Applying Clausius relation with energy-supply defined by the unified first law of thermodynamics formalism to the apparent horizon of a massive gravity model in cosmology proposed lately, the corrected entropic formul...Applying Clausius relation with energy-supply defined by the unified first law of thermodynamics formalism to the apparent horizon of a massive gravity model in cosmology proposed lately, the corrected entropic formula of the apparent horizon is obtaJned with the help of the modified Friedmann equations. This entropy-area relation, together with the identified Misner-Sharp internal energy, verifies the first law of thermodynamics for the apparent horizon with a volume change term for consistency. On the other hand, by means of the corrected entropy-area formula and the Clausius relation δQ = T dS, where the heat flow δQ is the energy-supply of pure matter projecting on the vector ξ tangent to the apparent horizon and should be looked on as the amount of energy crossing the apparent horizon during the time interval dt and the temperature of the apparent horizon for energy crossing during the same interval is 1/（2πτA）, the modified Friedmann equations governing the dynamical evolution of the universe are reproduced with the known energy density and pressure of massive graviton. The integration constant is found to correspond to a cosmological term which could be absorbed into the energy density of matter. Having established the correspondence of massive cosmology with the unified first law of thermodynamics on the apparent horizon, the validity of the generalized second law of thermodynamics is also discussed by assuming the thermal equilibrium between the apparent horizon and the matter field bounded by the apparent horizon. It is found that, in the limit Hc → 0, which recovers the Minkowski reference metric solution in the fiat case, the generalized second law of thermodynamics holds if α3 ＋ 4α4 〈 0. Without this condition, even for the simplest model of dRGT massive cosmology with α3= α4 = 0, the generalized second law of thermodynamics could be violated.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10747155, 11205131, 11175270, 11005164, and 10935013, ChongqingChongqing Science and Technology Commission under Grant No. 2010BB0408Local Support from Argonne National Laboratory
文摘Applying Clausius relation with energy-supply defined by the unified first law of thermodynamics formalism to the apparent horizon of a massive gravity model in cosmology proposed lately, the corrected entropic formula of the apparent horizon is obtaJned with the help of the modified Friedmann equations. This entropy-area relation, together with the identified Misner-Sharp internal energy, verifies the first law of thermodynamics for the apparent horizon with a volume change term for consistency. On the other hand, by means of the corrected entropy-area formula and the Clausius relation δQ = T dS, where the heat flow δQ is the energy-supply of pure matter projecting on the vector ξ tangent to the apparent horizon and should be looked on as the amount of energy crossing the apparent horizon during the time interval dt and the temperature of the apparent horizon for energy crossing during the same interval is 1/（2πτA）, the modified Friedmann equations governing the dynamical evolution of the universe are reproduced with the known energy density and pressure of massive graviton. The integration constant is found to correspond to a cosmological term which could be absorbed into the energy density of matter. Having established the correspondence of massive cosmology with the unified first law of thermodynamics on the apparent horizon, the validity of the generalized second law of thermodynamics is also discussed by assuming the thermal equilibrium between the apparent horizon and the matter field bounded by the apparent horizon. It is found that, in the limit Hc → 0, which recovers the Minkowski reference metric solution in the fiat case, the generalized second law of thermodynamics holds if α3 ＋ 4α4 〈 0. Without this condition, even for the simplest model of dRGT massive cosmology with α3= α4 = 0, the generalized second law of thermodynamics could be violated.
