**Abstract: **We consider the dynamics of a barotropic cosmological fluid in an anisotropic, Bianchi type I space-time in Eddington-inspired Born–Infeld (EiBI) gravity. By assuming isotropic pressure distribution, we obtain the general solution of the field equations in an exact parametric form. The behavior of the geometric and thermodynamic parameters of the Bianchi type I Universe is studied, by using both analytical and numerical methods, for some classes of high density matter, described by the stiff causal, radiation, and pressureless fluid equations of state. In all cases the study of the models with different equations of state can be reduced to the integration of a highly nonlinear second order ordinary differential equation for the energy density. The time evolution of the anisotropic Bianchi type I Universe strongly depends on the initial values of the energy density and of the Hubble function. An important observational parameter, the mean anisotropy parameter, is also studied in detail, and we show that for the dust filled Universe the cosmological evolution always ends into isotropic phase, while for high density matter filled universes the isotropization of Bianchi type I universes is essentially determined by the initial conditions of the energy density.

**Abstract: **We analytically calculate some orbital effects induced by the Lorentz-invariance momentum-conservation parameterized post-Newtonian (PPN) parameter \(\alpha_3\) in a gravitationally bound binary system made of a primary orbited by a test particle. We neither restrict ourselves to any particular orbital configuration nor to specific orientations of the primary's spin axis \( {\hat{\psi}}\). We use our results to put preliminary upper bounds on \(\alpha_3\) in the weak-field regime by using the latest data from Solar System's planetary dynamics. By linearly combining the supplementary perihelion precessions \(\Delta\dot\varpi\) of the Earth, Mars and Saturn, determined by astronomers with the Ephemerides of Planets and the Moon (EPM) 2011 ephemerides for the general relativistic values of the PPN parameters \(\beta=\gamma=1\), we infer \(|\alpha_3|\lesssim 6\times 10^{-10}\). Our result is about three orders of magnitude better than the previous weak-field constraints existing in the literature and of the same order of magnitude of the constraint expected from the future BepiColombo mission to Mercury. It is, by construction, independent of the other preferred-frame PPN parameters \(\alpha_1,\alpha_2\), both preliminarily constrained down to a \(\approx 10^{-6}\) level. Future analyses should be performed by explicitly including \(\alpha_3\) and a selection of other PPN parameters in the models fitted by the astronomers to the observations and estimating them in dedicated covariance analyses.

**Abstract: **In 2008, a team of astronomers reported an anomalous retrograde precession of the perihelion of Saturn amounting to \(\Delta \dot{\omega}_{\mathrm{SATURN}}=-0.006(2)\) arcsec per century (arcsec cy\(^{-1}\)). This unexplained precession was obtained after taking into account all classical and relativistic effects in the context of the highly refined EPM2008 ephemerides. More recent analyzes have not confirmed this effect, but they have found similar discrepancies in other planets. Our objective in this paper is to discuss a non-standard model involving transversal gravitomagnetism generated by the Sun as a possible source of these potential anomalies, to be confirmed by further data analyses. In order to compute the Lense–Thirring perturbations induced by the suggested interaction, we should consider the orientation of the Sun's rotational axis in Carrington elements and the inclination of the planetary orbits with respect to the ecliptic plane. We find that an extra component of the gravitomagnetic field not predicted by General Relativity could explain the reported anomalies without conflicting with the Gravity Probe B experiment and the orbits of the geodynamics satellites.

**Abstract: **In this work, we review a plethora of modified theories of gravity with generalized curvature-matter couplings. The explicit nonminimal couplings, for instance, between an arbitrary function of the scalar curvature* R* and the Lagrangian density of matter, induces a non-vanishing covariant derivative of the energy-momentum tensor, implying non-geodesic motion and, consequently, leads to the appearance of an extra force. Applied to the cosmological context, these curvature-matter couplings lead to interesting phenomenology, where one can obtain a unified description of the cosmological epochs. We also consider the possibility that the behavior of the galactic flat rotation curves can be explained in the framework of the curvature-matter coupling models, where the extra terms in the gravitational field equations modify the equations of motion of test particles and induce a supplementary gravitational interaction. In addition to this, these models are extremely useful for describing dark energy-dark matter interactions and for explaining the late-time cosmic acceleration.

**Abstract: **Beginning roughly two hundred years after the big-bang, a tresino phase transition generated Compton-scale composite particles and converted most of the ordinary plasma baryons into new forms of dark matter. Our model consists of ordinary electrons and protons that have been bound into mostly undetectable forms. This picture provides an explanation of the composition and history of ordinary to dark matter conversion starting with, and maintaining, a critical density Universe. The tresino phase transition started the conversion of ordinary matter plasma into tresino-proton pairs prior to the the recombination era. We derive the appropriate Saha–Boltzmann equilibrium to determine the plasma composition throughout the phase transition and later. The baryon population is shown to be quickly modified from ordinary matter plasma prior to the transition to a small amount of ordinary matter and a much larger amount of dark matter after the transition. We describe the tresino phase transition and the origin, quantity and evolution of the dark matter as it takes place from late in the early Universe until the present.

**Abstract: **We review and critically discuss the current understanding of galaxy formation and evolution limited to Early Type Galaxies (ETGs) as inferred from the observational data and briefly contrast the hierarchical and quasi-monolithic paradigms of formation and evolution. Since in Cold Dark Matter (CDM) cosmogony small scale structures typically collapse early and form low-mass haloes that subsequently can merge to assembly larger haloes, galaxies formed in the gravitational potential well of a halo are also expected to merge thus assembling their mass hierarchically. Mergers should occur all over the Hubble time and large mass galaxies should be in place only recently. However, recent observations of high redshift galaxies tell a different story: massive ETGs are already in place at high redshift. To this aim, we propose here a revision of the quasi-monolithic scenario as an alternative to the hierarchical one, in which mass assembling should occur in early stages of a galaxy lifetime and present recent models of ETGs made of Dark and Baryonic Matter in a Λ-CDM Universe that obey the latter scheme. The galaxies are followed from the detachment from the linear regime and Hubble flow at z ≥ 20 down to the stage of nearly complete assembly of the stellar content (*z *∼ 2 − 1) and beyond. It is found that the total mass (*M*_{h} = *M*_{DM} + *M*_{BM} ) and/or initial over-density of the proto-galaxy drive the subsequent star formation histories (SFH). Massive galaxies (*M*_{h} ~ _10^{12}*M*_{⊙}) experience a single, intense burst of star formation (with rates ≥ 10^{3}*M*⊙/yr) at early epochs, consistently with observations, with a weak dependence on the initial over-density; intermediate mass haloes (*M*_{h}~_ 10^{10} − 10^{11}*M*⊙) have star formation histories that strongly depend on their initial over-density; finally, low mass haloes (*M*_{h} ~_ 10^{9}*M*⊙) always have erratic, burst-like star forming histories. The present-day properties (morphology, structure, chemistry and photometry) of the model galaxies closely resemble those of the real galaxies. In this context, we also try to cast light on the physical causes of the Stellar Mass-Radius Relation (MRR) of galaxies. The MRR is the result of two complementary mechanisms: *i.e.*, local physical processes that fix the stellar mass and the radius of each galaxy and cosmological global, statistical principles, which shape the distribution of galaxies in the MR-plane. Finally, we also briefly comment on the spectro-photometric properties of the model galaxies and how nicely they match the observational data. The picture emerging from this analysis is that the initial physical conditions of a proto-galaxy, *i.e., nature*, seem to play the dominant role in building up the ETGs we see today, whereas *nurture *by recurrent captures of small objects is a secondary actor of the fascinating and intriguing story of galaxy formation and evolution.