In the present work, we have considered a modified gravity model dubbed as ‘logarithmicf (T) gravity’ as reported by Bamba et al. (J. Cosmol. Astropart. Phys 1101: 21, 2011) and investigated the behavior of Ricci dark energy interacting with pressureless dark Matter. We have chosen the interaction term in the form Q=3 Hdrm and investigated the behavior of the Hubble parameter H as a function of the redshift z. For this reconstructed H, we have investigated the behavior of the fractional density contribution due to the Ricci dark energy and torsion. Subsequently, we investigated the equation of state parameter w RDE which is found to have a phantom-like behavior for all choices of c 2 in the Ricci dark energy density.

In this work we consider f(T) modified teleparallel gravity where T is the torsion scalar. This has been proposed as the natural gravitational alternative for dark energy. We perform a detailed dynamical analysis of these models and find conditions for the cosmological viability of f(T) dark energy models as geometrical constraints on the derivatives of these models. We show that in the phase space exists two cosmologically viable trajectory which (i) The universe would start from an unstable radiation point, then pass a saddle standard matter point which is followed by accelerated expansion de sitter point. (ii) The universe starts from a saddle radiation epoch, then falls onto the stable matter era and the system can not evolve to the dark energy dominated epoch. Finally, for a number of f(T) dark energy models were proposed in the more literature, the viability conditions are investigated. So, this gravity is the good candidate for dark energy.

In this work, we discussed the ‘modified holographic Ricci dark energy’ cosmological model based on El-Nabulsi fractional action cosmology. corresponding related cosmological parameters have been reconstructed. It has been observed that the equation of state parameter behaves like quintessence. Finally, through a test by the squared speed of sound, the proposed reconstruction model is found to be classically unstable.

In the framework of fractional action cosmology, we have reconstructed the scalar potentials and scalar fields, namely, quintessence, phantom, tachyon, k-essence, Dirac-Born-Infeld-essence, hessence, dila- ton field, and Yang-Mills field. To get more physical picture of the variation of the scalar field and potential with time, we express a scale factor in emergent, logamediate, and intermediate scenarios, under which the universe expands differently.

Cold dark matter hierarchical clustering (CDMHC) cosmology based on the Jeans (1902) criterion for gravitational instability gives predictions about the early universe contrary to fluid mechanics and observations. Jeans neglected viscosity, diffusivity, and turbulence: factors that determine gravitational structure formation and contradict small structures (CDM halos) forming from non-baryonic dark matter particle candidates. From hydro-gravitational-dynamics (HGD) cosmology, viscous-gravitational fragmentation produced supercluster (1046kg), cluster, and galaxy (1042kg) mass clouds in the primordial plasma with the large fossil density (r0=3×10-17 kg m-3) of the first fragmentation at 1012 s, and a linear and spiral clump morphology reflecting stretching-compression rates near vortex lines of the plasma turbulence at the 1013 s plasma-gas transition. Gas proto-galaxies fragmented into proto-globular-star-cluster mass (1036 kg) clumps of proto-planet clouds, presently frozen as earth-mass (1024-25 kg) Jovian planets of the baryonic dark matter, about 30.000.000 rogue plants per star. All stars from these planets. They appear in planetary nebulae and are misinterpreted as dark energy. Observations contradict the CDMHCC prediction of large explosive population III first stars at 1016 s, but support the gentle formation of small population II first stars at 1013 s in globule star-clusters from HGD.