Gravitational pressure,apparent horizon and thermodynamics of FLRW universe in the teleparallel gravity

In the context of the teleparallel equivalent of general relativity the concept of gravitational pressure and gravitational energy-momentum arisen in a natural way. In the case of a Friedmann–Lemaitre–Robertson–Walker space FLRW we obtain the total energy contained inside the apparent horizon and the radial pressure over the apparent horizon area. We use these definitions to written a thermodynamics relation (T_{A}dS_{A} = dE_{A}+P_{A}dV_{A}) at the apparent horizon, where (E_{A}) is the total energy inside the apparent horizon, (V_{A}) is the areal volume of the apparent horizon, (P_{A}) is the radial pressure over the apparent horizon area, (S_{A}) is the entropy which can be assumed as one quarter of the apparent horizon area only for a non stationary apparent horizon. We identify (T_{A}) as the temperature at the surface of the apparent horizon. We shown that for all expanding accelerated FLRW model of universe the radial pressure is positive.