While in the standard cosmological model the accelerated expansion of the Universe is explained by invoking the presence of the cosmological constant term, it is still unclear the true origin of this stunning observational fact. It is therefore interesting to explore alternatives to the simplest scenario, in particular by assuming a more general framework where the fluid responsible of the accelerated expansion is characterised by a time-dependant equation of state. Usually these models, dubbed dark energy models, are purely phenomenological, but in this work we concentrate on a theoretically justified model, the ghost dark energy model. Within the framework of the spherical collapse model, we evaluate effects of dark energy perturbations both at the linear and non-linear level and transfer these results into an observable quantity, the mass function, by speculatively taking into account contributions of dark energy to the mass of the halos. We showed that the growth rate is higher in ghost models and that perturbations enhance the number of structures with respect to the ΛCDM model, with stronger effects when the total mass takes into account dark energy clumps.

In this work we examine the recently proposed phenomenological emergent dark energy (PEDE) model by [1], using the latest observational data in both expansion and perturbation levels. Applying the statistical Bayesian evidence as well as the AIC and BIC information criteria, we compare the PEDE model with the concordance CDM model in both flat and non-flat universes. We combine the observational datasets as (i) expansion data (except CMB), (ii) expansion data (including CMB) and (iii) expansion data jointed to the growth rate dataset. Our statistical results show that the flat-CDM model is still the best model. In the case of expansion data (including CMB), we observe that the flat-PEDE model is well consistent with observations as well as the concordance CDM universe. While in the cases of (i) and (iii), the PEDE models in both of the flat and non-flat geometries are not favored. In particular, we see that in the perturbation level the PEDE model can not fit the observations as equally as standard CDM cosmology. As the ability of the model, we show that the PEDE models can alleviate the tension of Hubble constant value appearing between the local observations and Planck inferred estimation in standard cosmology.

In this work we investigate the spherical collapse model in flat FRW dark energy universes. We consider the Holographic Dark Energy (HDE) model as a dynamical dark energy scenario with a slowly time-varying equation-of-state (EoS) parameter w de in order to evaluate the effects of the dark energy component on structure formation in the universe. We first calculate the evolution of density perturbations in the linear regime for both phantom and quintessence behavior of the HDE model and compare the results with standard Einstein-de Sitter (EdS) and ΛCDM models. We then calculate the evolution of two characterizing parameters in the spherical collapse model, i.e., the linear density threshold δ c and the virial overdensity parameter ∆ vir . We show that in HDE cosmologies the growth factor g(a) and the linear overdensity parameter δ c fall behind the values for a ΛCDM universe while the virial overdensity ∆ vir is larger in HDE models than in the ΛCDM model. We also show that the ratio between the radius of the spherical perturbations at the virialization and turn-around time is smaller in HDE cosmologies than that predicted in a ΛCDM universe. Hence the growth of structures starts earlier in HDE models than in ΛCDM cosmologies and more concentrated objects can form in this case. It has been shown that the non-vanishing surface pressure leads to smaller virial radius and larger virial overdensity ∆ vir . We compare the predicted number of halos in HDE cosmologies and find out that in general this value is smaller than for ΛCDM models at higher redshifts and we compare different mass function prescriptions. Finally, we compare the results of the HDE models with observations.

Recent observations of gravitational waves motivate investigations for the existence of Primordial Black Holes (PBHs). We propose the observation of gravitational microlensing of distant quasars for the range of infrared to the submillimeter wavelengths by sub-lunar PBHs as lenses. The advantage of observations in the longer wavelengths, comparable to the Schwarzschild radius of the lens (i.e. R sch λ) is the detection of the wave optics features of the gravitational microlensing. The observation of diffraction pattern in the microlensing light curve of a quasar can break the degeneracy between the lens parameters and determine directly the lens mass as well as the distance of the lens from the observer. We estimate the wave optics optical-depth, also calculate the rate of ∼ 0.1 to ∼ 0.3 event per year per a quasar, assuming that hundred percent of dark matter is made of sublunar PBHs. Also, we propose a long-term survey of quasars with the cadence of almost one hour to few days to resolve the wave optics features of the light curves to discover PBHs and determine the fraction of dark matter made of sub-lunar PBHs as well as their mass function.

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