Given the early onset of this redness, it unfortunately can be several things including conjunctivitis (inflammation of the clear skin-like covering of the white of the eye), episcleritis/scleritis (inflammation of the actual white part of the eye) or intraocular inflammation.
As you are completely asymptomatic, however, I suspect this is either an episcleritis or an early viral conjunctivitis (pink-eye is the common vernacular). Episcleritis often just presents as redness without any symptoms and patients end up coming in just because so many people ask them what's wrong, not that they have any symptoms.
I would say if you do not go on to develop discharge, pain, light sensitivity, changes in vision or symptoms such as these or redness in the other eye, then it is okay to just observe this for resolution.
If it is a viral conjuncitivits (pink-eye), then you may begin to have symptoms in the other in a few days. A viral conjunctivitis just has to run it's course; because it is not a bacteria, it dose not respond to antibiotic drops. The key with these is just infection control (frequent handwashing, avoiding touching the eyes/face, avoiding contact with sick or immune compromised persons).
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Disclaimer: My opinion is solely informative and does not constitute an informed medical opinion or recommendation. For an informed medical opinion and/or recommendation you must see an eye doctor.