The phrase "under the sun" is often used to convey the idea of everything that exists in the world. However, there are plenty of synonyms that can be used to substitute this phrase. For instance, phrases such as 'in the world, 'on earth', 'in existence', 'everywhere', 'in as long as anyone can remember', and 'in this world' are perfect substitutes that convey the same meaning. Other possible synonyms for 'under the sun' include, 'in all creation', 'in the cosmos', 'throughout the universe', 'in all of human experience', 'in every corner of the world', and 'in all the world's history'. These synonyms can be used to give variety to your writing and convey the same meaning with a different twist.