f(T) cosmology with nonzero curvature

We investigate exact and analytic solutions in [Formula: see text] gravity within the context of a Friedmann–Lemaître–Robertson–Walker background space with nonzero spatial curvature. For the power-law theory [Formula: see text] we find that the field equations admit an exact solution with a linear scalar factor for negative and positive spatial curvature. That Milne-like solution is asymptotic behavior for the scale factor near the initial singularity for the model [Formula: see text]. The analytic solution for that specific theory is presented in terms of Painlevé series for [Formula: see text]. Moreover, from the value of the resonances of the Painlevé series we conclude that the Milne-like solution is always unstable while for large values of the independent parameter, the field equations provide an expanding universe with a de Sitter expansion of a positive cosmological constant. Finally, the presence of the cosmological term [Formula: see text] in the studied [Formula: see text] model plays no role in the general behavior of the cosmological solution and the universe immerge in a de Sitter expansion either when the cosmological constant term [Formula: see text] in the [Formula: see text] model vanishes.

Torsion Gravity

Based on the discovery by astrophysicists of dark matter halos around galaxies, stars and planets, it became possible to abandon the speculative concept of the spatial curvature of Einstein's space-time fabric and geometric gravity. Torsional gravity and spinors in fundamental theoretical physics should be based on a new cosmology, including a dark matter halo rotating with planets, stars and galaxies and forming funnels in the continuous space environment of a quantum vacuum (dark matter). The article discusses the nature of tornado and tropical hurricanes.

Observational cosmology

The main strands of observation in cosmology are presented. These are redshift surveys using standard candles; galaxy distributions; age estimates drawing on a number of strands of evidence; and the CMB radiation. The chapter begins with a discussion of systemtic and statistical error in measurements, and explains the terminology of “Lambda CDM” model. Observations are combined with the Friedman equation in order to constrain the density parameters in a LCDM model. Data from supernova surveys are used to obtain the Hubble parameter and the deceleration parameter, and hence evidence of an accelerating expansion. Evidence of the BAO process is deduced from sky surveys, and used to constrain the spatial curvature. The CMB radiation is discussed at length. The Sachs-Wolfe effect is obtained by a simple calculation,. The method to deduce spatial curvature from the position of the acoustic peaks is outlined. Further features such as spectal index and polarization are briefly discussed.

Testing the consistency between cosmological data: the impact of spatial curvature and the dark energy EoS

The results of joint analyses of available cosmological data have motivated an important debate about a possible detection of a non-zero spatial curvature. If confirmed, such a result would imply a change in our present understanding of cosmic evolution with important theoretical and observational consequences. In this paper we discuss the legitimacy of carrying out joint analyses with the currently available data sets and explore their implications for a non-flat universe and extensions of the standard cosmological model. We use a robust tension estimator to perform a quantitative analysis of the physical consistency between the latest data of Cosmic Microwave Background, type Ia supernovae, Baryonic Acoustic Oscillations and Cosmic Chronometers. We consider the flat and non-flat cases of the ΛCDM cosmology and of two dark energy models with a constant and varying dark energy EoS parameter. The present study allows us to better understand if possible inconsistencies between these data sets are significant enough to make the results of their joint analyses misleading, as well as the actual dependence of such results with the spatial curvature and dark energy parameterizations. According to our results, we conclude that a joint analysis in the context of a non-flat universe including the CMB data is only possible if the CMB Lens is taken into account, otherwise, it potentially leads to misleading conclusions.