61 research outputs found
Non-integrability of density perturbations in the FRW universe
We investigate the evolution equation of linear density perturbations in the
Friedmann-Robertson-Walker universe with matter, radiation and the cosmological
constant. The concept of solvability by quadratures is defined and used to
prove that there are no "closed form" solutions except for the known Chernin,
Heath, Meszaros and simple degenerate ones. The analysis is performed applying
Kovacic's algorithm. The possibility of the existence of other, more general
solutions involving special functions is also investigated.Comment: 13 pages. The latest version with added references, and a relevant
new paragraph in section I
The Mixmaster Universe in Five Dimensions
We consider a five dimensional vacuum cosmology with Bianchi type-IX spatial
geometry and an extra non-compact coordinate. Finding a new class of solutions,
we examine and rule out the possibility of deterministic chaos. We interpret
this result within the context of induced matter theory.Comment: 13 page
Brane universes tested by supernovae
We discuss observational constrains coming from supernovae Ia
\cite{Perlmutter99} imposed on the behaviour of the Randall-Sundrum models. In
the case of dust matter on the brane, the difference between the best-fit
general relativistic model with a -term \cite{Perlmutter99} and the
best-fit brane models becomes detectable for redshifts . It is
interesting that brane models predict brighter galaxies for such redshifts
which is in agreement with the measurement of the supernova
\cite{Riess01} and with the New Data from the High Z Supernovae Search Team
\cite{schmit02}. We also demonstrate that the fit to supernovae data can also
be obtained, if we admit the "super-negative" dark energy
on the brane, where the dark energy in a way mimics the influence of the
cosmological constant. It also appears that the dark energy enlarges the age of
the universe which is demanded in cosmology. Finally, we propose to check for
dark radiation and brane tension by the application of the angular diameter of
galaxies minimum value test.Comment: 4 pages, 5 figures, REVTEX4, amended versio
Extended Quintessence with non-minimally coupled phantom scalar field
We investigate evolutional paths of an extended quintessence with a
non-minimally coupled phantom scalar field to the Ricci curvature. The
dynamical system methods are used to investigate typical regimes of dynamics at
the late time. We demonstrate that there are two generic types of evolutional
scenarios which approach the attractor (a focus or a node type critical point)
in the phase space: the quasi-oscillatory and monotonic trajectories approach
to the attractor which represents the FRW model with the cosmological constant.
We demonstrate that dynamical system admits invariant two-dimensional
submanifold and discussion that which cosmological scenario is realized depends
on behavior of the system on the phase plane . We formulate
simple conditions on the value of coupling constant for which
trajectories tend to the focus in the phase plane and hence damping
oscillations around the mysterious value . We describe this condition in
terms of slow-roll parameters calculated at the critical point. We discover
that the generic trajectories in the focus-attractor scenario come from the
unstable node. It is also investigated the exact form of the parametrization of
the equation of state parameter (directly determined from dynamics)
which assumes a different form for both scenarios.Comment: revtex4, 15 pages, 9 figures; (v2) published versio
Effective dynamics of the closed loop quantum cosmology
In this paper we study dynamics of the closed FRW model with holonomy
corrections coming from loop quantum cosmology. We consider models with a
scalar field and cosmological constant. In case of the models with cosmological
constant and free scalar field, dynamics reduce to 2D system and analysis of
solutions simplify. If only free scalar field is included then universe
undergoes non-singular oscillations. For the model with cosmological constant,
different behaviours are obtained depending on the value of . If the
value of is sufficiently small, bouncing solutions with asymptotic de
Sitter stages are obtained. However if the value of exceeds critical
value then solutions become oscillatory. Subsequently we study
models with a massive scalar field. We find that this model possess generic
inflationary attractors. In particular field, initially situated in the bottom
of the potential, is driven up during the phase of quantum bounce. This
subsequently leads to the phase of inflation. Finally we find that, comparing
with the flat case, effects of curvature do not change qualitatively dynamics
close to the phase of bounce. Possible effects of inverse volume corrections
are also briefly discussed.Comment: 18 pages, 11 figure
Acceleration of the Universe driven by the Casimir force
We investigate an evolutional scenario of the FRW universe with the Casimir
energy scaling like . The Casimir effect is used to explain the
vacuum energy differences (its value measured from astrophysics is so small
compared to value obtained from quantum field theory calculations). The
dynamics of the FRW model is represented in terms of a two-dimensional
dynamical system to show all evolutional paths of this model in the phase space
for all admissible initial conditions. We find also an exact solution for non
flat evolutional paths of Universe driven by the Casimir effect. The main
difference between the FRW model with the Casimir force and the CDM
model is that their generic solutions are a set of evolutional paths with a
bounce solution and an initial singularity, respectively. The evolutional
scenario are tested by using the SNIa data, FRIIb radiogalaxies, baryon
oscillation peak and CMB observation. We compare the power of explanation of
the model considered and the CDM model using the Bayesian information
criterion and Bayesian factor. Our investigation of the information criteria of
model selection showed the preference of the CDM model over the model
considered. However the presence of negative like the radiation term can remove
a tension between the theoretical and observed primordial He and D
abundance.Comment: RevTeX4, 17 pages, 9 figure
Observational hints on the Big Bounce
In this paper we study possible observational consequences of the bouncing
cosmology. We consider a model where a phase of inflation is preceded by a
cosmic bounce. While we consider in this paper only that the bounce is due to
loop quantum gravity, most of the results presented here can be applied for
different bouncing cosmologies. We concentrate on the scenario where the scalar
field, as the result of contraction of the universe, is driven from the bottom
of the potential well. The field is amplified, and finally the phase of the
standard slow-roll inflation is realized. Such an evolution modifies the
standard inflationary spectrum of perturbations by the additional oscillations
and damping on the large scales. We extract the parameters of the model from
the observations of the cosmic microwave background radiation. In particular,
the value of inflaton mass is equal to GeV. In
our considerations we base on the seven years of observations made by the WMAP
satellite. We propose the new observational consistency check for the phase of
slow-roll inflation. We investigate the conditions which have to be fulfilled
to make the observations of the Big Bounce effects possible. We translate them
to the requirements on the parameters of the model and then put the
observational constraints on the model. Based on assumption usually made in
loop quantum cosmology, the Barbero-Immirzi parameter was shown to be
constrained by from the cosmological observations. We have
compared the Big Bounce model with the standard Big Bang scenario and showed
that the present observational data is not informative enough to distinguish
these models.Comment: 25 pages, 8 figures, JHEP3.cl
Universe from vacuum in loop-string cosmology
In this paper we study the description of the Universe based on the low
energy superstring theory modified by the Loop Quantum Gravity effects.This
approach was proposed by De Risi et al. in the Phys. Rev. D {\bf 76} (2007)
103531. We show that in the contrast with the string motivated pre-Big Bang
scenario, the cosmological realisation of the -duality transformation is not
necessary to avoid an initial singularity. In the model considered the universe
starts its evolution in the vacuum phase at time . In this phase
the scale factor , energy density and coupling of the
interactions . After this stage the universe evolves to the
non-singular hot Big Bang phase . Then the
standard classical universe emerges. During the whole evolution the scale
factor increases monotonically. We solve this model analytically. We also
propose and solve numerically the model with an additional dilaton potential in
which the universe starts the evolution from the asymptotically free vacuum
phase and then evolves non-singularly to the emerging dark energy
dominated phase with the saturated coupling constant .Comment: JHEP3 LaTeX class, 19 pages, 9 figures, v2: added some comments and
references, v3: new numerical result added, new figure
Cosmological model with macroscopic spin fluid
We consider a Friedmann-Robertson-Walker cosmological model with some exotic
perfect fluid with spin known as the Weyssenhoff fluid. The possibility that
the dark energy may be described in part by the Weyssenhoff fluid is discussed.
The observational constraint coming from supernovae type Ia observations is
established. This result indicates that, whereas the cosmological constant is
still needed to explain current observations, the model with spin fluid is
admissible. For high redshifts the differences between the model with
spin fluid and the cold dark matter model with a cosmological constant become
detectable observationally for the flat case with .
From the maximum likelihood method we obtain the value of
. This gives us the limit
at the level. While the model with
``brane effects'' is preferred by the supernovae Ia data, the model with spin
fluid is statistically admissible. For comparison, the limit on the spin fluid
coming from cosmic microwave background anisotropies is also obtained. The
uncertainties in the location of a first peak give the interval . From big bang nucleosynthesis we
obtain the strongest limit . The
interconnection between the model considered and brane models is also pointed
out.Comment: RevTeX4, 15 pages, 10 figures; some minor change
Particle-Like Description in Quintessential Cosmology
Assuming equation of state for quintessential matter: , we
analyse dynamical behaviour of the scale factor in FRW cosmologies. It is shown
that its dynamics is formally equivalent to that of a classical particle under
the action of 1D potential . It is shown that Hamiltonian method can be
easily implemented to obtain a classification of all cosmological solutions in
the phase space as well as in the configurational space. Examples taken from
modern cosmology illustrate the effectiveness of the presented approach.
Advantages of representing dynamics as a 1D Hamiltonian flow, in the analysis
of acceleration and horizon problems, are presented. The inverse problem of
reconstructing the Hamiltonian dynamics (i.e. potential function) from the
luminosity distance function for supernovae is also considered.Comment: 35 pages, 26 figures, RevTeX4, some applications of our treatment to
investigation of quintessence models were adde
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