Also known as Einstein-Rosen Bridges are theoretically possible going by Einstein’s theory, and equations of general relativity. Basically wormholes take advantage of our 3 dimensional space and are able to “bend” it. Picture a sheet of paper; now put two circular holes on each end of that sheet of paper. Normally the quickest way to join one point to the other would be to draw a straight line between them. Now instead, you could fold the piece of paper so each hole is touching meaning that there is no longer any distance between them. This is an analogy of how a wormhole works except instead of a circular hole on a 2D plane, the entry and exit points of an Einstein-Rosen bridge can be visualised as spheres in a 3D space.
While the theory of general relativity allows the existence of wormholes, we have not yet found physical evidence. The first wormhole solution discovered was the Schwarzschild wormhole presented in the Schwarzschild metric describing an eternal black hole. However this is not stable enough and would collapse before anything could cross from one end to the other. Traversable wormholes could exist of there was a form of exotic matter with a negative energy to stabilise them.
The Casmir effect shows that quantum field theory allows the energy density in some space to be relatively lower than the ordinary vacuum of space. A lot of physicists (like Stephen Hawking) use this to argue that it is possible to stabilise a traversable wormhole. However there are no known natural processes that would cause a traversable wormhole to stabilise.
The quantum foam hypothesis can be used to suggest the spontaneous appearance of tiny black holes at the Planck scale. Stable versions of these tiny wormholes have been suggested as dark matter candidates. It is also possible that one of these wormholes opened into a previously empty space from another universe, held open by a cosmic string (1D string) with a negative mass then it could be inflated to a macroscopic size by cosmic inflation. Is it possible this happened at the start of the Big Bang?