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RE: Detecting nuggets of dark matter
Are there theories that dark matter particles are actually microscopic black holes? Can such theories be considered seriously?
A black hole seems to be a good candidate for a dark matter particle. It does not emit light and is likely to interact only gravitationally (i. e. unlikely to have a (big) electric charge).
Naively I would have said no, because micro black holes evaporates (and a viable dark matter candidate must be stable). After checking, there is actually one theory that proposes this idea. The research paper is available here. I however haven't read it so that I can't tell.
Primordial black holes are in contrast good candidates to explain dark matter, and this hypothesis could be challenge by the future experiments hunting for gravitational waves.
Aha, primordial black holes then. Aren't they too big for dark matter, which supposedly should be uniformly distributed in the Universe?
Dark matter is not uniformly distributed in t he universe. There are areas where a larger density is needed, and vice versa. The model is pretty constrained, especially since the discovery of gravitational waves, but it is not excluded. And as anything that is not excluded is alive ... :)
Will there be any relationship between matter and energy for this case?
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.261301
I am sorry, but I am not sure to understand the question. Dark matter has to account for a significant fraction of the energy budget of the universe, so that I would tend to answer 'yes' to your question.
By the way, the article you are referring to has nothing to do with the topic addressed is this post, as this consists in a string theory model for cosmology.
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