X-ray background and peculiar velocities provide insights into the Big Bang model, primarily through the understanding of cosmic expansion and structure formation. The microwave background radiation, originating from about 300,000 years after the Big Bang, cooled to its current temperature of slightly under 3 K as the universe expanded. Galaxies exhibit peculiar velocities that are proportional to their distance, supporting the theory of an expanding universe that began nearly 14 billion years ago. While the diffuse X-ray background can be resolved into individual sources, its exact role in distinguishing cosmological models remains unclear. In contrast, statistical analysis of peculiar velocities can effectively test different cosmological models, particularly those involving dark matter and structure formation.