In this work, we study the extended viscous dark energy models in the context of matter perturbations. To do this, we assume an alternative interpretation of the flat Friedmann-Lemaître-Robertson-Walker Universe, through the nonadditive entropy and the viscous dark energy. We implement the relativistic equations to obtain the growth of matter fluctuations for a smooth version of dark energy. As result, we show that the matter density contrast evolves similarly to the $Λ$CDM model in high redshift; in late time, it is slightly different from the standard model. Using the latest geometrical and growth rate observational data, we carry out a Bayesian analysis to constrain parameters and compare models. We see that our viscous models are compatible with cosmological probes, and the $Λ$CDM recovered with a $1σ$ confidence level. The viscous dark energy models relieve the tension of $H_0$ in $2 \sim 3 σ$. Yet, by involving the $σ_8$ tension, some models can alleviate it. In the model selection framework, the data discards the extended viscous dark energy models.
In this paper we study the evolution of the equation of state of viscous dark energy in the scope of Bianchi type III space-time. We consider the case when the dark energy is minimally coupled to the perfect fluid as well as direct interaction with it. The viscosity and the interaction between the two fluids are parameterized by constants $ζ_{0}$ and $σ$ respectively. We have made a detailed investigation on the cosmological implications of this parametrization. To differentiate between different dark energy models, we have performed a geometrical diagnostic by using the statefinder pair $\{s,…
Treating dark matter at large scales as an effectively viscous fluid provides an improved framework for the calculation of the density and velocity power spectra compared to the standard assumption of an ideal pressureless fluid. We discuss how this framework can be made concrete through an appropriate coarse-graining procedure. We also review results that demonstrate that it improves the convergence of cosmological perturbation theory.
The bulk viscosity is introduced to model unified dark matter. The viscous unified model assumes the universe is filled with a single fluid with the bulk viscosity. We review the general framework of the viscous cosmology. The Hubble parameter has a direct connection with the bulk viscosity coefficient. For concrete form of the bulk viscosity, the Hubble parameter which has the scaling relation with the redshift can be obtained. We discuss two viscosity models and the cosmological evolution to which they lead. Using SNe Ia data, the viscosity model can be fitted. We briefly review the fitting …
Phantom dark energy is a proposal that explains the current observations that mildly favor the equation of state of dark energy $ω^{de}$ crossing -1 at 68% confidence level. However, phantom fields are generally ruled out by ultraviolet quantum instabilities. To overcome this discrepancy, in this paper we propose a mechanism to show that how the presence of bulk viscosity in the cosmic fluid can temporarily drive the fluid into the phantom region ($ω<-1$). As time is going on, phantom decays and ultimately $ω^{de}$ approaches to -1. Then we show these quintessence and phantom descriptions of n…
We study the evolution of the dark energy parameter within the scope of a spatially non-flat and isotropic Friedmann-Robertson-Walker (FRW) model filled with barotropic fluid and bulk viscous stresses. We have obtained cosmological solutions which exhibit without a big rip singularity. It is concluded that in both non-interacting and interacting cases non-flat open universe crosses the phantom region. We find that during the evolution of the universe, the equation of state (EoS) for dark energy $ω_{D}$ changes from $ω^{eff}_{D} < -1$ to $ω^{eff}_{D} > -1$, which is consistent with recent obser…
We discuss bulk viscous cosmological models. Since the bulk viscous pressure is negative, viable viscous cosmological scenarios with late time accelerated expansion can in principle be constructed. After discussing some alternative models based on bulk viscous effects we will focus on a model very similar to the standard $Λ$CDM. We argue that a $Λ${\rm v}CDM model, where we assign a very small (albeit perceptible) bulk viscosity to dark matter is in agreement with available cosmological observations. Hence, we work with the concept of viscous Cold Dark Matter ({\rm v}CDM). At the level of the …
In this paper, we continue our previous work of studying viscous generalized Chaplygin gas (VGCG) as a unified dark fluid but including the bulk viscosity perturbation. By using the currently available cosmic observational data from SNLS3, BAO, HST and recently released Planck, we gain the constraint on bulk viscosity coefficient: $ζ_0=0.0000138_{- 0.0000105- 0.0000138- 0.0000138}^{+ 0.00000614+ 0.0000145+ 0.0000212}$ in $1, 2, 3σ$ regions respectively via Markov Chain Monte Carlo method. The result shows that when considering perturbation of bulk viscosity, the currently cosmic observations f…
A solution to the coincidence and Big Rip problems on the bases of an anisotropic space-time is proposed. To do so, we study the interaction between viscous dark energy and dark matter in the scope of the Bianchi type-I Universe. We parameterize the viscosity and the interaction between the two fluids by constants $ζ_{0}$ and $σ$ respectively. A detailed investigation on the cosmological implications of this parametrization has been made. We have also performed a geometrical diagnostic by using the statefinder pairs $\{s, r\}$ and $\{q, r\}$ in order to differentiate between different dark ene…
In this paper, we test the spherical collapse of a viscous unified dark fluid (VUDF) which has constant adiabatic sound speed and show the nonlinear collapse for VUDF, baryons, and dark matter which are important to form the large scale structure of our Universe. By varying the values of model parameters $α$ and $ζ_{0}$, we discuss their effects on the nonlinear collapse of the VUDF model, and compare its result to $ΛCDM$ model. The analyzed results show that, within the spherical top-hat collapse framework, larger values of $α$ and smaller values of $ζ_{0}$ make the structure formation earlie…
We revise the conditions for the physical viability of a cosmological model in which dark matter has bulk viscosity and also interacts with dark energy. We have also included radiation and baryonic matter components; all matter components are represented by perfect fluids, except the dark matter, that is treated as an imperfect fluid. We impose upon the model the condition of a complete cosmological dynamics that results in an either null or negative bulk viscosity, but the latter also disagrees with the Local Second Law of Thermodynamics. The model is also compared with cosmological observati…
We propose an approach considering the nonextensive effects in the context of the Verlinde theory in order to address an extended cosmological model in the context of viscous dark energy. Specifically, this model leads to a tiny perturbation in the dynamics of the expansion of the universe through the generalized Friedmann equations so-called the extended $Λ$CDM model. From the observational test standpoint, we make a Bayesian analysis of the models of bulk viscosity for dark energy which follows the Eckart theory of bulk viscosity. These models are investigated through the context of both mod…
The possibility of dark matter being a dissipative component represents an option for the standard view where cold dark matter (CDM) particles behave on large scales as an ideal fluid. By including a physical mechanism to the dark matter description like viscosity we construct a more realistic model for the universe. Also, the known small scale pathologies of the standard CDM model either disappear or become less severe. We study clustering properties of a $Λ$CDM-like model in which dark matter is described as a bulk viscous fluid. The linear power spectrum, the nonlinear spherical "top hat" c…
In this paper we have investigated the general form of viscous and non-viscous dark energy equation of state (EoS) parameter in the scope of anisotropic Bianchi type I space-time. We show that the presence of bulk viscosity causes transition of $ω^{de}$ from quintessence to phantom but the phantom state is an unstable state (as expected) and EoS of DE tends to $-1$ at late time. Then we show this phantomic description of the viscous dark energy and reconstruct the potential of the phantom scalar field. It is found that bulk viscosity pushes the universe to a darker region. We have also shown t…
We assume cold dark matter to possess a small bulk-viscous pressure which typically attenuates the growth of inhomogeneities. Explicit calculations, based on Eckart's theory of dissipative processes, reveal that for viscous cold dark matter the usual Newtonian approximation for perturbation scales smaller than the Hubble scale is no longer valid. We advocate the use of a neo-Newtonian approach which consistently incorporates pressure effects into the fluid dynamics and correctly reproduces the general relativistic dynamics. This result is of interest for numerical simulations of nonlinear stru…
We study a cosmological model composed of a dark energy fluid interacting with a viscous matter fluid in a spatially flat Universe. The matter component represents the baryon and dark matter and it is taken into account, through a bulk viscosity, the irreversible process that the matter fluid undergoes because of the accelerated expansion of the universe. The bulk viscous coefficient is assumed to be proportional to the Hubble parameter. The radiation component is also taken into account in the model. The model is constrained using the type Ia supernova observations, the shift parameter of the…
Considering the cosmological redshift $z_c$ , the mass of GW source extracted from GW signal is $1+z_c$ times larger than its intrinsic value, and distance between detector and GW source should be regarded as luminosity distance. However, besides cosmological redshift, there are other kinds of redshifts should be considered, which is actually ignored, in the analysis of GW data, such as Doppler redshift and gravitational redshift, so the parameters extracted from GW may deviate from their intrinsic values. Another factor that may affect GW is the viscous medium in propagation path of GW, which…
We investigate the global 21-cm brightness temperature in the context of viscous dark energy (VDE) models. The bulk viscosity of dark energy perturbs the Hubble evolution of the Universe which could cool baryons faster, and hence, alter the 21-cm brightness temperature. An additional amount of entropy is also produced as an outcome of the viscous flow. We study the combined contribution of Hawking radiation from primordial black holes, decay and annihilation of particle dark matter and baryon-dark matter scattering in the backdrop of VDE models towards modification of the 21-cm temperature. We…
We study the entropy-corrected version of the holographic dark energy (HDE) model in the framework of modified FRW cosmology. We consider a non-flat universe filled with an interacting viscous entropy-corrected HDE (ECHDE) with dark matter. We also include the case of variable gravitational constant G in our model. We obtain the equation of state and the deceleration parameters of the interacting viscous ECHDE. Moreover, we reconstruct the potential and the dynamics of the quintessence, tachyon, K-essence and dilaton scalar field models according to the evolutionary behavior of the interacting…
Modern cosmology suggests that the Universe contains two dark components -- dark matter and dark energy -- both unkown in laboratory physics and both lacking direct evidence. Alternatively, a unified dark sector, described by a single fluid, has been proposed. Dissipation is a common phenomenon in nature and it thus seems natural to consider models dominated by a viscous dark fluid. We focus on the study of bulk viscosity, as isotropy and homogeneity at large scales implies the suppression of shear viscosity, heat flow and diffusion. The generic ansatz $ξ\propto ρ^ν$ for the coefficient of bul…
The viscosity of dark matter in cosmological models may cause an accelerated expansion and when this effect is sufficiently large, it can explain the dark energy. In this work, attributing the origin of viscosity to self-interaction of dark matter, we study the viscous cosmology at small redshift $(0\leq z\leq2.5)$. Assuming the cluster scale to be virialized and by modeling a power law behavior of velocity gradients, we calculate the Hubble expansion rate, $H(z)$ and the deceleration parameter, $q(z)$. We then perform a $χ^{2}$ analysis to estimate the best fit model parameters. By using the …
The EDGES experiment has detected the global absorption signal of 21 cm line at $z\sim17$ in cosmic dawn era and reported its amplitude larger than the standard cosmological prediction. One of the possible explanation requires that the baryons were much cooler than the standard scenario. This requires an interaction between the dark and baryonic sectors with some appropriate cross-section, $ \hatσ $. In this work, we examine the role that dissipative effects of cosmic fluid might play in influencing the 21 cm signal. We show that the presence of viscous dissipation of dark matter can significa…
Is the accelerating expansion of the Universe true, inferred through observations of distant supernovae, and is the implied existence of an enormous amount of anti-gravitational dark energy material driving the accelerating expansion of the universe also true? To be physically useful these propositions must be falsifiable; that is, subject to observational tests that could render them false, and both fail when viscous, diffusive, astro-biological and turbulence effects are included in the interpretation of observations. A more plausible explanation of negative stresses producing the big bang i…
The objective of the present work is to study a cosmological model for a spatially flat Universe whose constituents are a dark energy field and a matter field which includes baryons and dark matter. The constituents are supposed to be in interaction and irreversible processes are taken into account through the inclusion of a non-equilibrium pressure. The non-equilibrium pressure is considered to be proportional to the Hubble parameter within the framework of a first order thermodynamic theory. The dark energy and matter fields are coupled by their barotropic indexes, which are considered as fu…
We investigate the viscous Ricci dark energy (RDE) model by assuming that there is bulk viscosity in the linear barotropic fluid and the RDE. In the RDE model without bulk viscosity, the universe is younger than some old objects at some redshifts. Since the age of the universe should be longer than any objects in the universe, the RDE model suffers the age problem, especially when we consider the object APM 08279+5255 at $z=3.91$, whose age is $t = 2.1$ Gyr. In this letter, we find that once the viscosity is taken into account, this age problem is alleviated.
Some cosmological scenarios with bulk viscosity for the dark energy fluid are considered. Based on some considerations related to hydrodynamics, two different equations of state for dark energy are assumed, leading to power-law and logarithmic effective corrections to the pressure. The models are tested with the latest astronomical data from Type Ia supernovae (Pantheon sample), measurements of the Hubble parameter $H(z)$, Baryon Acoustic Oscillations and Cosmic Microwave Background radiation. In comparison with $Λ$CDM model, some different results are obtained and their viability is discussed…
The Universe is modeled as consisting of pressureless baryonic matter and a bulk viscous fluid which is supposed to represent a unified description of the dark sector. In the homogeneous and isotropic background the \textit{total} energy density of this mixture behaves as a generalized Chaplygin gas. The perturbations of this energy density are intrinsically nonadiabatic and source relative entropy perturbations. The resulting baryonic matter power spectrum is shown to be compatible with the 2dFGRS and SDSS (DR7) data. A joint statistical analysis, using also Hubble-function and supernovae Ia …
In a homogeneous and isotropic universe bulk viscosity is the unique viscous effect capable to modify the background dynamics. Effects like shear viscosity or heat conduction can only change the evolution of the perturbations. The existence of a bulk viscous pressure in a fluid, which in order to obey to the second law of thermodynamics is negative, reduces its effective pressure. We discuss in this study the degeneracy in bulk viscous cosmologies and address the possibility that phantom dark energy cosmology could be caused by the existence of non-equilibrium pressure in any cosmic component.…
Self interacting dark matter (SIDM) provides us with a consistent solution to certain astrophysical observations in conflict with collision-less cold DM paradigm. In this work we estimate the shear viscosity $(η)$ and bulk viscosity $(ζ)$ of SIDM, within kinetic theory formalism, for galactic and cluster size SIDM halos. To that extent we make use of the recent constraints on SIDM crossections for the dwarf galaxies, LSB galaxies and clusters. We also estimate the change in solution of Einstein's equation due to these viscous effects and find that $σ/m$ constraints on SIDM from astrophysical d…
We examine linear perturbation theory to evaluate the contribution of viscosity coefficient in the growing of dark matter perturbations in the context of the bulk viscous dark energy model inspired by thermodynamical dissipative phenomena proposed by [B. Mostaghel et al., 2017, The European Physical Journal C, 77, 541]. As the cosmological implementations, we investigate the {\it Integrated Sachs-Wolfe} (ISW) auto-power spectrum, the ISW-galaxy cross-power spectrum and derive limits on $fσ_8$. The dimensionless bulk viscosity coefficient ($γ$) in the absence of interaction between dark sectors…
We study the non-linear spherical "top hat" collapse for Chaplygin and viscous unified cosmologies. The term unified refers to models where dark energy and dark matter are replaced by one single component. For the generalized Chaplygin gas (GCG) we extend previous results of [R. A. A. Fernandes {\it et al}. Physical Review D 85, 083501 (2012)]. We discuss the differences at non-linear level between the GCG with $α=0$ and the $Λ$CDM model. We show that both are indeed different. The bulk viscous model which differs from the GCG due to the existence of non-adiabatic perturbations is also studied…
Based on the assumption that the dark energy possessing bulk viscosity is homogenously and isotropically permeated in the universe, we propose three new viscous dark energy (VDE) models to characterize the accelerating universe. By constraining these three models with the latest cosmological observations, we find that they just deviate very slightly from the standard cosmological model and can alleviate effectively the current $H_0$ tension between the local observation by the Hubble Space Telescope and the global measurement by the Planck Satellite. Interestingly, we conclude that a spatially…
We discuss the possibility to implement a viscous cosmological model, attributing to the dark matter component a behaviour described by bulk viscosity. Since bulk viscosity implies negative pressure, this rises the possibility to unify the dark sector. At the same time, the presence of dissipative effects may alleviate the so called small scale problems in the $Λ$CDM model. While the unified viscous description for the dark sector does not lead to consistent results, the non-linear behaviour indeed improves the situation with respect to the standard cosmological model.
Cosmological perturbations of sufficiently long wavelength admit a fluid dynamic description. We consider modes with wavevectors below a scale $k_m$ for which the dynamics is only mildly non-linear. The leading effect of modes above that scale can be accounted for by effective non-equilibrium viscosity and pressure terms. For mildly non-linear scales, these mainly arise from momentum transport within the ideal and cold but inhomogeneous fluid, while momentum transport due to more microscopic degrees of freedom is suppressed. As a consequence, concrete expressions with no free parameters, excep…
Inspired by thermodynamical dissipative phenomena, we consider bulk viscosity for dark fluid in a spatially flat two-component Universe. Our viscous dark energy model represents Phantom crossing avoiding Big-Rip singularity. We propose a non-minimal derivative coupling scalar field with zero potential leading to accelerated expansion of Universe in the framework of bulk viscous dark energy model. In this approach, coupling constant ($κ$) is related to viscosity coefficient ($γ$) and energy density of dark energy at the present time ($Ω_{\rm DE}^0$). This coupling is bounded as $κ\in [-1/9H_0^2…
We explore flat ΛCDM models with bulk viscosity, and study the role of the bulk viscosity in the evolution of these universe models. The dynamical equations for these models are obtained and solved for some cases of bulk viscosity. We obtain differential equations for the Hubble parameter H and the energy density of dark matter ρ, for which we give analytical solutions for some cases and for the general case we give a numerical solution. Also we calculate the statefinder parameters for this model and display them in the s-r-plane.
In this present article, we study different accretion properties regarding viscous accretion of dark energy. Modified Chaplygin gas is chosen as the dark energy candidate. Viscosity is encountered with the help of Shakura-Sunyaev viscosity parameter. We study sonic speed vs radial distance curves. We compare between adiabatic and dark energy dominated cases and follow that sonic speed falls as we go nearer to the central gravitating object. As viscosity is imposed, a threshold drop in accretion sonic speed is followed. Average rate of fall in accretion sonic speed is increased with black hole'…
We investigate the cosmological perturbation dynamics for a universe consisting of pressureless baryonic matter and a viscous fluid, the latter representing a unified model of the dark sector. In the homogeneous and isotropic background the \textit{total} energy density of this mixture behaves as a generalized Chaplygin gas. The perturbations of this energy density are intrinsically non-adiabatic and source relative entropy perturbations. The resulting baryonic matter power spectrum is shown to be compatible with the 2dFGRS and SDSS (DR7) data. A joint statistical analysis, using also Hubble-f…
In this work we study the evolution of a spatially flat Universe by considering a viscous dark matter and perfect fluids for dark energy and radiation, including an interaction term between dark matter and dark energy. In the first part, we analyse the general properties of the Universe by performing a stability analysis and then we constrain the free parameters of the model using the latest and cosmological-independent measurements of the Hubble parameter. We find consistency between the viscosity coefficient and the condition imposed by the second law of the Thermodynamics. The second part i…
In this paper, we study the $f(T,\mathcal{T})$ gravity model in the presence of the bulk viscosity by the flat-FRW metric. The field equation is obtained by teleparallel gravity with tetrad field. The universe components are considered as matter and dark energy which the dark energy component associates from the viscous $f(T,\mathcal{T})$ gravity. After calculating the Friedmann equations, we obtain the energy density, the pressure and the EoS of dark energy in terms of the redshift parameter. Afterward, we plot the corresponding cosmological parameters versus the redshift parameter and examin…
In this paper, we study the model of $f(T, B)$ gravity with viscous fluid in flat-FRW metric, in which $T$ and $B$ are torsion scalar and boundary term, respectively. We obtain the Friedmann equations in the framework of modified teleparallel gravity by tetrad components. We consider an interacting model between matter and dark energy so that universe dominates by viscous fluid. Then, we write the corresponding cosmological parameters in terms of the redshift parameter, and, we parameterize the Hubble parameter with experimental data. In what follows, we plot the corresponding cosmological par…
In this work we explore the thermodynamic aspects of dark energy for late future time universe in two different scenarios: as a perfect fluid with constant and variable equation of state parameter; and as dissipative fluid described by a barotropic equation of state with bulk viscosity in the framework of the Eckart theory and the full Israel-Stewart theory. We explore cosmological solutions for a flat, homogeneous and isotropic universe; and we assume the late future time behavior when the dark energy dominates the cosmic evolution. When modeled as a perfect fluid with a dynamical equation of…
Fluids often display dissipative properties. We explore dissipation in the form of bulk viscosity in the cold dark matter fluid. We constrain this model using current data from supernovae, baryon acoustic oscillations and the cosmic microwave background. Considering the isotropic and homogeneous background only, viscous dark matter is allowed to have a bulk viscosity $\lesssim 10^7$ Pa$\cdot$s, also consistent with the expected integrated Sachs-Wolfe effect (which plagues some models with bulk viscosity). We further investigate the small-scale formation of viscous dark matter halos, which turn…
In this paper, we investigate Bianchi type-$VI$ cosmological model for the universe filled with dark energy and viscous fluid in the presence of cosmological constant. Also, we show accelerating expansion of the universe by drawing volume scale, pressure and energy density versus cosmic time. In order to solve the Einstein field equations, we assume the expansion scalar is proportional to a component of the shear tensor. Therefore, we obtain the directional scale factors and show the EOS parameter crosses over phantom divided-line.
The cosmological observations suggest that the presently accelerating universe should be filled by an exotic form of matter, violating the strong energy condition, of unknown nature and origin. We propose the viscous dark matter of a source of acceleration in the form of Chaplygin gas which is characterized by equation of state in the phenomenological form $p=-\frac{A}{ρ^α}$, where $p$ and $ρ$ are pressure and energy density respectively ($A$ and $α$ are constants). Chaplygin gas is interpreted in terms of viscous matter and without the cosmological constant. The acceleration effect is caused …
In present article we consider an axion F(R) gravity model and described with the help of holographic principle the cosmological models of viscous dark fluid coupled with axion matter in a spatially flat Friedmann-Robertson-Walker (FRW) universe. This description based on generalized infrared-cutoff holographic dark energy, proposed by Nojiri and Odintsov. We explored the Little Rip, the Pseudo Rip, and the power-law bounce cosmological models in terms of the parameters of the inhomogeneous equation of the state of viscous dark fluid and calculated the infrared cutoffs analytically. We represe…
We analyze characteristic properties of two different cosmological models: (i) a one-component dark energy model where the bulk viscosity $ζ$ is associated with the fluid as a whole, and (ii) a two-component model where $ζ$ is associated with a dark matter component $ρ_{\rm m}$ only, the dark energy component considered inviscid. Shear viscosity is omitted. We assume throughout the simple equation of state $p=wρ$, with $w$ a constant. In the one-component model we consider two possibilities, either to take $ζ$ proportional to the scalar expansion (equivalent to the Hubble parameter), in which …
We model the dark sector of the cosmic substratum by a viscous fluid with an equation of state $p=-ζΘ$, where $Θ$ is the fluid-expansion scalar and $ζ$ is the coefficient of bulk viscosity for which we assume a dependence $ζ\propto ρ^ν$ on the energy density $ρ$. The homogeneous and isotropic background dynamics coincides with that of a generalized Chaplygin gas with equation of state $p = - A/ρ^α$. The perturbation dynamics of the viscous model, however, is intrinsically non-adiabatic and qualitatively different from the Chaplygin-gas case. In particular, it avoids short-scale instabilities a…
In this paper, two inhomogeneous single fluid models for the Universe, which are able to naturally solve the $H_{0}$ tension problem, are discussed. The analysis is based on a Bayesian Machine Learning approach that uses a generative process. The adopted method allows to constrain the free parameters of each model by using the model itself, only. The observable is taken to be the Hubble parameter, obtained from the generative process. Using the full advantages of our method, the models are constrained for two redshift ranges. Namely, first this is done with mock $H(z)$ data over $z\in [0,2.5]$…
We present a general formalism to study the growth of dark matter perturbations when dark energy perturbations and interactions between dark sectors are present. We show that dynamical stability of the growth of structure depends on the type of coupling between dark sectors. By taking the appropriate coupling to ensure the stable growth of structure, we observe that the effect of the dark sectors' interaction overwhelms that of dark energy perturbation on the growth function of dark matter perturbation. Due to the influence of the interaction, the growth index can differ from the value without…
An isotropic and homogeneous cosmological model with a source of dark energy is studied. That source is simulated with a viscous relativistic fluid with minimal causal correction. In this model the restrictions on the parameters coming from the following conditions are analized: a) energy density without singularities along time, b) scale factor increasing with time, c) universe accelerated at present time, d) state equation for dark energy with "w" bounded and close to -1. It is found that those conditions are satified for the following two cases. i) When the transport coefficient (τ_{Π}), as…
We have put forward a new unified framework which provides a consistent and rather complete account of the growth index of matter perturbations in the regime where the dark energy is allowed to have clustering. In particular, we find that the growth index is not only affected by the cosmological parameters but rather it depends on the choice of the considered dark energy (homogeneous or clustered). Using the {\em Planck} priors and performing a standard $χ^2$-minimization between theoretical expectations and growth data, we statistically quantify the ability of the growth index to represent th…
