I am currently an undergraduate student who has a strong interest in becoming a theoretical physicist. I have applied to 4 physics grad schools this year but it seems that my chances for going to grad school this fall 2021 is dismal; I got rejected from my safety school and a top physics grad school and the remaining ones are also quite tough to get into. I do not think I will be able to make it to the other grad schools. As of now, I have done well in undergrad but my major flaw is that I had zero undergrad physics research experience (I have done two self studies, one a graduate Quantum Mechanics course and another a Mathematical Analysis course, but that's about it). I was about to get a research experience (voluneer) during the summer 2020 but due to the COVID 19 pandemic that got cancelled. Basically, I didn't want to multitask during my undergrad years with courses + research because I didn't want to mess anything up.
Here is what I want to do in graduate school: I want to go into Mathematical Physics, with emphasis on String Theory Methods. My long term goal is to study the very early universe where quantum gravity is important and where all 4 fundamental forces are thought to be unified. For grad school, however, I want to focus on something more concrete, something people see (or can imagine) in their every day lives and so my focus for grad school is string theory methods for condensed matter physics.
What I Did during Undergrad: I am a Physics and Mathematics major (Bachelors of Science with Highest Honors) and I plan to graduate this May 2021 (since I will be finished with my requirements I will have to graduate this May as per my university policy). I have taken the Physics GRE during my junior year.
(1) Should I work for a professor in experiment(from my school) (particle physics or condensed matter) from May 2021 - August 2022? I am willing to volunteer with no pay.
(2) Should I work for a professor in theory (from my school) from May 2021 - August 2022?
(3) Should I ask a mathematics professor (from my school) for informal mentorship from May 2021 - August 2022?
(4) Can I apply for an REU or is that too late?