Maybe "Tom the Universe" (2011), an Escape Pod original by Larry Hodges.
Meet Tom, an undergrad in neuroscience, Mary, his girlfriend, and Joey, a friend of his.
Tom wonders about how the "interconnectivity required for human consciousness" can possibly happen, and theorizes that it's due to a singularity (by physics definition) in the brain. Thrilled, he decides to experiment on it, especially, to expand it - as he has no expertise in physics though, he asks a physics grad student for help. The other student doesn't dwell into the consequences of such a thing if it was to be done, thinking it's pure theory talk.
The interconnectivity required for human consciousness could only be satisfied by infinite density at a single point. A singularity.
Unless Mr. Holmes was mistaken, every one of us carries a singularity in our head. The mass doesn’t register in our universe, or else your body–and everything else for a long way around–would fall into it and squoosh, a quick way to end one’s existence. No, the singularity is just a point that floats around, stuck in your brain, presumably created while your brain was being created, with its mass in some alternate universe or state.
Tom then proceeds to blast himself with tachyons thanks to the physics lab's tachyon emitter; but upon doing so, he makes his own expanded singularity disbalance the universe, and colliding with a nearby "brane" - a kind of universe container? - which destroys the concept of existence in the universe, and turns Tom's expanded consciousness into a whole universe, which he also names Tom.
The tachyons were travelling faster than the speed of light.
He assured me that tachyons were harmless, essentially massless–my eyes glazed over when he started talking about “imaginary mass”–and would shoot right through anything at faster than light speeds. I felt in sudden need of a tachyon shower.
Mary and Joey had wandered off, which I thought strange at the time since we were at a key stage of our work, but I didn’t need them for this and so didn’t stop to wonder where they might be. (If I knew then what I knew now. . . .) When no one was looking, I turned the tachyon emitter on full blast, entered the tachyon field chamber through the “Do Not Enter!” sign, and the rest is. . . .
I started to say “history,” but of course it was actually the end of history. The singularity in my brain expanded like any other “Big Bang,” creating a universe and destroying ours.
By this point the level of Physicese goes way too far beyond my reach, to the point that I can only tell you he fiddles with the universe, tries to replay/simulate scenarios, and eventually gets destroyed in turn when he tries to save Mary from a meteor by "expanding" her singularity; but Joey's gets expanded too, colliding with Mary's, and colliding in turn with all the other branes, ending Tom's universe.
Singularities everywhere begin to expand. Not just the billions inside human brains, but also the quadrillions inside intelligent creatures throughout my universe. Quadrillions of new universes emerge and expand, in close proximity to their neighbors, overloading the uncountable branes. The branes, no longer in equilibrium, collide with each other like dominoes throughout the cosmos. One by one they pop like soap bubbles, until there is nothing, there never has been anything, and just as my existence ends, there is no pain.
Found with the Google query
"singularity" "mass" site:escapepod.org.