Toward a concordance teleparallel Cosmology II: Linear perturbation

Late time cosmic acceleration may be achieved by modifying gravity on large scales. This should also have consequences on the evolution of perturbations. We thus extend our study of exponential infrared $f(T)$ teleparallel gravity to examine the viability of the theory at the linear perturbation level, evaluating the full CMB and matter power spectra. As the theory does not introduce extra free parameters, it fits within the minimal six parameter space of standard $\Lambda$CDM. Using Planck 2018 CMB (TT+TE+EE+lensing) alone, best fits predict those parameters to be almost identical to $\Lambda$CDM, with slightly smaller $\chi^2_{min}$. The resulting $H_0=72.24\pm 0.64$ km/s/Mpc, which "practically" alleviates the tension with local measurements, due to late time phantom behaviour. Inclusion of BAO data however reduces $H_0$, reflecting furthermore systematic deviations from data that are also present in supernova distances and the growth rate of structure (increasing the apparent tension in the latter case). As the theory, unlike other viable $f(T)$ models, does not reduce to $\Lambda$CDM through extra free parameters, those conclusions are generic; applying to any modified gravity or dynamical dark energy with phantom behaviour. With best fit parameters, the present scenario produces a CMB spectrum almost identical to $\Lambda$CDM, with slight deviation at low-multipole $\ell < 30$, where cosmic variance is large. The matter power spectrum is also quite close to $\Lambda$CDM; with percent level scale free modifications affecting modes significantly smaller than the horizon, arising primarily from modified background evolution. More significant deviations appear on larger scales, and may in principle distinguish modified gravity scenarios of the type studied here from dynamical dark energy.