I am an international student currently getting my bachelors at a US university. I've recently been offered a scholarship to go onto graduate school by the government of my home country (all expenses paid, thank god). Two questions: 1) is there an option to not apply for funding for my PhD? 2) I believe that my application is pretty competitive on its own 2 feet and surely being granted an external scholarship will make it look even better -- but does not requiring funding significantly boost my chances of getting in?
For context: I'm shooting for HEP theory which is notorious for its cutthroat competition. 3.8 GPA, double major in Math (applied math to be specific), 2 years of research (potential publication), straight As in all my physics/math classes... Is this competitive for HEP theory in schools such as Stanford/CalTech/MIT/etc?