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 which avoids bigrip singularity. We propose a non-minimal derivative coupling scalar field with zero potential leading to accelerated expansion of the Universe in the framework of bulk viscous dark energy model. In this approach, the coupling constant, κ, is related to viscosity coefficient, γ , and the present dark energy density, Ω 0 DE . This coupling is bounded as. We implement recent observational data sets including a joint light-curve analysis (JLA) for SNIa, gamma ray bursts (GRBs) for most luminous astrophysical objects at high redshifts, baryon acoustic oscillations (BAO) from different surveys, Hubble parameter from HST project, Planck CMB power spectrum and lensing to constrain model free parameters. The joint analysis of JLA + GRBs + BAO + HST shows that Ω 0 DE = 0.696 ± 0.010, γ = 0.1404 ± 0.0014 and H 0 = 68.1 ± 1.3. Planck TT observation provides γ = 0.32 +0.31 −0.26 in the 68% confidence limit for the viscosity coefficient. The cosmographic distance ratio indicates that current observed data prefer to increase bulk viscosity. The competition between phantom and quintessence behavior of the viscous dark energy model can accommodate cosmological old objects reported as a sign of age crisis in the ΛCDM model. Finally, tension in the Hubble parameter is alleviated in this model. a

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 Mostaghel et al. (2017). As the cosmological implementations, we investigate the Integrated Sachs-Wolfe (ISW) auto-power spectrum, the ISW-galaxy cross-power spectrum and derive limits on f σ 8 . The dimensionless bulk viscosity coefficient (γ) in the absence of interaction between dark sectors, modifies the Hubble parameter and the growth function, while the Poisson equation remains unchanged. Increasing γ reduces the dark matter growing mode at the early epoch while a considerable enhancement will be achieved at the late time. This behavior imposes non-monotonic variation in the time evolution of gravitational potential generating a unique signature on the CMB photons. The bulk viscous dark energy model leads to almost a decreasing in ISW source function at the late time. Implementation of the Redshift Space Distortion (RSD) observations based on "Gold-2017" catalogue, shows Ω 0 m = 0.303 +0.044 −0.038 , γ = 0.033 +0.098 −0.033 and σ 8 = 0.769 +0.080 −0.089 at 1σ level of confidence. Finally, tension in the σ 8 is alleviated in our viscous dark energy model.

In this work we study the simultaneous effect of primordial non-Gaussianity and the modification of the gravity in f (R) framework on large scale structure observations. We show that nonGaussianity and modified gravity introduce a scale dependent bias and growth rate functions. The deviation from ΛCDM in the case of primordial non-Gaussian models is in large scales, while the growth rate deviates from ΛCDM in small scales for modified gravity theories. We show that the redshift space distortion can be used to distinguish positive and negative fNL in standard background, while in f (R) theories they are not easily distinguishable. The galaxy power spectrum is generally enhanced in presence of non-Gaussianity and modified gravity. We also obtain the scale dependence of this enhancement. Finally we define galaxy growth rate and galaxy growth rate bias as new observational parameters to constrain cosmology.

The minimal warm inflation model was constructed as a warm inflation setup with direct interaction between inflaton and (non-Abelian) gauge fields. The model was shown to be compatible with observation for some forms of potential. As a result of direct analysis of CMB data, the model presents a reasonable phase-space of its parameter compatible with observation and the Transplanckian censorship conjecture (TCC).

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