According to our current understanding of the universe, its observable diameter is estimated to be about 93 billion light-years. However, it's important to note that the expansion of the universe complicates this calculation. The distance between two points can increase over time due to the expansion, even at speeds less than the speed of light.
Assuming you could somehow travel at the speed of light, time dilation effects would come into play. As you approach the speed of light, time would appear to slow down for you relative to an observer at rest. From your perspective, the journey may appear to take no time at all, while an observer outside your reference frame would perceive the journey to take a considerable amount of time.
However, from the perspective of an outside observer, let's calculate an approximation of the time it would take to travel the diameter of the observable universe. Since the universe is expanding, we can't simply divide the diameter by the speed of light to get the travel time. Nevertheless, assuming a constant expansion rate, we can use the current value of the Hubble constant, which represents the rate of expansion of the universe.
The Hubble constant is currently estimated to be around 73 kilometers per second per megaparsec (km/s/Mpc). A megaparsec is approximately 3.09 million light-years. So, if we use this value, we can estimate the travel time as follows:
Travel time ≈ (Observable universe diameter) / (Speed of light × Hubble constant)
Using the observable diameter of 93 billion light-years (which includes the effects of expansion) and the speed of light (approximately 299,792,458 meters per second), we can estimate the travel time:
Travel time ≈ (93 billion light-years) / (299,792,458 m/s × 73 km/s/Mpc × 3.09 × 10^19 km/Gly) Travel time ≈ (93 × 10^9 light-years) / (2.25 × 10^25 km)
Calculating this value gives an estimation of the travel time, but please note that this estimation assumes a constant expansion rate and does not consider other complexities such as the effects of general relativity.