When I use the word modern world is it lower case or upper case.

Lower case.

When referring to "modern world," it is generally preferred to capitalize the first letter of each word, making it upper case. This is known as "title case," which is commonly used for titles, headings, and proper nouns in English. It helps make the term more noticeable and distinguish it as a specific concept or entity. However, it's important to note that capitalization rules can vary depending on different style guides or specific contexts. Therefore, in certain cases or contexts, such as in informal writing or specific publications, it may be acceptable to use lower case for "modern world." To ensure consistency and accuracy, it's always recommended to follow the specific guidelines or preferences of the writing style you are using or consult relevant sources such as style manuals or established resources.