  We study a symmetric teleparallel gravity with a Lagrangian of logarithmic
form. The full model leads to an accelerated universe and for specific values
of the free parameters the Hubble rate reduces to the well-known
Dvali-Gabadadze-Porrati model, though the evolution of the gravitational
potentials are different. We consider different branches of the logarithmic
model, among which are self-accelerated branch and normal branch. The
phenomenology of both the background and linear perturbations is discussed,
including all the relevant effects on cosmic microwave background radiation
(CMB) angular power spectrum, lensing and matter power spectra. To this
purpose, we modified the Einstein-Boltzmann code mgcamb. Finally, we derive
bounds on the free parameters which are in agreement with early dark energy
constraint from CMB and big bang nucleosynthesis constraint on the helium
abundance.
