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Rastall's theory is a modification of General Relativity, based on the non-conservation of the stress-energy tensor. The latter is encoded in a parameter γ such that γ = 1 restores the usual ∇ ν T µν = 0 law. We test Rastall's theory in cosmology, on a flat Robertson-Walker metric, investigating a two-fluid model and using the type Ia supernovae Constitution dataset. One of the fluids is pressureless and obeys the usual conservation law, whereas the other is described by an equation of state p x = w x ρ x , with w x constant. The Bayesian analysis of the Constitution set does not strictly constrain the parameter γ and prefers values of w x close to −1. We then address the evolution of small perturbations and show that they are dramatically unstable if w x = −1 and γ = 1, i.e. General Relativity is the favored configuration. The only alternative is w x = −1, for which the dynamics becomes independent from γ. *

We use the framework of a recently proposed model of reduced relativistic gas (RRG) to obtain the bounds for Ω's of Dark Matter and Dark Energy (in the present case, a cosmological constant), taking into consideration an arbitrary warmness of Dark Matter. An equivalent equation of state has been used by Sakharov to predict the oscillations in the matter power spectrum. Two kind of tests are accounted for in what follows, namely the ones coming from the dynamics of the conformal factor of the homogeneous and isotropic metric and also the ones based on linear cosmic perturbations. The RRG model demonstrated its high effectiveness, permitting to explore a large volume in the space of mentioned parameters in a rather economic way. Taking together the results of such tests as Supernova type Ia (Union2 sample), H(z), CMB (R factor), BAO and LSS (2dfGRS data), we confirm that ΛCDM is the most favored model. At the same time, for the 2dfGRS data alone we found that an alternative model with a very small quantity of a Dark Matter is also viable. This output is potentially relevant in view of the fact that the LSS is the only test which can not be affected by the possible quantum contributions to the low-energy gravitational action.

In the Friedmann cosmology, the deceleration of the expansion q plays a fundamental role. We derive the deceleration as a function of redshift q(z) in two scenarios: CDM model and modified Chaplygin gas (MCG) model. The function for the MCG model is then fitted to the cosmological data in order to obtain the cosmological parameters that minimize χ 2 . We use the Fisher matrix to construct the covariance matrix of our parameters and reconstruct the q(z) function. We use Supernovae Ia, WMAP5, and BAO measurements to obtain the observational constraints. We determined the present acceleration as q 0 = −0.65 ± 0.19 for the MCG model using the Union2 dataset of SNeIa, BAO, and CMB and q 0 = −0.67 ± 0.17 for the Constitution dataset, BAO and CMB. The transition redshift from deceleration to acceleration was found to be around 0.80 for both datasets. We have also determined the dark energy parameter for the MCG model: X0 = 0.81 ± 0.03 for the Union2 dataset and X0 = 0.83 ± 0.03 using the Constitution dataset.

We study the matter density fluctuations in the running cosmological constant (RCC) model using linear perturbations in the longitudinal gauge. Using this observable, we calculate the growth rate of structures and the matter power spectrum, and compare these results to SDSS data and the available data for linear growth rate. The distribution of collapsed structures may also constrain models of dark energy. It is shown that the RCC model enhances departures from the ΛCDM model for both cluster number and cumulative cluster number predicted. In general, increasing the characteristic parameter ν leads to significant growth of the cluster number. We found that the theory of perturbations provides a useful tool to distinguish between the new model RCC and the standard cosmological model ΛCDM.

In the present investigation we use observational data of $$ f \sigma _ {8} $$ f σ 8 to determine observational constraints in the plane $$(\Omega _{m0},\sigma _{8})$$ ( Ω m 0 , σ 8 ) using two different methods: the growth factor parametrization and the numerical solutions method for density contrast, $$\delta _{m}$$ δ m . We verified the correspondence between both methods for three models of accelerated expansion: the $$\Lambda CDM$$ Λ C D M model, the $$ w_{0}w_{a} CDM$$ w 0 w a C D M model and the running cosmological constant RCC model. In all case we consider also the curvature as free parameter. The study of this correspondence is important because the growth factor parametrization method is frequently used to discriminate between competitive models. Our results we allow us to determine that there is a good correspondence between the observational constrains using both methods. We also test the power of the $$ f\sigma _ {8} $$ f σ 8 data to constraints the curvature parameter within the $$ \Lambda CDM $$ Λ C D M model. For this we use a non-parametric reconstruction using Gaussian processes. Our results show that the $$ f\sigma _ {8}$$ f σ 8 data with the current precision level does not allow to distinguish between a flat and non-flat universe.

The Reduced Relativistic Gas (RRG) model was introduced by A. Sakharov in 1965 for deriving the cosmic microwave background (CMB) spectrum. It was recently reinvented by some of us to achieve an interpolation between the radiation and dust epochs in the evolution of the Universe. This model circumvents the complicated structure of the Boltzmann-Einstein system of equations and admits a transparent description of warm-dark-matter effects. It is extended here to include, on a phenomenological basis, an out-of-equilibrium interaction between radiation and baryons which is supposed to account for relevant aspects of pre-recombination physics in a simplified manner. Furthermore, we use the tight-coupling approximation to explore the influence of both this interaction and of the RRG warmness parameter on the anisotropy spectrum of the CMB. The predictions of the model are very similar to those of the CDM model if both the interaction and the dark-matter warmness parameters are of the order of 10 −4 or smaller. As far as the warmness parameter is concerned, this is in good agreement with previous estimations on the basis of results from structure formation.

Resumo O modelo cosmológico de Eudoxo de Cnido (408 - 355 a.C.), o modelo das esferas concêntricas, representa o primeiro modelo matemático da cosmologia, o qual tenta explicar o movimento dos corpos celestes. Através dos comentários de Aristóteles (384 - 322 a.C.), dos escritos de Simplício (490 - 560 d.C.) e das abordagens feitas por historiadores e matemáticos do século XIX, será apresentada a reconstrução matemática clássica deste modelo. Também utilizamos um método matemático moderno, o método das matrizes de rotação, para ilustrar os movimentos planetários que resultam do modelo de Eudoxo, e determinar a equação paramétrica da hipópede. Devido à inexistência dos registros históricos originais do modelo, é necessário abordar as principais críticas a esta reconstrução clássica do século XIX, entre elas, a unicidade da reconstrução do modelo. No entanto, mesmo com todas as incertezas na reconstrução, ao longo dos séculos, o modelo de Eudoxo se apresenta como a primeira tentativa de entender, com as observações e as ferramentas da matemática da época, os movimentos do Sol, da Lua e os movimentos retrógrados dos planetas, e este trabalho dedica-se a discutir estas características de forma ampla, esgotando as principais obras apresentadas na literatura.

The quantum contributions to the gravitational action are relatively easy to calculate in the higher derivative sector of the theory. However, the applications to the postinflationary cosmology and astrophysics require the corrections to the Einstein-Hilbert action and to the cosmological constant, and those we can not derive yet in a consistent and safe way. At the same time, if we assume that these quantum terms are covariant and that they have relevant magnitude, their functional form can be defined up to a single free parameter, which can be defined on the phenomenological basis. It turns out that the quantum correction may lead, in principle, to surprisingly strong and interesting effects in astrophysics and cosmology a .

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