If you want to avoid adding any preservatives in your wine, you'll need to store your wine in the fridge with the lid on loosely.
If you want to tighten the cap, you'll need to rack your wine until no sediment builds up for one week of cold-crashing. You can expect this to take about 3 to 4 racks, or around 3 weeks — however, these are approximations. The important thing is that there's no sediment buildup for at least one week of cold-crashing. Once you've determined that there's no sediment, you're good to tighten the cap!