In the present work the power spectrum of a particular class of tachyon fields is compared with the one corresponding to a cosmological constant model. This is done for different barotropic indexes $\gamma_0$ and the background space time is assumed to be of the spatially flat Friedmann-Robertson-Walker type. The differential equation describing the perturbations is solved numerically and the power spectrum at the scale factor value $a=1$ is plotted for each case. The result is that the power spectrum of the standard tachyon field differs in many magnitude orders from the $\Lambda$CDM. However, the one with $\gamma_0=1.91$, which corresponds to a complementary tachyon field, coincides fairly well with the concordance model. Therefore, we conclude that the perturbed solutions constitute an effective method to distinguish between the different $\gamma_0$ values for the tachionization $\Lambda$CDM model and the fiducial model. The Statefinder parameters $\{r, s\}$, measuring the deviations of the analysed model from the concordance model, are also explicitly calculated. Our result suggest that, depending on the value of $\gamma_0$, these models can explain the observed expansion history or the perturbation power spectrum of the universe, but they may have problems in describing both features simultaneously.Comment: 7 pages, 7 figures, accepted for publication in General Relativity and Gravitatio

In this work we study a phenomenological non-gravitational interaction between dark matter and dark energy. The scenario studied in this work extends the usual interaction model proportional to the derivative of the dark component density adding to the coupling a non-linear term of the form Q = ρ /3(α + βρ). This dark sector interaction model could be interpreted as a particular case of a running vacuum model of the type Λ(H) = n0 +n1H 2 +n2H 4 in which the vacuum decays into dark matter. For a flat FRW Universe filled with dark energy, dark matter and decoupled baryonic matter and radiation we calculate the energy density evolution equations of the dark sector and solve them. The different sign combinations of the two parameters of the model show clear qualitative different cosmological scenarios, from basic cosmological insights we discard some of them. The linear scalar perturbation equations of the dark matter were calculated. Using the CAMB code we calculate the CMB and matter power spectra for some values of the parameters α and β and compare it with ΛCDM. The model modify mainly the lower multipoles of the CMB power spectrum remaining almost the same the high ones. The matter power spectrum for low wave numbers is not modified by the interaction but after the maximum it is clearly different. Using observational data from Planck, and various galaxy surveys we obtain the constraints of the parameters, the best fit values obtained are the combinations α = (3.7 ± 7) × 10 −4 , −(1.5 × 10 −5 eV −1 ) 4 β < (0.07eV −1 ) 4 . * Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México. josue@fis.unam.mx

A cosmological scenario where dark matter interacts with a variable vacuum energy for a spatially flat Friedmann-Robertson-Walker spacetime is proposed and analysed to show that with a linear equation of state and a particular interaction in the dark sector it is possible to get a model of an Emergent Universe. In addition, the viability of two particular models is studied by taking into account recent observations. The updated observational Hubble data and the JLA supernovae data are used in order to constraint the cosmological parameters of the models and estimate the amount of dark energy in the radiation era. It is shown that the two models fulfil the severe bounds of Ωx(z 1100) < 0.009 at the 2σ level of Planck.