We present a new viable modified theory of gravity in which the matter sector is characterized by a logarithmic Lagrangian density. The modified Einstein’s field equations are derived, and they are characterized by the emergence of an effective gravitational coupling constant and an effective negative cosmological constant both coupled to the Lagrangian of matter. Applied to the Friedmann-Robertson-Walker cosmological framework, it leads to motivating phenomenology. In particular, the universe is free from the initial singularity, and a unified description of the early inflationary phase, the succeeding non-accelerating, matter-dominated expansion, and then the transition to a late-time accelerating phase is obtained as well. Moreover, the effective dark energy sector can be quintessence, yet the universe starts contracting if the phantom divide-line is crossed. The model is confronted with observations that agree with recent astronomical data. Moreover, the model gives rise to Einstein’s field equations which resemble the equations obtained in unimodular gravity.

我们提出了一种新的可行的修正引力理论，其中物质部门的特征是对数拉格朗日密度。导出了修正的爱因斯坦场方程，它们的特点是出现了一个有效的引力耦合常数和一个有效的负宇宙学常数，它们都与物质的拉格朗日耦合。应用于弗里德曼-罗伯逊-沃克宇宙学框架，它导致了激励现象学。尤其是宇宙脱离了初始奇点，得到了早期暴胀阶段、随后的非加速、物质主导的膨胀，然后过渡到后期加速阶段的统一描述。而且，有效的暗能量部门可以是精髓，然而，如果越过幻影分界线，宇宙就会开始收缩。该模型面临与最近的天文数据一致的观测结果。此外，该模型产生了爱因斯坦场方程，类似于在单模引力中获得的方程。