Would the universe even start? Would it collapse or act differently? What if, instead, the mass changed right now?
Edit: Since this is too broad lets narrow it to two scenarios:
What happens to stars? (answered by Student4life)
How would the general evolution of the universe be different? (also kinda answered by Student4life)
I assume your question was asked with the implicit "and everything else is kept the same" (still GR + standard model, just with one parameter tweaked).
This would have a large effect, because now the neutron would be much more stable! The neutron is already quite stable (~ 10 minute half life), due to the tight energy constraints in the reaction decaying to a proton, electron, and electron antineutrino.
mass of neutron (939.565378 MeV/c^2) - mass of proton (938.272046 MeV/c^2) = 1.293332 MeV/c^2
This is roughly the mass of an electron (in our actual universe), 511 keV/c^2. After doubling the electron mass, instead of ~ 782 keV of available energy to share kinematically amongst the products, it drops to about third of this. (Related question: Why is the free neutron lifetime so long?)
This would greatly affect the primordial nucleosynthesis after the big bang. The initial neutron-to-proton ratio would be changed drastically. The main reactions leading to their 1-to-7 initial equilibrium involve a process similar to neutron decay or its reverse. Likely neutrons and protons would now occur much closer to equal initial densities with the heavier electron mass. This means after freeze out there would be much more helium than hydrogen. Much of the fuel of stars would already be consumed! (NOTE: I am unsure of the actual effect on primordial nucleosynthesis and if someone could comment further on this, instead of my handwavy guess, it would be appreciated.)
Furthermore, the change in electron mass will also affect the kinematics of the main star fusion processes.
The first step of the main fusion process currently in our sun, is the fusing of protons to yield helium II which then decays to deuterium and an positron. These steps are the rate limiting steps for our sun, and essentially control its lifetime. The decay to deuterium is so kinematically constrained that the excess energy is less than the mass of an electron:
$$ {}^1_1 H + {}^1_1 H \rightarrow {}^2_1 D + e^+ + \nu_e + 0.42 \ \mathrm{MeV} $$
The dominant decay route of helium II is to just decay by proton emission back to two protons. Therefore the main fusion process of our sun will fail to 'ignite', if the mass of the electron was double its current value.
Several steps in the CNO hydrogen burning cycle are also quite energy constrained. The most constrained of which is the following involving Nitrogen-13
$${}^{13}_7 N \rightarrow {}^{13}_6 C + e^+ + \nu_e + 1.20 \ \mathrm{MeV}$$
So doubling the electron mass will roughly halve the available energy for that step.
The cosmos as we know it would be wildly different if the electron mass was doubled, due mainly I believe to the kinematic restrictions in reactions involving nucleons.
Some other changes:
Chemical bond energies are roughly proportional to the mass of the electron. The characteristic radius goes as the inverse of the electron mass. Bond angles and predominant oxidation states of the elements will stay the same. So comparatively, chemistry will not change as much. The phase state diagrams will likely look similar, just scaled in energy.
Javier, brings up some interesting points. However, protons and neutrons get most their mass from relativistic quarks. If the quarks could be slowed down they would weigh a few electron masses. So what ever is responsible for giving the electrons mass its value seems to be giving the quarks their rest mass. I just checked the up and down,they are around 4 times as massive as the electron. Wow! That little of a difference.
So if you were to change the mass of the electron it looks like you would be changing a lot of other stuff, with it. The mass of protons and neutrons might go up or decrease. Consider if they go up along with the electron. Then there might be a sort of self correcting mechanism. Maybe, its no accident that the proton is 2000x heavier than the electron. Sort of a pseudo constant of nature.
A very rough estimate, with rough reasoning, is that all atomic orbital would be shrunk by a factor 1 of the square root of two. if that happened rite now, we would not survive. As for weather the big bang would collapse i don't know.
The view is that the big happened and that then formed electrons. So electrons are more of effect than a cause. Of course, a perfect theory would connect electrons to the very beginning.
