Warp 2 barrier

From Memory Alpha, the free Star Trek reference.

The warp 2 barrier was a limit of warp speed in the preliminary stages of warp technology (21st and 22nd centuries). It was not until the 2140s that a warp engine conceived at the Warp Five Complex by Henry Archer broke this barrier. Commanders A.G. Robinson and Jonathan Archer demonstrated this advanced warp engine in the second NX class prototype, the NX-Beta. (ENT: "First Flight")

Multiple "warp barriers" were conceived over the years: this includes the warp 3, warp 5, warp 10, and the so-called "time barrier". Incidentally, these barriers were brought on by the onset of technological limits of the time and as an effort to spur advanced warp speed theory and research.