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2016 Reconstruction, Thermodynamics and Stability of Λ CDM Model in f ( T, T ) Gravity

We reconstruct the ΛCDM model for f ( T, T ) Theory, where T is the torsion scalar and T the trace of the energy-momentum tensor. The result shows that the action of ΛCDM is a combination of a linear term, a constant ( − 2Λ) and a non-linear term given by the product √− TF g h ( T 1 / 3 / 16 πG ) (16 πG T + T + 8Λ) i , with F g being a generic function. We show that to maintain conservation of energy-momentum tensor should impose that F g [ y ] must be linear on the trace T . This reconstruction decays in the f ( T ) Theory for F g ≡ Q , with Q a constant. Our reconstruction describes the cosmological eras to the present time. The model present stability within the geometric and matter perturbations for the choice F g = y , where y = ( T 1 / 3 / 16 πG ) (16 πG T + T + 8Λ), except for geometric part to de Sitter model. We impose the ﬁrst and second laws of thermodynamics to the ΛCDM and ﬁnd the condition where they are satisﬁed, that is, T A , G eff > 0, however where this is not possible for cases where we choose, leading to a breakdown of positive entropy and Misner-Sharp energy. and second laws of thermodynamics. In the GR, it has been shown that the ﬁrst law of thermodynamics can be shown as dE = T dS + WdV [13]. This law can also be represented in the modiﬁed versions of gravity, but with an additive content of entropy production, for a non-equilibrium description [14]. We have done here an analysis which yields the conditions for satisfying the classical thermodynamics laws. We adopt the units as k B = c = ~ = 1 and the Newton constant G − 1 / 2 = M Plank = 1 . 2 × 10 19 GeV