So apparently a purely mathematical explanation is not desired.
Here is the non-mathematical explanation.
See Collapse of the universe is closer than ever before
Sooner or later a radical shift in the forces of the universe will
cause every little particle in it to become extremely heavy.
Everything -- every grain of sand on Earth, every planet in the solar
system and every galaxy -- will become millions of billions times
heavier than it is now, and this will have disastrous consequences:
The new weight will squeeze all material into a small, super hot and
super heavy ball, and the universe as we know it will cease to exist.
This violent process is called a phase transition and is very similar
to what happens when, for example water turns to steam or a magnet
heats up and loses its magnetization. The phase transition in the
universe will happen if a bubble is created where the Higgs-field
associated with the Higgs-particle reaches a different value than the
rest of the universe. If this new value results in lower energy and if
the bubble is large enough, the bubble will expand at the speed of
light in all directions. All elementary particles inside the bubble
will reach a mass, that is much heavier than if they were outside the
bubble, and thus they will be pulled together and form supermassive
A phase transition means the collapse of the entire universe, back to the starting point of the 'big bang'.
It pretty much seems to me that the OP's scenario would surely probably almost certainly maybe perhaps undoubtedly trigger this bubble everywhere in the universe at once. No propagation. No traveling out at the speed of c. The number of Higgs bosons would double, in the same Higgs field. Apparently, you are doubling the 'mass' in the entire universe all at once. I can not see any result BUT that the existing physical constants would all be changed. But the math is purely hypothetical, as I elaborated in a previous answer, and is not certain.
From the same article:
Although the new calculations predict that a collapse is now more
likely than ever before, it is actually also possible, that it will
not happen at all. It is a prerequisite for the phase change that the
universe consists of the elementary particles that we know today,
including the Higgs particle. If the universe contains undiscovered
particles, the whole basis for the prediction of phase change
"Then the collapse will be canceled," says Jens Frederik Colding Krog.
In these years the hunt for new particles is intense. Only a few years
ago the Higgs-particle was discovered, and a whole field of research
known as high-energy physics is engaged in looking for more new
particles. At CP3 several physicists are convinced that the Higgs
particle is not an elementary particle, but that it is made up of even
smaller particles called techni-quarks. Also the theory of super
symmetry predicts the existence of yet undiscovered particles,
existing somewhere in the universe as partners for all existing
particles. According to this theory there will be a selectron for the
electron, a fotino for the photon, etc.
You can not look at this as simply merging universes, you are merging elementary particles from each universe. You are merging the basic physical constants. You are merging the physics and the rules of physics of two universes. But are you merging the fields? And do the elementary particles behave the same in each universe? Are the universal constants the same in each? Are the laws of physics exactly the same?
The question is purely hypothetical.