There are several synonyms for the phrase "bow down before", which means to show deference or respect to someone or something. One alternative is "kneel before", which has religious connotations and is often used as a sign of worship or obeisance. Another option is "prostrate oneself before", which implies an even greater level of submission or reverence. "Submit to" or "yield to" are more general alternatives that convey a sense of giving in to someone or something else. Alternatively, one could use "acknowledge" or "recognize" as milder alternatives that still convey respect or deference.