It has been recently proposed DeVito [(2019) On the meaning of Fermi's paradox. Futures, 389–414] that a minimal number of contacts with alien radio-communicative civilizations could be justified by their logarithmically slow rate of growth in the Galaxy. Here we further develop this approach to the Fermi paradox, with the purpose of expanding the ensemble of the possible styles of growth that are consistent with the hypothesis of a minimal number of contacts. Generalizing the approach in DeVito (2019), we show that a logarithmic style of growth is still found. We also find that a style of growth following a power law would be admissible, however characterized by an exponent less than one, hence describing a sublinear increase in the number of communicative civilizations, still qualitatively in agreement with DeVito (2019). No solutions are found indicating a superlinear increase in the number of communicative civilizations, following for example an exponentially diverging law, which would cause, in the long run, an unsustainable proliferation. Although largely speculative, our findings corroborate the idea that a sublinear rate of increase in the number of communicative civilizations in the Galaxy could constitute a further resolution of Fermi paradox, implying a constant and minimal – but not zero – number of contacts.

中文翻译：

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银河系中交流文明数量的演变：对费米悖论的影响

最近有人提出了德维托[（2019）关于费米悖论的意义。期货, 389–414]最小的与外星无线电通信文明的接触次数可以通过它们在银河系中对数缓慢的增长速度来证明是合理的。在这里，我们进一步发展了这种解决费米悖论的方法，目的是扩大与最小接触数量假设一致的可能增长方式的集合。概括 DeVito (2019) 中的方法，我们表明仍然发现了对数增长方式。我们还发现，遵循幂律的增长方式是可以接受的，但其特征是指数小于 1，因此描述了交流文明数量的亚线性增长，这在质量上仍与 DeVito (2019) 一致。没有找到表明交流文明数量超线性增长的解决方案，例如，遵循指数发散的规律，从长远来看，这将导致不可持续的扩散。尽管在很大程度上是推测性的，但我们的发现证实了这样一种观点，即银河系中交流文明数量的亚线性增长率可能构成费米悖论的进一步解决方案，这意味着接触的数量恒定且最小——但不是零。