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arXiv 1609.08373gr-qc
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$f(T,B)$引力中的热力学和宇宙学重建

Thermodynamics and cosmological reconstruction in $f(T,B)$ gravity

Sebastian Bahamonde, M. Zubair, G. Abbas

摘要:

最近,它制定了一个远程并行理论称为$f(T,B)$重力连接$f(T)$和$f(R)$在适当的限制。在这个理论中,作用量中的函数被假定为依赖于挠率标量$T$以及与挠率发散有关的边界项$B=2\nabla_μT^μ$。在这项工作中,我们研究了平坦的Friedmann-Lemathtre-Robertson-Walker(FLRW)宇宙学在这个理论中的不同特征。首先,我们证明了FLRW方程可以转化为克劳修斯关系式$\hat{T}_hS_{\rm eff}=-dE+WdV$的形式,其中$\hat{T}_h$是视界温度,$S_{\rm eff}$是熵,它包含视界熵和由于非平衡引入的附加熵项的贡献。我们还制定了约束的有效性的广义热力学第二定律(GRESS)。此外,使用宇宙学重建技术,我们表明,$f(T,B)$和$-T+F(B)$重力可以模仿幂律,deSitter和$Λ$ CDM模型。最后,我们建立了扰动演化方程,并分析了一些重要宇宙学解的稳定性。

英文摘要:

Recently, it was formulated a teleparallel theory called $f(T,B)$ gravity which connects both $f(T)$ and $f(R)$ under suitable limits. In this theory, the function in the action is assumed to depend on the torsion scalar $T$ and also on a boundary term related with the divergence of torsion, $B=2\nabla_μT^μ$. In this work, we study different features of a flat Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology in this theory. First, we show that the FLRW equations can be transformed to the form of Clausius relation $\hat{T}_hS_{\rm eff}=-dE+WdV$, where $\hat{T}_h$ is the horizon temperature and $S_{\rm eff}$ is the entropy which contains contributions both from horizon entropy and an additional entropy term introduced due to the non-equilibrium. We also formulate the constraint for the validity of the generalised second law of thermodynamics (GSLT). Additionally, using a cosmological reconstruction technique, we show that both $f(T,B)$ and $-T+F(B)$ gravity can mimic power-law, de-Sitter and $Λ$CDM models. Finally, we formulate the perturbed evolution equations and analyse the stability of some important cosmological solutions.

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