I have a GRE score of 6.0 writing, 170 reading, and 168 quantitative, and a 4.0 GPA. I also have 4 semesters of soft matter theory research and 1 summer of particle physics theory research. I'm applying to do theory to many schools, including MIT, SUNY Stony Brook, Stanford, Harvard, UMass, Yale, UConn, and more. I heard that if you submit your applications earlier you have a better chance of getting accepted than if you submit them closer to the deadline. However, I just got back my first PGRE score: 760. I think that my second PGRE score, which I should be getting in about 3 weeks, will probably be higher (probably above 800). So, should I submit my applications earlier, sending my first PGRE score with them, and then send the new PGRE score when it arrives? Or should I wait until the second PGRE score comes out and then submit the applications with just that score? EDIT: And if I do the former, should I include something in my cover letter explaining that I have a probably-better PGRE score on the way?