In the context of f(R, T) theories of gravity, we study the evolution of scalar cosmological perturbations in the metric formalism. According to restrictions on the background evolution, a specific model within these theories is assumed in order to guarantee the standard continuity equation. Using a completely general procedure, we find the complete set of differential equations for the matter density perturbations. In the case of sub-Hubble modes, the density contrast evolution reduces to a second-order equation. We show that for well-motivated f(R, T) Lagrangians the quasistatic approximation yields to very different results from the ones derived in the frame of the concordance Lambda CDM model constraining severely the viability of such theories.

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Dynamics of scalar perturbations in f(R, T) gravity

We investigate the properties of the FLRW flat cosmological models in which the vacuum energy density evolves with time, $\ensuremath{\Lambda}(t)$. Using different versions of the $\ensuremath{\Lambda}(t)$ model, namely, quantum field vacuum, power series vacuum and power law vacuum, we find that the main cosmological functions such as the scale factor of the Universe, the Hubble expansion rate $H$, and the energy densities are defined analytically. Performing a joint likelihood analysis of the recent supernovae type Ia data, the cosmic microwave background shift parameter and the baryonic acoustic oscillations traced by the Sloan Digital Sky Survey galaxies, we put tight constraints on the main cosmological parameters of the $\ensuremath{\Lambda}(t)$ scenarios. Furthermore, we study the linear matter fluctuation field of the above vacuum models. We find that the patterns of the power series vacuum $\ensuremath{\Lambda}={n}_{1}H+{n}_{2}{H}^{2}$ predict stronger small scale dynamics, which implies a faster growth rate of perturbations with respect to the other two vacuum cases (quantum field and power law), despite the fact that all the cosmological models share the same equation of state parameter. In the case of the quantum field vacuum $\ensuremath{\Lambda}={n}_{0}+{n}_{2}{H}^{2}$, the corresponding matter fluctuation field resembles that of the traditional $\ensuremath{\Lambda}$ cosmology. The power law vacuum ($\ensuremath{\Lambda}\ensuremath{\propto}{a}^{\ensuremath{-}n}$) mimics the classical quintessence cosmology, the best fit being tilted in the phantom phase. In this framework, we compare the observed growth rate of clustering measured from the optical galaxies with those predicted by the current $\ensuremath{\Lambda}(t)$ models. Performing a Kolmogorov-Smirnov statistical test we show that the cosmological models which contain a constant vacuum ($\ensuremath{\Lambda}\mathrm{CDM}$), quantum field vacuum, and power law vacuum provide growth rates that match well with the observed growth rate. However, this is not the case for the power series vacuum models (in particular, the frequently adduced $\ensuremath{\Lambda}\ensuremath{\propto}H$ model) in which clusters form at significantly earlier times ($z\ensuremath{\ge}4$) with respect to all other models ($z\ensuremath{\sim}2$). Finally, we derived the theoretically predicted dark matter halo mass function and the corresponding distribution of cluster-size halos for all the models studied. Their expected redshift distribution indicates that it will be difficult to distinguish the closely resembling models (constant vacuum, quantum field, and power law vacuum), using realistic future x-ray surveys of cluster abundances. However, cluster surveys based on the Sunayev-Zeldovich detection method give some hope to distinguish the closely resembling models at high redshifts.

/pdf/hubble-expansion-and-structure-formation-in-time-varying-4bj6yypa18.pdf

Hubble expansion and structure formation in time varying vacuum models

In this review we consider in detail different theoretical topics associated with interaction in the dark sector. We study linear and nonlinear interactions which depend on the dark matter and dark energy densities. We consider a number of different models (including the holographic dark energy and dark energy in a fractal universe), with interacting dark energy and dark matter, have done a thorough analysis of these models. The main task of this review was not only to give an idea about the modern set of different models of dark energy, but to show how much can be diverse dynamics of the universe in these models. We find that the dynamics of a universe that contains interaction in the dark sector can differ significantly from the Standard Cosmological Model.

Cosmological evolution with interaction between dark energy and dark matter

We reconcile seemingly conflicting statements in the literature about the behavior of cosmological solutions in modified theories of gravity where the Einstein-Hilbert Lagrangian for gravity is modified by the addition of a function of the Ricci scalar, $f(R)$. Using the example of $f(R)=\ifmmode\pm\else\textpm\fi{}{\ensuremath{\mu}}^{4}/R$ we show that only such choices of $f(R)$ where ${\mathrm{d}}^{2}f/\mathrm{d}{R}^{2}g0$ have stable high-curvature limits and well-behaved cosmological solutions with a proper era of matter domination. The remaining models enter a phase dominated by both matter and scalar kinetic energy where the scalar curvature remains low.

/pdf/stability-of-cosmological-solutions-in-frmodels-of-gravity-18ggecbics.pdf

Stability of cosmological solutions in fRmodels of gravity

In this review we consider in detail different theoretical topics associated with interaction in the dark sector. We study linear and nonlinear interactions which depend on the dark matter and dark energy densities. We consider a number of different models (including the holographic dark energy and dark energy in a fractal universe) with interacting dark energy (DE) and dark matter (DM), have done a thorough analysis of these models. The main task of this review was not only to give an idea about the modern set of different models of dark energy, but to show how much can be diverse dynamics of the universe in these models. We find that the dynamics of a Universe that contains interaction in the dark sector can differ significantly from the Standard Cosmological Model (SCM).

Cosmological Evolution With Interaction Between Dark Energy And Dark Matter

To reconstruct dark energy models the redshift z
 eq
 , marking the end of radiation era and the beginning of matter-dominated era, can play a role as important as z
 t
 , the redshift at which deceleration parameter experiences a signature flip. To implement the idea we propose a variable equation of state for matter that can bring a smooth transition from radiation to matter-dominated era in a single model. A popular Λ∝
 ρ dark energy model is chosen for demonstration but found to be unacceptable. An alternative Λ∝
 ρ
 a
 3 model is proposed and found to be more close to observation.

A better way to reconstruct dark energy models

Dark energy models inspired by the cosmological holographic principle are studied in homogeneous isotropic spacetime with a general choice for the dark energy density $\rho_{d}=3(\alpha H^{2}+\beta\dot{H})$
 . Special choices of the parameters enable us to obtain three different holographic models, including the holographic Ricci dark energy (RDE) model. Effect of interaction between dark matter and dark energy on the dynamics of those models are investigated for different popular forms of interaction. It is found that crossing of phantom divide can be avoided in RDE models for β>0.5 irrespective of the presence of interaction. A choice of α=1 and β=2/3 leads to a varying Λ-like model introducing an IR cutoff length Λ−1/2. It is concluded that among the popular choices an interaction of the form Q∝Hρm suits the best in avoiding the coincidence problem in this model.

Interacting holographic dark energy models: a general approach

Dark energy models inspired by the cosmological holographic principle are studied in homogeneous isotropic spacetime with a general choice for the dark energy density $\rho_d=3(\alpha H^2+\beta\dot{H})$. Special choices of the parameters enable us to obtain three different holographic models, including the holographic Ricci dark energy(RDE) model. Effect of interaction between dark matter and dark energy on the dynamics of those models are investigated for different popular forms of interaction. It is found that crossing of phantom divide can be avoided in RDE models for $\beta>0.5$ irrespective of the presence of interaction. A choice of $\alpha=1$ and $\beta=2/3$ leads to a varying $\Lambda$-like model introducing an IR cutoff length $\Lambda^{-1/2}$. It is concluded that among the popular choices an interaction of the form $Q\propto H\rho_m$ suits the best in avoiding the coincidence problem in this model.

Interacting holographic dark energy models: A general approach

To explore possibilities of avoiding coincidence problem in $f(R)$ gravity we consider models in Einstein conformal frame which are equivalent to Einstein gravity with a minimally coupled scalar field. As the conformal factor determines the coupling term and hence the interaction between matter and dark energy, the function $f(R)$ can in principle be determined by choosing an appropriate function for the deceleration parameter only. Possible behavior of $f(R)$ to avoid coincidence problem are investigated in two such cases.

The coincidence problem in $f(R)$ gravity models

To explore possibilities of avoiding coincidence problem in $$f(R)$$
 gravity we consider models in Einstein conformal frame which are equivalent to Einstein gravity with a minimally coupled scalar field. As the conformal factor determines the coupling term and hence the interaction between matter and dark energy, the function $$f(R)$$
 can in principle be determined by choosing an appropriate function for the deceleration parameter only. Possible behavior of $$f(R)$$
 to avoid coincidence problem are investigated in two such cases.

S. Som

Papers

A better way to reconstruct dark energy models

Interacting holographic dark energy models: a general approach

Interacting holographic dark energy models: A general approach

The coincidence problem in $f(R)$ gravity models

The coincidence problem in f(R) gravity models