14 research outputs found
Bounding the Hubble flow in terms of the w parameter
The last decade has seen increasing efforts to circumscribe and bound the
cosmological Hubble flow in terms of model-independent constraints on the
cosmological fluid - such as, for instance, the classical energy conditions of
general relativity. Quite a bit can certainly be said in this regard, but much
more refined bounds can be obtained by placing more precise constraints (either
theoretical or observational) on the cosmological fluid. In particular, the use
of the w-parameter (w=p/rho) has become increasingly common as a surrogate for
trying to say something about the cosmological equation of state. Herein we
explore the extent to which a constraint on the w-parameter leads to useful and
nontrivial constraints on the Hubble flow, in terms of constraints on density
rho(z), Hubble parameter H(z), density parameter Omega(z), cosmological
distances d(z), and lookback time T(z). In contrast to other partial results in
the literature, we carry out the computations for arbitrary values of the space
curvature k in [-1,0,+1], equivalently for arbitrary Omega_0 <= 1.Comment: 15 page
Cosmological milestones and energy conditions
Until recently, the physically relevant singularities occurring in FRW
cosmologies had traditionally been thought to be limited to the "big bang", and
possibly a "big crunch". However, over the last few years, the zoo of
cosmological singularities considered in the literature has become considerably
more extensive, with "big rips" and "sudden singularities" added to the mix, as
well as renewed interest in non-singular cosmological events such as "bounces"
and "turnarounds". In this talk, we present an extensive catalogue of such
cosmological milestones, both at the kinematical and dynamical level. First,
using generalized power series, purely kinematical definitions of these
cosmological events are provided in terms of the behaviour of the scale factor
a(t). The notion of a "scale-factor singularity" is defined, and its relation
to curvature singularities (polynomial and differential) is explored. Second,
dynamical information is extracted by using the Friedmann equations (without
assuming even the existence of any equation of state) to place constraints on
whether or not the classical energy conditions are satisfied at the
cosmological milestones. Since the classification is extremely general, and
modulo certain technical assumptions complete, the corresponding results are to
a high degree model-independent.Comment: 8 pages, 1 table, conference proceedings for NEB XII conference in
Nafplio, Greec
The Hubble series: Convergence properties and redshift variables
In cosmography, cosmokinetics, and cosmology it is quite common to encounter
physical quantities expanded as a Taylor series in the cosmological redshift z.
Perhaps the most well-known exemplar of this phenomenon is the Hubble relation
between distance and redshift. However, we now have considerable high-z data
available, for instance we have supernova data at least back to redshift
z=1.75. This opens up the theoretical question as to whether or not the Hubble
series (or more generally any series expansion based on the z-redshift)
actually converges for large redshift? Based on a combination of mathematical
and physical reasoning, we argue that the radius of convergence of any series
expansion in z is less than or equal to 1, and that z-based expansions must
break down for z>1, corresponding to a universe less than half its current
size.
Furthermore, we shall argue on theoretical grounds for the utility of an
improved parameterization y=z/(1+z). In terms of the y-redshift we again argue
that the radius of convergence of any series expansion in y is less than or
equal to 1, so that y-based expansions are likely to be good all the way back
to the big bang y=1, but that y-based expansions must break down for y<-1, now
corresponding to a universe more than twice its current size.Comment: 15 pages, 2 figures, accepted for publication in Classical and
Quantum Gravit
Cosmodynamics: Energy conditions, Hubble bounds, density bounds, time and distance bounds
We refine and extend a programme initiated by one of the current authors
[Science 276 (1997) 88; Phys. Rev. D56 (1997) 7578] advocating the use of the
classical energy conditions of general relativity in a cosmological setting to
place very general bounds on various cosmological parameters. We show how the
energy conditions can be used to bound the Hubble parameter H(z), Omega
parameter Omega(z), density rho(z), distance d(z), and lookback time T(z) as
(relatively) simple functions of the redshift z, present-epoch Hubble parameter
H_0, and present-epoch Omega parameter Omega_0. We compare these results with
related observations in the literature, and confront the bounds with the recent
supernova data.Comment: 21 pages, 2 figure
Classical and semi-classical energy conditions
The standard energy conditions of classical general relativity are (mostly)
linear in the stress-energy tensor, and have clear physical interpretations in
terms of geodesic focussing, but suffer the significant drawback that they are
often violated by semi-classical quantum effects. In contrast, it is possible
to develop non-standard energy conditions that are intrinsically non-linear in
the stress-energy tensor, and which exhibit much better well-controlled
behaviour when semi-classical quantum effects are introduced, at the cost of a
less direct applicability to geodesic focussing. In this article we will first
review the standard energy conditions and their various limitations. (Including
the connection to the Hawking--Ellis type I, II, III, and IV classification of
stress-energy tensors). We shall then turn to the averaged, nonlinear, and
semi-classical energy conditions, and see how much can be done once
semi-classical quantum effects are included.Comment: V1: 25 pages. Draft chapter, on which the related chapter of the book
"Wormholes, Warp Drives and Energy Conditions" (to be published by Springer),
will be based. V2: typos fixed. V3: small typo fixe
Could the cosmic acceleration be transient? A cosmographic evaluation
A possible slowing down of the cosmic expansion is investigated through a
cosmographic approach. By expanding the luminosity distance to fourth order and
fitting the SN Ia data from the most recent compilations (Union, Constitution
and Union 2), the marginal likelihood distributions for the deceleration
parameter today suggest a recent reduction of the cosmic acceleration and
indicate that there is a considerable probability for . Also in contrast
to the prediction of the CDM model, the cosmographic
reconstruction permits a cosmic expansion history where the cosmic acceleration
could already have peaked and be presently slowing down, which would imply that
the recent accelerated expansion of the Universe is a transient phenomenon. It
is also shown that to describe a transient acceleration the luminosity distance
needs to be expanded at least to fourth order. The present cosmographic results
depend neither on the validity of general relativity nor on the matter-energy
contents of the Universe.Comment: 11 pages, 4 figures. Accepted for publication in Classical and
Quantum Gravit
Scale-Free model for governing universe dynamics
We investigate the effects of scale-free model on cosmology, providing, in
this way, a statistical background in the framework of general relativity. In
order to discuss properties and time evolution of some relevant universe
dynamical parameters (cosmographic parameters), such as (Hubble
parameter), (deceleration parameter), (jerk parameter) and
(snap parameter), which are well re-defined in the framework of scale-free
model, we analyze a comparison between WMAP data. Hence the basic purpose of
the work is to consider this statistical interpretation of mass distribution of
universe, in order to have a mass density dynamics, not inferred from
Friedmann equations, via scale factor . This model, indeed, has been used
also to explain a possible origin and a viable explanation of cosmological
constant, which assumes a statistical interpretation without the presence of
extended theories of gravity; hence the problem of dark energy could be
revisited in the context of a classical probability distribution of mass, which
is, in particular, for the scale-free model, , with
. The CDM model becomes, with these considerations, a
consequence of the particular statistics together with the use of general
relativity.Comment: 7 pages, 4 figure
How strong is the evidence for accelerated expansion?
We test the present expansion of the universe using supernova type Ia data
without making any assumptions about the matter and energy content of the
universe or about the parameterization of the deceleration parameter. We assume
the cosmological principle to apply in a strict sense. The result strongly
depends on the data set, the light-curve fitting method and the calibration of
the absolute magnitude used for the test, indicating strong systematic errors.
Nevertheless, in a spatially flat universe there is at least a 5 sigma evidence
for acceleration which drops to 1.8 sigma in an open universe.Comment: 16 pages, 3 figure