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A general rule for the modern era — observed by far too few, unfortunately — is that science and religion should not pick fights with each other. There's no value to it, and the tiffs tend to spoil both.
Studying cosmology is a perfectly fine thing to do, as a profession or avocation. Buddhism isn't against the acquisition of knowledge per se; knowledge is quite useful in many practical situations. But knowledge of this practical sort will not lead to liberation, and disputes over the 'truth' of practical knowledge can interfere with the quest for liberation to the extent such disputes de-evolve into anger, jealousy, and/or acrimony. If someone wants to study cosmology as a buddhist, the hope is they will bring the buddhist practice to their acquisition of knowledge: seeking understanding with dispassion, clarity, detachment, and compassion.
Buddhist monasticism doesn't seem to have developed as the Christian monastic tradition did, with monks engaged in intellectual, academic, scientific, and philosophical thought. I don't see any reason why they couldn't, but most established traditions take a conservative and narrow view on monk's activities. But for lay practitioners the question is moot; it isn't what they do to make a living that matters, but how they do what they do.
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Is pursuing cosmology discouraged in Buddhism
Pursuing Cosmology has nothing to do with the Buddha's teaching which teaches how to become free from suffering, so yes it is discouraged. The time is way better spent on meditation practice, studying the Dhamma and doing good for oneself and others.
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The Buddha didn't gave cosmology, e.g. Scientists, secularism (todays largest Religion) much value, actually non at all and also explained why:Lokayatika Sutta, as for example.
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Cosmology as a scientific endeavour is perfectly fine, and is acceptable as Right Livelihood for lay persons.
From a religious or philosophical perspective, some other religions or religious thinkers, including during the Buddha's time, are concerned with questions like "did the universe always exist, or was it created?" And "will the universe be destroyed in future?".
This leads to metaphysical and philosophical speculations like "where was I before the universe was created?" and "where will I be when the universe is destroyed?"
It is such speculations that the Buddha considered futile and may lead to vexation.