No, the expansion of the universe does not imply that time is flowing backward. The concept of the universe expanding refers to the idea that the distances between galaxies and other cosmic structures are increasing over time. This expansion is described by the metric expansion of space, a fundamental feature of the Big Bang cosmological model.
Time, as we perceive it, continues to flow forward in the same direction. The expansion of the universe affects the spatial dimensions rather than the temporal dimension. From our perspective, time continues to move forward, and events unfold in the future relative to the present.
It's important to note that the expansion of the universe is a description of the overall large-scale behavior of the cosmos. On smaller scales, such as within galaxies and solar systems, other forces and dynamics dominate, and the local experience of time is not affected by the expansion of the universe.
In summary, the expansion of the universe does not imply that time flows backward. Time continues to flow forward, and the expansion primarily affects the spatial dimensions of the universe on large scales.