We make a systematic study of the cosmological dynamics for a number of f (R) gravity theories in Palatini formalism, using phase space analysis as well as numerical simulations. Considering homogeneous and isotropic models, we find a number of interesting results: (i) models based on theories of the type (a) f (R) = R − β/R n and (b) f (R) = R + αln R − β, unlike the metric formalism, are capable of producing the sequence of radiation-dominated, matter-dominated and de-Sitter periods, and (ii) models based on theories of the type (c) f (R) = R + αR m − β/R n can produce early as well as late accelerating phases but an early inflationary epoch does not seem to be compatible with the presence of a subsequent radiation-dominated era. Thus for the classes of models considered here, we have been unable to find the sequence of all four dynamical epochs required to account for the complete cosmological dynamics, even though three out of four phases are possible.We also place observational constraints on these models using the recently released supernovae data by the Supernova Legacy Survey as well as the baryon acoustic oscillation peak in the SDSS luminous red galaxy sample and the CMB shift parameter. The best-fit values are found to be n = 0.027, α = 4.63 for the models based on (a) and α = 0.11, β = 4.62 for the models based on (b), neither of which are significantly preferred over the ΛCDM model. Moreover, the logarithmic term alone is not capable of explaining the late acceleration. The models based on (c) are also consistent with the data with suitable choices of their parameters.We also find that some of the models for which the radiation-dominated epoch is absent prior to the matter-dominated era also fit the data. The reason for this apparent contradiction is that the combination of the data considered here does not place stringent enough constraints on the cosmological evolution prior to the decoupling epoch, which highlights the importance of our combined theoretical-observational approach to constrain models.

We consider f (R) modified gravity theories in the metric variation formalism and attempt to reconstruct the function f (R) by demanding a background ΛCDM cosmology. In particular we impose the following requirements: a. A background cosmic history H(z) provided by the usual flat ΛCDM parametrization though the radiation (w ef f = 1/3), matter (w ef f = 0) and deSitter (w ef f = −1) eras. b. Matter and radiation dominate during the 'matter' and 'radiation' eras respectively i.e. Ωm = 1 when w ef f = 0 and Ωr = 1 when w ef f = 1/3. We have found that the cosmological dynamical system constrained to obey the ΛCDM cosmic history has four critical points in each era which correspondingly lead to four forms of f (R). One of them is the usual general relativistic form f (R) = R − 2Λ. The other three forms in each era, reproduce the ΛCDM cosmic history but they do not satisfy requirement b. stated above.

In this paper we study the isotropization of a generalized scalar-tensor theory with a massive scalar field. We find it depends on a condition on the Brans-Dicke coupling function and the potential, and show that asymptotically the metric functions always tend toward a power or exponential law of the proper time. These results generalize and unify those of de Sitter in the case of a cosmological constant and of Cooley and Kitada in the case of an exponential potential.

Abstract. The whole class of minimally coupled and massive scalar fields which may be responsible for flattening of galactic rotation curves is found. An interesting relation with a class of scalar-tensor theories able to isotropise anisotropic models of Universe is shown. The resulting metric is found and its stability and scalar field properties are tested with respect to the presence of a second scalar field or a small perturbation of the rotation velocity at galactic outer radii.

We look for necessary isotropization conditions of Bianchi class A models with curvature in the presence of a massive and minimally coupled scalar field when a function ℓ of the scalar field tends to a constant, diverges monotonically or with sufficiently small oscillations. Isotropization leads the metric functions to tend to a power or exponential law of the proper time t and the potential, respectively, to vanish as t−2 or to a constant. Moreover, isotropization always requires late-time accelerated expansion and flatness of the universe.

Using some supernovae and CMB data, we constrain the Cardassian, Randall-Sundrum, and Dvali-Gabadadze-Porrati brane-inspired cosmological models. We show that a transient acceleration and an early loitering period are usually excluded by the data. Moreover, the three models are equivalent to some usual quintessence/ghost dark energy models defined by a barotropic index γ φ depending on the redshift. We calculate this index for each model and show that they mimic a universe close to a ΛCDM model today.

We study the generalized scalar-tensor theory with a potential in the Bianchi type I model by using the ADM formalism. We examine the conditions needed for the Universe to be in expansion, isotropic and with a positive potential at late times in the Brans-Dicke and Einstein frames. In particular, we analyse the two important cases where metric functions tend, in an asymptotic way, toward power or exponential laws in the Einstein frame.

We put forward a new model-independent reconstruction scheme for dark energy which utilizes the expected geometrical features of the luminosity-distance relation. The important advantage of this scheme is that it does not assume explicit ansatzes for cosmological parameters but only some very general cosmological properties via the geometrical features of the reconstructed luminosity-distance relation. Using the recently released supernovae data by the Supernova Legacy Survey together with a phase space representation, we show that the reconstructed luminosity-distance curves best fitting the data correspond to a slightly varying dark energy density with the Universe expanding slightly slower than the CDM model. However, the CDM model fits the data at 1 significance level and the fact that our best fitting luminosity-distance curve is lower than that of the corresponding CDM model could be due to systematics. The transition from an accelerating to a decelerating expansion occurs at a redshift larger than z 0:35. Interpreting the dark energy as a minimally coupled scalar field we also reconstruct the scalar field and its potential. We constrain m 0 using the baryon acoustic oscillation peak in the SDSS luminous red galaxy sample and find that the best fit is obtained with m 0 0:27, in agreement with the CMB data.