A time barrier was a warp barrier and the barrier between alternate universes like Elysia and the prime universe.

The warp barrier known as time barrierEdit

USS Enterprise, The Cage (remastered)

USS Enterprise, a starship that had surpassed the time barrier.

The Time barrier was a theoretical limit in warp drive technology, which restricted the top speed of warp-powered vessels. The barrier was broken in the 23rd century.

In 2254, when the crew of the USS Enterprise discovered what they thought were survivors from the SS Columbia, which had crashed on Talos IV in 2236, José Tyler noted that the survivors would not believe how fast they could get back to Earth, due to the breaking of the time barrier that had occurred since the Columbia had crashed. For some time after the breakthrough, warp speeds were referred to as time warp factors. (TOS: "The Cage")

Multiple production sources, including the books The Making of Star Trek and the Star Trek Encyclopedia as well as an unseen display screen intended for use in "In a Mirror, Darkly, Part II", give the Enterprise launch date as 2245, suggesting the barrier was broken before then. According to the book Star Trek Maps, it was in fact broken in the year 2243, due to improvements in matter/antimatter engine design, that made it possible to use more powerful warp field generators.
The warp speed limit for this barrier is not stated in "The Cage". However, according to ENT: "These Are the Voyages...", starships in 2161 were capable of warp 7 and, according to TOS: "Arena" and "The Changeling" (both set in 2267), while it was risky to sustain a speed of warp 7 or above for the Enterprise, the engine was capable of achieving warp 9.

Time barrier of ElysiaEdit

The small alternate universe known as Elysia was a parallel time continuum that periodically touched the prime universe in the Delta Triangle region. Elysia was described by Devna, as a pocket in the garment of time. The collisions between the two universes produced time warp vortexes in the time barrier between the universes that allowed passage from one side to the other at high warp speed. (TAS: "The Time Trap")

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