80 research outputs found
Cosmological model with decaying vacuum energy law from principles of quantum mechanics
We construct the cosmological model to explain the cosmological constant
problem. We built the extension of the standard cosmological model CDM
by consideration of decaying vacuum energy represented by the running
cosmological term. From the principles of quantum mechanics one can find that
in the long term behavior survival probability of unstable states is a
decreasing function of the cosmological time and has the inverse power-like
form. This implies that cosmological constant where and
are constants. We investigate the dynamics of this model using
dynamical system methods due to a link to the cosmologies. We have
found the exact solution for the scale factor as well as the indicators of its
variability like the deceleration parameter and the jerk. From the calculation
of the jerk we obtain a simple test of the decaying vacuum in the FRW universe.
Using astronomical data (SNIa, , CMB, BAO) we have estimated the model
parameters and compared this model with the CDM model. Our statistical
results indicate that the decaying vacuum model is a little worse than the
CDM model. But the decaying vacuum cosmological model explains the
small value of the cosmological constant today.Comment: 24 pages, 5 figure
Does the diffusion DM-DE interaction model solve cosmological puzzles?
We study dynamics of cosmological models with diffusion effects modeling dark
matter and dark energy interactions. We show the simple model with diffusion
between the cosmological constant sector and dark matter, where the canonical
scaling law of dark matter is modified by an additive
to the form
. We reduced this model to the
autonomous dynamical system and investigate it using dynamical system methods.
This system possesses a two-dimensional invariant submanifold on which the
DM-DE interaction can be analyzed on the phase plane. The state variables are
density parameter for matter (dark and visible) and parameter
characterizing the rate of growth of energy transfer between the dark sectors.
A corresponding dynamical system belongs to a general class of jungle type of
cosmologies represented by coupled cosmological models in a Lotka-Volterra
framework. We demonstrate that the de Sitter solution is a global attractor for
all trajectories in the phase space and there are two repellers: the
Einstein-de Sitter universe and the de Sitter universe state dominating by the
diffusion effects. We distinguish in the phase space trajectories, which become
in good agreement with the data. They should intersect a rectangle with sides
of , at the
95\% CL. Our model could solve some of the puzzles of the CDM model,
such as the coincidence and fine-tuning problems. In the context of the
coincidence problem, our model can explain the present ratio of to
, which is equal at a 2
confidence level.Comment: 27 pages, 17 figure
Cosmology with decaying cosmological constant -- exact solutions and model testing
We study dynamics of cosmological models which are a natural
generalization of the standard cosmological model (the CDM model). We
consider a class of models: the ones with a prescribed form of
. This type of a
parametrization is motivated by different cosmological approaches.
We interpret the model with running Lambda () as a special model of
an interacting cosmology with the interaction term in which
energy transfer is between dark matter and dark energy sectors. For the
cosmology with a prescribed form of we have found the
exact solution in the form of Bessel functions. Our model shows that fractional
density of dark energy is constant and close to zero during the
early evolution of the universe.
We have also constrained the model parameters for this class of models using
the astronomical data such as SNIa data, BAO, CMB, measurements of and
the Alcock-Paczy{\'n}ski test. In this context we formulate a simple criterion
of variability of with respect to in terms of variability of the
jerk or sign of estimator . The
case study of our model enable us to find an upper limit
( C.L.) describing the variation from the cosmological constant while
the LCDM model seems to be consistent with various data.Comment: 24 pages, 15 figures; We pointed out that most stringent limit on
parameter \alpha^2 can be obtained if we apply Starobinsky argument and use
constraint of Ade et al. (arXiv:1502.01590). Let us note that while the
corresponding limit on the parameter \alpha^2 parameter is about twice less
than the limit obtained from our estimation, but it is obtained independently
of Starobinsky's argumen
Which cosmological models -- with dark energy or modified FRW dynamics?
Recent measurements of distant type Ia supernovae (SNIa) as well as other
observations indicate that our universe is in accelerating phase of expansion.
In principle there are two alternative explanation for such an acceleration.
While in the first approach an unknown form of energy violating the strong
energy condition is postulated, in second one some modification of FRW dynamics
is postulated. The both approaches are in well agreement with present day
observations which is the manifestation of the degeneracy problem appearing in
observational cosmology. We use the Akaike (AIC) and Bayesian (BIC) information
criteria of model selection to overcome this degeneracy and to determine a
model with such a set of parameters which gives the most preferred fit to the
SNIa data. We consider five representative evolutional scenarios in each of
groups. Among dark energy proposal the CDM model, CDM model with
phantom field, CDM model with topological defect, model with Chaplygin gas, and
the model with the linear dynamical equation of state parameter. As an
alternative prototype scenarios we consider: brane world Dvali Gabadadze
Porrati scenario, brane models in Randall-Sundrum scenario, Cardassian models
with dust matter and radiation, bouncing model with the cosmological constant
and metric-affine gravity (MAG) inspired cosmological models. Applying the
model selection criteria we show that both AIC and BIC indicates that
additional contribution arises from nonstandard FRW dynamics are not necessary
to explain SNIa. Adopting the model selection information criteria we show that
the AIC indicates the flat phantom model while BIC indicates both flat phantom
and flat CDM models.Comment: 17 pages 6 figure
Testing and selection cosmological models with dark energy
It is described dynamics of a large class of accelerating cosmological models
in terms of dynamical systems of the Newtonian type. The evolution of the
models is reduced to the motion of a particle in a potential well parameterized
by the scale factor. This potential function can be reconstructed from distant
supernovae type Ia data and many cosmological models represented in terms of
the potential becomes in a good agreement with current observational data. It
is proposed to use the information criteria to overcome this degeneracy within
a class of A) dark energy models and B) simple models basing on modification of
the FRW equation. Two class of models can be recommended by the Akaike (AIC)
and Schwarz (BIC) information criteria: the phantom and CDM models.Comment: Talk at Albert Einstein Century International Conference at Palais de
l'Unesco, Paris, France, 18-23 July 2005; to appear in the Proceedings; AIP
style files included, 6 pages, 2 figure
Dynamical complexity of the Brans-Dicke cosmology
The dynamics of the Brans-Dicke theory with a quadratic scalar field
potential function and barotropic matter is investigated. The dynamical system
methods are used to reveal complexity of dynamical evolution in homogeneous and
isotropic cosmological models. The structure of phase space crucially depends
on the parameter of the theory as well as barotropic
matter index . In our analysis these parameters are treated as
bifurcation parameters. We found sets of values of these parameters which lead
to generic evolutional scenarios. We show that in isotropic and homogeneous
models in the Brans-Dicke theory with a quadratic potential function the de
Sitter state appears naturally. Stability conditions of this state are fully
investigated. It is shown that these models can explain accelerated expansion
of the Universe without the assumption of the substantial form of dark matter
and dark energy. The Poincare construction of compactified phase space with a
circle at infinity is used to show that phase space trajectories in a physical
region can be equipped with a structure of a vector field on nontrivial
topological closed space. For we show new types of
early and late time evolution leading from the anti-de Sitter to the de Sitter
state through an asymmetric bounce. In the theory without a ghost we find
bouncing solutions and the coexistence of the bounces and the singularity.
Following the Peixoto theorem some conclusions about structural stability are
drawn.Comment: 34 pages, 14 figs; (v2) 36 pages, 16 figs, refs. added, JCAP (in
press
Simple cosmological model with inflation and late times acceleration
In the framework of polynomial Palatini cosmology, we investigate a simple
cosmological homogeneous and isotropic model with matter in the Einstein frame.
We show that in this model during cosmic evolution, it appears the early
inflation and the accelerating phase of the expansion for the late times. In
this frame we obtain the Friedmann equation with matter and dark energy in the
form of a scalar field with the potential whose form is determined in a
covariant way by the Ricci scalar of the FRW metric. The energy density of
matter and dark energy are also parametrized through the Ricci scalar. The
early inflation is obtained only for an infinitesimally small fraction of
energy density of matter. Between the matter and dark energy, there exists
interaction because the dark energy is decaying. For characterization of
inflation we calculate the slow roll parameters and the constant roll parameter
in terms of the Ricci scalar. We have found a characteristic behaviour of the
time dependence of density of dark energy on the cosmic time following the
logistic-like curve which interpolates two almost constant value phases. From
the required numbers of -folds we have found a bound on model parameter.Comment: 8 pages, 10 figure
Chasing Lambda
Recent astronomical observations of SNIa, CMB, as well as BAO in the Sloan
Digital Sky Survey, suggest that the current Universe has entered a stage of an
accelerated expansion with the transition redshift at . While the
simplest candidates to explain this fact is cosmological constant/vacuum
energy, there exists a serious problem of coincidence. In theoretical cosmology
we can find many possible approaches alleviating this problem by applying new
physics or other conception of dark energy. We consider state of art candidates
for the description of accelerating Universe in the framework of the Bayesian
model selection. We point out advantages as well as troubles of this approach.
We find that the combination of four data bases gives a stringent posterior
probability of the CDM model which is 74%. This fact is a quantitative
exemplification of a turmoil in modern cosmology over the problem.Comment: Talk presented at the "A Century of Cosmology - Past, Present and
Future" conference, S.Servolo(Venice), Italy, August 27-31 2007. To be
published in Il Nuovo Ciment
Cosmological dynamics with non-minimally coupled scalar field and a constant potential function
Dynamical systems methods are used to investigate global behavior of the
spatially flat Friedmann-Robertson-Walker cosmological model in gravitational
theory with a non-minimally coupled scalar field and a constant potential
function. We show that the system can be reduced to an autonomous
three-dimensional dynamical system and additionally is equipped with an
invariant manifold corresponding to an accelerated expansion of the universe.
Using this invariant manifold we find an exact solution of the reduced
dynamics. We investigate all solutions for all admissible initial conditions
using theory of dynamical systems to obtain a classification of all evolutional
paths. The right-hand sides of the dynamical system depend crucially on the
value of the non-minimal coupling constant therefore we study bifurcation
values of this parameter under which the structure of the phase space changes
qualitatively. We found a special bifurcation value of the non-minimal coupling
constant which is distinguished by dynamics of the model and may suggest some
additional symmetry in matter sector of the theory.Comment: 39 pages, 8 multiple figs; v2. 41 pages, 8 multiple figs. published
versio
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