Einstein’s other gravity and the acceleration of the Universe

Spacetime curvature plays the primary role in general relativity but Einstein later considered a theory where torsion was the central quantity. Just as the Einstein-Hilbert action in the Ricci curvature scalar $R$ can be generalized to $f(R)$ gravity, we consider extensions of teleparallel, or torsion scalar $T$, gravity to $f(T)$ theories. The field equations are naturally second order, avoiding pathologies, and can give rise to cosmic acceleration with unique features.

Figure 1

Effective dark energy equation of state is plotted vs scale factor for the exponential $f(T)$ model of Eq. (15). The model acts like a cosmological constant at high redshift and in the future, crossing $w=-1$ in between but in the opposite manner from $f(R)$ gravity.