Accelerating $f(T)$ gravity models constrained by recent cosmological data

Generalized teleparallel gravity, also referred to as $f(T)$ gravity, has been recently proposed as an extended theory of gravitation able to give rise to an accelerated expansion in a matter-only universe. The cosmic speedup is driven by an effective torsion fluid whose equation of state depends on the $f(T)$ function entering the modified gravity Lagrangian. We focus on two particular choices for $f(T)$ which share the nice property of emulating a phantom divide crossing as suggested by some recent data. We check their viability, contrasting the predicted background dynamics with the Hubble diagram as traced by both type Ia supernovae and gamma ray bursts, the measurement of the rate expansion $H(z)$, the baryon acoustic oscillations at different redshifts, and the cosmic microwave background radiation distance priors. Both $f(T)$ models turn out to be in very good agreement with this large data set, so we also investigate whether it is possible to discriminate among them, relying on the different growth factors.

Figure 1

Present-day value of the torsion EOS for the tanh model, setting ${\Omega }_M=0.20$ (dot-dashed blue line), 0.25 (solid black line), 0.30 (dashed red line), and the fiducial ${\Omega }_r$ used in the text.

Figure 2

Contour plots in the $(n,p)$ plane, imposing $w_T(z=0)=-1.0$ for the exp model with ${\Omega }_M=0.20$ (dot-dashed blue line), 0.25 (solid black line), 0.30 (dashed red line), and the fiducial ${\Omega }_r$ used in the text. Note that the lower set of contours is almost perfectly superimposed.

Figure 3

Best fit curves superimposed to the $\mathrm{SNeIa}+\mathrm{GRB}$ Hubble diagram (left panel) and $H(z)$ data (right panel) for the tanh (red solid line) and exp (blue dashed line) models. Note that the $\mu (z)$ curves are almost perfectly superimposed, so no difference is seen in the plot.

Figure 4

Constrained effective torsion fluid EOS $w_T(z)$ for the tanh (left panel) and exp (right panel) $f(T)$ models.

Figure 5

Growth factor $g(z)$ for the tanh (red solid line) and exp (blue dashed line) $f(T)$ models superimposed to the 28, 29 data.