Perturbations in Tachyon Dark Energy and their Effect on Matter Clustering

A non-canonical scalar tachyon field is a viable candidate for dark energy and has been found to be in good agreement with observational data. Background data alone cannot completely rule out degeneracy between this model and others. To further constrain the parameters, apart from the distance measurements, we study perturbations in the tachyon scalar field and how they affect matter clustering. We consider two tachyon potentials for this study, an inverse square potential and an exponential potential. We study the evolution of the gravitational potential, matter density contrast, and dark energy density contrast, and compare them with the evolution in the $\Lambda CDM$ model. Although perturbations in dark energy at sub-Hubble scales are negligible in comparison with matter perturbations, they cannot be ignored at Hubble and super-Hubble scales ($\lambda_p > 1000$ Mpc). We also study the evolution of growth function and growth rate of matter, and find that the growth rate is significantly suppressed in dark energy dominated era with respect to the growth rate for $\Lambda CDM$ model. A comparison of these models with Redshift Space Distortion growth rate data is presented by way of calculating $f\sigma_8(z)$. There is a tension of $2.9\sigma$ ($2.26\sigma$ ) between growth rate data and Planck-2015 (Planck-2018) Cosmic Microwave Background Radiation data for $\Lambda CDM$ model. We present constraints on free parameters of these models and show that perturbations in the tachyon scalar field reduce this tension between different data sets.