Greetings. I am a junior at a Singaporean university in the top 50. My GPA is decent but not too great ~ 3.2/4. I have significant research experience in numerical cosmology, quantum foundations and have good recommendation letters. I have yet to give my physics GRE and General GRE-and I am preparing for them now. I had initially started a double major in physics and pure mathematics but couldn't continue as the workload prevented me from doing research-also, the math is the cause for the poor grades.
I am extremely interested in graduate school in either cosmology or neurophysics. I have shortlisted Stanford, Rice, UT Austin (Weinberg theory group) and CalTech. I had to eliminate the north due to extreme weather conditions.
What are my chances in the listed schools and what can I do to improve them?