188 research outputs found
Extended logotropic fluids as unified dark energy models
We here study extended classes of logotropic fluids as \textit{unified dark
energy models}. Under the hypothesis of the Anton-Schmidt scenario, we consider
the universe obeying a single fluid whose pressure evolves through a
logarithmic equation of state. This result is in analogy with crystals under
isotropic stresses. Thus, we investigate thermodynamic and dynamical
consequences by integrating the speed of sound to obtain the pressure in terms
of the density, leading to an extended version of the Anton-Schmidt cosmic
fluids. Within this picture, we get significant outcomes expanding the
Anton-Schmidt pressure in the infrared regime. The low-energy case becomes
relevant for the universe to accelerate without any cosmological constant. We
therefore derive the effective representation of our fluid in terms of a
Lagrangian , depending on the kinetic term
only. We analyze both the relativistic and non-relativistic limits. In the
non-relativistic limit we construct both the Hamiltonian and Lagrangian in
terms of density and scalar field , whereas in the
relativistic case no analytical expression for the Lagrangian can be found.
Thus, we obtain the potential as a function of , under the hypothesis of
irrotational perfect fluid. We demonstrate that the model represents a natural
generalization of \emph{logotropic dark energy models}. Finally, we analyze an
extended class of generalized Chaplygin gas models with one extra parameter
. Interestingly, we find that the Lagrangians of this scenario and the
pure logotropic one coincide in the non-relativistic regime.Comment: 6 pages, 3 figure
Cosmic acceleration from a single fluid description
We here propose a new class of barotropic factor for matter, motivated by
properties of isotropic deformations of crystalline solids. Our approach is
dubbed Anton-Schmidt's equation of state and provides a non-vanishing, albeit
small, pressure term for matter. The corresponding pressure is thus
proportional to the logarithm of universe's volume, i.e. to the density itself
since . In the context of solid state physics, we
demonstrate that by only invoking standard matter with such a property, we are
able to frame the universe speed up in a suitable way, without invoking a dark
energy term by hand. Our model extends a recent class of dark energy paradigms
named \emph{logotropic} dark fluids and depends upon two free parameters,
namely and . Within the Debye approximation, we find that and
are related to the Gr\"uneisen parameter and the bulk modulus of crystals. We
thus show the main differences between our model and the logotropic scenario,
and we highlight the most relevant properties of our new equation of state on
the background cosmology. Discussions on both kinematics and dynamics of our
new model have been presented. We demonstrate that the CDM model is
inside our approach, as limiting case. Comparisons with CPL parametrization
have been also reported in the text. Finally, a Monte Carlo analysis on the
most recent low-redshift cosmological data allowed us to place constraints on
and . In particular, we found and .Comment: 13 pages, 7 figure
Extended Gravity Cosmography
Cosmography can be considered as a sort of a model-independent approach to
tackle the dark energy/modified gravity problem. In this review, the success
and the shortcomings of the CDM model, based on General Relativity and
standard model of particles, are discussed in view of the most recent
observational constraints. The motivations for considering extensions and
modifications of General Relativity are taken into account, with particular
attention to and theories of gravity where dynamics is
represented by curvature or torsion field respectively. The features of
models are explored in metric and Palatini formalisms. We discuss the
connection between gravity and scalar-tensor theories highlighting the
role of conformal transformations in the Einstein and Jordan frames.
Cosmological dynamics of models is investigated through the
corresponding viability criteria. Afterwards, the equivalent formulation of
General Relativity (Teleparallel Equivalent General Relativity) in terms of
torsion and its extension to gravity is considered. Finally, the
cosmographic method is adopted to break the degeneracy among dark energy
models. A novel approach, built upon rational Pad\'e and Chebyshev polynomials,
is proposed to overcome limits of standard cosmography based on Taylor
expansion. The approach provides accurate model-independent approximations of
the Hubble flow. Numerical analyses, based on Monte Carlo Markov Chain
integration of cosmic data, are presented to bound coefficients of the
cosmographic series. These techniques are thus applied to reconstruct
and functions and to frame the late-time expansion history of the
universe with no \emph{a priori} assumptions on its equation of state. A
comparison between the CDM cosmological model with and
models is reported.Comment: 82 pages, 35 figures. Accepted for publication in IJMP
Kinematic model-independent reconstruction of Palatini cosmology
A kinematic treatment to trace out the form of cosmology, within the
Palatini formalism, is discussed by only postulating the universe homogeneity
and isotropy. To figure this out we build model-independent approximations of
the luminosity distance through rational expansions. These approximants extend
the Taylor convergence radii computed for usual cosmographic series. We thus
consider both Pad\'e and the rational Chebyshev polynomials. They can be used
to accurately describe the universe late-time expansion history, providing
further information on the thermal properties of all effective cosmic fluids
entering the energy momentum tensor of Palatini's gravity. To perform our
numerical analysis, we relate the Palatini's Ricci scalar with the Hubble
parameter and thus we write down a single differential equation in terms of
the redshift . Therefore, to bound , we make use of the most recent
outcomes over the cosmographic parameters obtained from combined data surveys.
In particular our clue is to select two scenarios, i.e. Pad\'e and
Chebyshev approximations, since they well approximate the luminosity
distance at the lowest possible order. We find that best analytical matches to
the numerical solutions lead to with free parameters given by the
set for Pad\'e approximation,
whereas with for rational Chebyshev approximation. Finally, our results are
compared with the CDM predictions and with previous studies in the
literature. Slight departures from General Relativity are also discussed.Comment: 10 pages, 6 figures. Accepted for publication in Gen. Rel. Gra
Cosmographic analysis with Chebyshev polynomials
The limits of standard cosmography are here revised addressing the problem of
error propagation during statistical analyses. To do so, we propose the use of
Chebyshev polynomials to parameterize cosmic distances. In particular, we
demonstrate that building up rational Chebyshev polynomials significantly
reduces error propagations with respect to standard Taylor series. This
technique provides unbiased estimations of the cosmographic parameters and
performs significatively better than previous numerical approximations. To
figure this out, we compare rational Chebyshev polynomials with Pad\'e series.
In addition, we theoretically evaluate the convergence radius of (1,1)
Chebyshev rational polynomial and we compare it with the convergence radii of
Taylor and Pad\'e approximations. We thus focus on regions in which convergence
of Chebyshev rational functions is better than standard approaches. With this
recipe, as high-redshift data are employed, rational Chebyshev polynomials
remain highly stable and enable one to derive highly accurate analytical
approximations of Hubble's rate in terms of the cosmographic series. Finally,
we check our theoretical predictions by setting bounds on cosmographic
parameters through Monte Carlo integration techniques, based on the
Metropolis-Hastings algorithm. We apply our technique to high-redshift cosmic
data, using the JLA supernovae sample and the most recent versions of Hubble
parameter and baryon acoustic oscillation measurements. We find that
cosmography with Taylor series fails to be predictive with the aforementioned
data sets, while turns out to be much more stable using the Chebyshev approach.Comment: 17 pages, 6 figures, 5 table
Effective field description of the Anton-Schmidt cosmic fluid
The effective theory of the Anton-Schmidt cosmic fluid within the Debye
approximation is investigated. In this picture, the universe is modeled out by
means of a medium without cosmological constant. In particular, the
Anton-Schmidt representation of matter describes the pressure of crystalline
solids under deformations imposed by isotropic stresses. The approach scheme is
related to the fact that the universe deforms under the action of the cosmic
expansion itself. Thus, we frame the dark energy term as a function of scalar
fields and obtain the corresponding dark energy potential .
Different epochs of the universe evolution are investigated in terms of the
evolution of . We show how the Anton-Schmidt equation of state is
capable of describing both late and early epochs of cosmic evolution. Finally,
numerical bounds on the Anton-Schmidt model with are derived through a
Markov Chain Monte Carlo analysis on the combination of data coming from type
Ia Supernovae, observations of Hubble parameter and baryon acoustic
oscillations. Statistical comparison with the CDM model is performed
by the AIC and BIC selection criteria. Results are in excellent agreement with
the low-redshift data. A further generalization of the model is presented to
satisfy the theoretical predictions at early-stage cosmology.Comment: 13 pages, Accepted for publication in Phys. Rev.
Late-time constraints on modified Gauss-Bonnet cosmology
In this paper, we consider a gravitational action containing a combination of
the Ricci scalar, , and the topological Gauss--Bonnet term, .
Specifically, we study the cosmological features of a particular class of
modified gravity theories selected by symmetry considerations, namely the
model. In the context of a spatially flat, homogeneous
and isotropic background, we show that the currently observed acceleration of
the Universe can be addressed through geometry, hence avoiding \emph{de facto}
the shortcomings of the cosmological constant. We thus present a strategy to
numerically solve the Friedmann equations in presence of pressureless matter
and obtain the redshift behavior of the Hubble expansion rate. Then, to check
the viability of the model, we place constraints on the free parameters of the
theory by means of a Bayesian Monte Carlo method applied to late-time cosmic
observations. Our results show that the model is capable of mimicking
the low-redshift behavior of the standard CDM model, though
substantial differences emerge when going toward high redshifts, leading to the
absence of a standard matter-dominated epoch. Finally, we investigate the
energy conditions and show that, under suitable choices for the values of the
cosmographic parameters, they are all violated when considering the mean value
of obtained from our analysis, as occurs in the case of a dark fluid.Comment: 10 pages, 3 figures, 1 tabl
- …