Let's say that I read an article on a scientific magazine about, I don't know, a new cosmological model or something theorized by a very smart guy.
Can I use it as the core idea of my sci-fi story or I could get in trouble?
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You're fine to base a story off a scientific idea. Some of the best works of fiction have been written as such. In fact unproven scientific theories have often given rise to actual technological discoveries, watch any star trek or great sci-fi film.
When you say "cosmological model" I assume you mean proposed model of the universe, string theory, something like that. You probably wouldn't be able to use an ACTUAL model or formula, but you wouldn't need to. It's a story spun from an idea which may then go on to inspire the next generation of scientists. I would credit the magazine and author article out of courtesy.
No. Copyright does not protect ideas, only a business or individual's specific presentation of those ideas. For instance, a scientist who writes an article about a new theory cannot claim copyright over that theory, and cannot prevent other scientists from discussing that theory in other articles. The scientist can, however, register the copyright over their own article, and can stop other people from reproducing it. Likewise, if a fiction writer writes a story about a trip to the moon they can register their copyright over their story, but they cannot stop other people from writing other stories about trips to the moon. It is the story as a whole that is covered by copyright, not the idea of a trip to the moon. Depending on what your idea is, you may be able to register it as a patent.
Perhaps it depends how you handle it? In general, yes fine, but you don't want to present anything as though it is your data or your intellect that drove the idea.
The authors' contact information is often available on the article. The journal often / always holds the rights after publication. if you are concerned due to the details of what you are considering, email the corresponding author (found on the title page of the article) and contact the journal. They will probably say it's fine and then you have a paper trail.
(I'm using a recent historical disaster in my story and wondering similar things about liability - I thought about using real names of some of the victims and then realized that would be over the line. At the moment I have the incident in my fiction story but have changed one or two key details. Not quite the same as what you are asking, but same neighborhood.)