Reconstruction of f(T) and f(R) gravity according to (m, n)-type holographic dark energy

Motivated by earlier works (Wu and Zhu. Phys. Lett. B, 660, 293 (2008); Daouda et al. Eur. Phys. J. C, 72, 1893 (2012)), we extend them by considering a newly proposed model of (m, n)-type holographic dark energy in f(R) and f(T) gravity theories, where R and T represent Ricci scalar and torsion scalar respectively. Specifically, we reconstruct the two later gravity models and discuss their viability and cosmography. The obtained gravity models are free from ghosts, consistent with local solar system tests, and describe effective positive gravitational constant.