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arXiv 1603.03046gr-qcastro-ph.COhep-th
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多重分形时空中的Lorentz破坏

Lorentz violations in multifractal spacetimes

Gianluca Calcagni

备注：
12 pages, 1 figure. v2: discussion expanded at several points, comparison with the Lorentz-violating Standard-Model extension added, references added
发表信息：
Eur. Phys. J. C 77, 291 (2017)
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摘要：

利用最近对黑洞合并产生的引力波（GW）的观测，我们对多重分形时空的能量给出了一个下限，超过这个下限，多重分形时空将显示出反常的几何形状，特别是违反洛伦兹不变性。在所谓的多重分数阶理论与$q$ -衍生物，我们表明，色散关系的变形比一般的量子引力方法（包括圈量子引力）强得多，与后者相反，目前的观测GWs可以放置非常强大的边界上的特征尺度，时空偏离标准闵可夫斯基。当测度中的指数固定在它们的中心值$1/2$时，多重分形效应应该变得明显的能量是$E_*>10^{14}\,{\rm GeV}$（因此将先前的界限提高了12个数量级）。我们还估计，为第一次，对数振荡的措施（对应于离散时空结构）的影响，并发现他们没有改变太多的界限，在他们的情况下，除非振荡的幅度是微调。这一特征在已知的量子引力场景中不可用，可能有助于该理论避免被伽马射线暴（GRB）观测排除在外，其中$E_*> 10^{17}\,{\rm GeV}$或更大。

英文摘要：

Using the recent observation of gravitational waves (GW) produced by a black-hole merger, we place a lower bound on the energy above which a multifractal spacetime would display an anomalous geometry and, in particular, violations of Lorentz invariance. In the so-called multifractional theory with $q$-derivatives, we show that the deformation of dispersion relations is much stronger than in generic quantum-gravity approaches (including loop quantum gravity) and, contrary to the latter, present observations on GWs can place very strong bounds on the characteristic scales at which spacetime deviates from standard Minkowski. The energy at which multifractal effects should become apparent is $E_*>10^{14}\,{\rm GeV}$ (thus improving previous bounds by 12 orders of magnitude) when the exponents in the measure are fixed to their central value $1/2$. We also estimate, for the first time, the effect of logarithmic oscillations in the measure (corresponding to a discrete spacetime structure) and find that they do not change much the bounds obtained in their absence, unless the amplitude of the oscillations is fine tuned. This feature, unavailable in known quantum-gravity scenarios, may help the theory to avoid being ruled out by gamma-ray burst (GRB) observations, for which $E_*> 10^{17}\,{\rm GeV}$ or greater.

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