting in a
concordant model of the universe with 90% dark matter, 10% baryons, no dark
energy, 15 Gyr as the age of the universe and a natural value for the
transition redshift z_0=0.35. Unlike a large local void, the model respects the
cosmological principle, further offering an explanation for the late onset of
the perceived acceleration as a consequence of the forming nonlinear
structures. Additional tests, such as quantitative predictions for angular
deviations due to an anisotropic void distribution and a theoretical derivation
of the model, can vindicate or falsify the interpretation that light
propagation in voids is responsible for the perceived acceleration.Comment: 33 pages, 2 figs; v2: minor clarifications, results unchanged; v3:
matches the version published in General Relativity and Gravitatio
Light propagation in statistically homogeneous and isotropic universes with general matter content
We derive the relationship of the redshift and the angular diameter distance
to the average expansion rate for universes which are statistically homogeneous
and isotropic and where the distribution evolves slowly, but which have
otherwise arbitrary geometry and matter content. The relevant average expansion
rate is selected by the observable redshift and the assumed symmetry properties
of the spacetime. We show why light deflection and shear remain small. We write
down the evolution equations for the average expansion rate and discuss the
validity of the dust approximation.Comment: 42 pages, no figures. v2: Corrected one detail about the angular
diameter distance and two typos. No change in result
The Metric of the Cosmos from Luminosity and Age Data
This paper presents the algorithm for determining the Lemaitre-Tolman (LT)
model that best fits given datasets for maximum stellar ages, and SNIa
luminosities, both as functions of redshift. It then applies it to current
cosmological data. Special attention must be given to the handling of the
origin, and the region of the maximum diameter distances. As with a previous
combination of datasets (galaxy number counts and luminosity distances versus
redshift), there are relationships that must hold at the region of the maximum
diameter distance, which are unlikely to be obeyed exactly by real data. We
show how to make corrections that enable a self-consistent solution to be
found. We address the questions of the best way to approximate discrete data
with smooth functions, and how to estimate the uncertainties of the output -
the 3 free functions that determine a specific LT metric. While current data
does not permit any confidence in our results, we show that the method works
well, and reasonable LT models do fit with or without a cosmological constant.Comment: 25 pages, 8 figures; matches published versio
Astronomical Distance Determination in the Space Age: Secondary Distance Indicators
The formal division of the distance indicators into primary and secondary leads to difficulties in description of methods which can actually be used in two ways: with, and without the support of the other methods for scaling. Thus instead of concentrating on the scaling requirement we concentrate on all methods of distance determination to extragalactic sources which are designated, at least formally, to use for individual sources. Among those, the Supernovae Ia is clearly the leader due to its enormous success in determination of the expansion rate of the Universe. However, new methods are rapidly developing, and there is also a progress in more traditional methods. We give a general overview of the methods but we mostly concentrate on the most recent developments in each field, and future expectations. © 2018, The Author(s)