35 research outputs found
Perturbed Spherically Symmetric Dust Solution of the Field Equations in Observational Coordinates with Cosmological Data Functions
Using the framework for solving the spherically symmetric field equations in
observational coordinates given in Araujo and Stoeger (1999), their formulation
and solution in the perturbed FLRW sperically symmetric case with observational
data representing galaxy redshifts, number counts and observer area distances,
both as functions of redshift on our past light cone, are presented. The
importance of the central conditions, those which must hold on our world line
C, is emphasized. In detailing the solution for these perturbations, we discuss
the gauge problem and its resolution in this context, as well as how errors and
gaps in the data are propagated together with the genuine perturbations. This
will provide guidance for solving, and interpreting the solutions of the more
complicated general perturbation problem with observational data on our past
light cone.Comment: Latex 23 pages, no figures, submitted to Astrophysical Journa
Galaxy Cosmological Mass Function
We study the galaxy cosmological mass function (GCMF) in a semi-empirical
relativistic approach using observational data provided by galaxy redshift
surveys. Starting from the theory of Ribeiro & Stoeger (2003,
arXiv:astro-ph/0304094) between the mass-to-light ratio, the selection function
obtained from the luminosity function (LF) data and the luminosity density, the
average luminosity and the average galactic mass are
computed in terms of the redshift. is also alternatively
estimated by a method that uses the galaxy stellar mass function (GSMF).
Comparison of these two forms of deriving the average galactic mass allows us
to infer a possible bias introduced by the selection criteria of the survey. We
used the FORS Deep Field galaxy survey sample of 5558 galaxies in the redshift
range and its LF Schechter parameters in the B-band, as well as
this sample's stellar mass-to-light ratio and its GSMF data. Assuming
as the local value of
the average galactic mass, the LF approach results in and .
However, using the GSMF results produces . We chose the latter result as it is less biased. We then obtained
the theoretical quantities of interest, such as the differential number counts,
to calculate the GCMF, which can be fitted by a Schechter function. The derived
GCMF follows theoretical predictions in which the less massive objects form
first, being followed later by more massive ones. In the range
the GCMF has a strong variation that can be interpreted as a higher rate of
galaxy mergers or as a strong evolution in the star formation history of these
galaxies.Comment: In memory of William R. Stoeger (1943-2014). LaTeX, 8 pages, 7
figures. Minor changes to match version sent to publisher. To appear in
"Astronomy and Astrophysics
Radial Density Statistics of the Galaxy Distribution and the Luminosity Function
This paper discusses a connection between the relativistic number counts of
cosmological sources and the observed galaxy luminosity function (LF).
Observational differential number densities are defined and obtained from
published LF data using such connection. We observe a distortion in the
observational quantities that increases with higher redshift values as compared
to the theoretical predictions. The use of different cosmological distance
measures plays a role in such a distortionComment: 3 pages, 3 figures. Abridged version of arXiv:1201.557
The Limits on Cosmological Anisotropies and Inhomogeneities from COBE Data
Assuming that the cosmological principle holds, Maartens, Ellis and Stoeger
(MES) recently constructed a detailed scheme linking anisotropies in the cosmic
background radiation (CMB) with anisotropies and inhomogeneities in the large
scale structure of the universe and showed how to place limits on those
anisotropies and inhomogeneities simply by using CMB quadrupole and octupole
limits. First we indicate and discuss the connection between the covariant
multipole moments of the temperature anisotropy used in the MES scheme and the
quadrupole and octupole results from COBE. Then we introduce those results into
the MES limit equations to obtain definite quantitative limits on the complete
set of cosmological measures of anisotropy and inhomogeneity.
We find that all the anisotropy measures are less than 10^{-4} in the case of
those not affected by the expansion rate H, and less than 10^{-6} Mpc^{-1} in
the case of those which are. These results quantitatively demonstrate that the
observable universe is indeed close to Friedmann-Lemaitre-Robertson-Walker
(FLRW) on the largest scales, and can be adequately modelled by an almost-FLRW
model -- that is, the anisotropies and inhomogeneities characterizing the
observable universe on the largest scales are not too large to be considered
perturbations to FLRW.Comment: Original paper with corrections. ApJ 476 435 (1997) erratum to appear
ApJ Sept 199
A Note on Infinities in Eternal Inflation
In some well-known scenarios of open-universe eternal inflation, developed by
Vilenkin and co-workers, a large number of universes nucleate and thermalize
within the eternally inflating mega-universe. According to the proposal, each
universe nucleates at a point, and therefore the boundary of the nucleated
universe is a space-like surface nearly coincident with the future light cone
emanating from the point of nucleation, all points of which have the same
proper-time. This leads the authors to conclude that at the proper-time t =
t_{nuc} at which any such nucleation occurs, an infinite open universe comes
into existence. We point out that this is due entirely to the supposition of
the nucleation occurring at a single point, which in light of quantum cosmology
seems difficult to support. Even an infinitesimal space-like length at the
moment of nucleation gives a rather different result -- the boundary of the
nucleating universe evolves in proper-time and becomes infinite only in an
infinite time. The alleged infinity is never attained at any finite time.Comment: 13 pages and 6 figure
The Angular-Diameter-Distance-Maximum and Its Redshift as Constraints on FLRW Models
The plethora of recent cosmologically relevant data has indicated that our
universe is very well fit by a standard Friedmann-Lema\^{i}tre-Robertson-Walker
(FLRW) model, with and -- or, more generally, by nearly flat FLRW models with parameters close
to these values. Additional independent cosmological information, particularly
the maximum of the angular-diameter (observer-area) distance and the redshift
at which it occurs, would improve and confirm these results, once sufficient
precise Supernovae Ia data in the range become available. We
obtain characteristic FLRW closed functional forms for and
, the angular-diameter distance and the density per
source counted, respectively, when , analogous to those we have
for . More importantly, we verify that for flat FLRW models
-- as is already known but rarely recognized -- the redshift of
, the maximum of the angular-diameter-distance, uniquely gives
, the amount of vacuum energy in the universe, independently
of , the Hubble parameter. For non-flat models determination of both
and gives both and , the
amount of matter in the universe, as long as we know independently.
Finally, determination of automatically gives a very simple
observational criterion for whether or not the universe is flat -- presuming
that it is FLRW.Comment: 17 Pages, 1 Figur
Conditions for spontaneous homogenization of the Universe
The present-day Universe appears to be homogeneous on very large scales. Yet
when the casual structure of the early Universe is considered, it becomes
apparent that the early Universe must have been highly inhomogeneous. The
current paradigm attempts to answer this problem by postulating the inflation
mechanism However, inflation in order to start requires a homogeneous patch of
at least the horizon size. This paper examines if dynamical processes of the
early Universe could lead to homogenization. In the past similar studies seem
to imply that the set of initial conditions that leads to homogenization is of
measure zero. This essay proves contrary: a set of initial conditions for
spontaneous homogenization of cosmological models can form a set of non-zero
measure.Comment: 7 pages. Fifth Award in the 2010 Gravity Research Foundation essay
competitio
LIMITS ON ANISOTROPY AND INHOMOGENEITY FROM THE COSMIC BACKGROUND RADIATION,
We consider directly the equations by which matter imposes anisotropies on
freely propagating background radiation, leading to a new way of using
anisotropy measurements to limit the deviations of the Universe from a
Friedmann-Robertson-Walker (FRW) geometry. This approach is complementary to
the usual Sachs-Wolfe approach: the limits obtained are not as detailed, but
they are more model-independent. We also give new results about combined
matter-radiation perturbations in an almost-FRW universe, and a new exact
solution of the linearised equations.Comment: 18 pages Latex