"Not tied down" is a phrase that denotes a feeling of freedom and flexibility. There are several synonyms for this phrase, which can help to convey a similar sentiment. Some of the most commonly used synonyms for "not tied down" include unattached, untethered, uncommitted, unencumbered, and unbound. Each of these words has its own nuance, depending on the context in which it is used. For example, "unattached" could refer to a person who is not currently in a romantic relationship, while "unencumbered" might be used to describe a person who is free from burdens or obligations. Using synonyms can be a great way to add depth and variety to your writing, and to find just the right word to convey your intended meaning.