Many scientists have attempted to come up with an explanation for this disconcerting lack of symmetry. I give a layman's overview of the problem and list the suggested solutions in this article. The latest suggestion that I want to discuss here is that a variant of General Relativity involving torsion could be responsible for the apparent asymmetry.
Introduction to the problem
Antiparticles have the same mass and spin properties as their particle siblings, but opposite charge - a fact which led to their discovery in 1932, when Carl Anderson noticed a track in a cloud chamber that looked exactly like the path of an electron except for one detail: the fact that it curves anticlockwise instead of clockwise in the magnetic field of the chamber indicates that the particle responsible for it was positively rather than negatively charged. The track had been left by a new kind of particle - a positive electron, or "positron" - which had been predicted to exist by Dirac four years prior to Anderson's discovery.
The reason that we had never seen one of these particles before is that positrons are rare: the term matter-antimatter asymmetry refers to the fact that the ratio of electrons to positrons has been observed to be staggeringly large.
The dominance of matter over antimatter was established during the first few seconds after the Big Bang. During this time, the enormous density of the Universe meant that temperatures were very high and particles and antiparticles bubbled in a hugely energetic plasma, undergoing millions of interactions per second.
In an interaction, particles collide and are destroyed, with new particles being born from the energy liberated by the destruction. But even this seemingly chaotic process follow rules: one such being that Baryon Number, B, defined as the number of particles minus number of antiparticles, is always conserved. This means that if before the interaction you had two particles and no antiparticles, then afterwards you must have either two particles and no antiparticles, or three particles and one antiparticle, or any other possibility such that B=2 just as it did before the interaction took place.
The problem currently faced is that the value of B in our universe today is observed to be a very large positive number, and there is no explanation as to why this should be the case. In a universe displaying an astonishing degree of symmetry, it feels surprising and unnatural to have such a blatant asymmetry built into the universe's initial conditions.
Torsion as a possible solution
A recent paper by Nikodem J. Poplawski of Indiana University is the latest to suggest a solution - not only to the conundrum of matter-antimatter asymmetry, but also to the puzzling nature of dark matter and the origin of dark energy.
The approach is to modify Einstein's theory of General Relativity to include a non-zero torsion tensor. The torsion tensor expresses the amount of 'twist' which exists in the fabric of space-time. The action of this term is to interact with the fields in Einstein's equations which represent fermions, causing their masses to change. It acts unequally on particles and antiparticles, creating an asymmetry. The result is that particles in the early universe decay into normal matter and antiparticles into dark matter. Therefore the authors suggest that the overall Baryon number of the Universe is in fact zero - there is exactly the same amount of matter as antimatter - but that the antimatter is present in the form of dark matter, which lurks in great clouds in galaxies, undetectable except by the gravitational effects of its mass.
The authors also claim that torsion leads to the conclusion that the cosmological constant is non-zero. This means that torsion provides an explanation for the presence of dark energy, the mysterious force which is causing the universe to expand at an ever-increasing rate.
The authors make no quantitative predictions of what ratio of matter to antimatter we could expect their theory to yield, so we cannot compare yet the universe that would result from such a theory to the one we observe in order to test the theory.