论文标题
多裂间距的暗能量
Dark energy in multi-fractional spacetimes
论文作者
论文摘要
我们研究了从几何形状变化，尤其是在具有$ q $衍生品和加权衍生物的所谓多段理论中，从几何变化中获得宇宙学延迟加速的可能性。在具有$ q $衍生的理论中，光度距离与一般相对论相同，因此几何形状不能像暗能量一样。在具有加权衍生物的理论中，单独的几何形状能够在不进行微调的情况下维持延迟加速阶段，同时与结构形成和大键核合成界限兼容。这建议以自然的方式将理论从小规模到大规模的重力修改扩展。令人惊讶的是，时空的Hausdorff尺寸被限制为接近拓扑维度4。在认为这一发现可能不是数值的巧合之后，我们得出结论，当今的加速度可以被视为新恢复法对时空几何形状的效果。
We study the possibility to obtain cosmological late-time acceleration from a geometry changing with the scale, in particular, in the so-called multifractional theories with $q$-derivatives and with weighted derivatives. In the theory with $q$-derivatives, the luminosity distance is the same as in general relativity and, therefore, geometry cannot act as dark energy. In the theory with weighted derivatives, geometry alone is able to sustain a late-time acceleration phase without fine tuning, while being compatible with structure-formation and big-bang nucleosynthesis bounds. This suggests to extend the theory, in a natural way, from just small-scale to also large-scale modifications of gravity. Surprisingly, the Hausdorff dimension of spacetime is constrained to be close to the topological dimension 4. After arguing that this finding might not be a numerical coincidence, we conclude that present-day acceleration could be regarded as the effect of a new restoration law for spacetime geometry.
