If I consider a hypothetical scenario where the expansion rate of the universe (described by the Hubble parameter is such that the recession velocity reaches the speed of light (c) at a certain distance, we can explore the implications.

Hubble's Law and Expansion Rate:

Hubble's Law states that the recession velocity (v) of a distant object is proportional to its distance (d) from the observer:

Hod

where:

• v = recession velocity,

• Ho = Hubble constant (expansion rate),

d = proper distance.

If we set v = c (the speed of light), then the distance at which this occurs is called the Hubble distance

d = C Ho

If the Expansion Rate Were Such That Ho = c/h

If we assume that the expansion rate is so extreme that objects at a distance dr recede at the speed of light, then:

Ho = d

But in standard cosmology, the Hubble constant is much smaller. The currently measured value is approximately:

Ho≈ 70 km/s/Mpc

Converting this to Sl units:

Ho≈ 2.27 × 10-18 s-1

It gives a Hubble distance:

dH C Ho ≈ 1.32 × 1026 m≈ 14 billion light-yea

Hypothetical Scenario: Ho = c (Much Smaller Distance)

If we imagine an extremely high expansion rate where Ho is much larger-say, such that objects just 1 meter away recede at the speed of light-then:

Ho = C 1m ≈ 3 × 108 s-1

It would imply an expansion rate so rapid in that the universe would double in size on timescales of nanoseconds, which is far beyond anything observed or predicted in standard cosmology (even in inflation).

According to Physical Implications:

• Such an extreme expansion rate would imply an exponentially inflating universe, similar to (but much faster than) cosmic inflation models.

• It would be impossible for structures like galaxies or even atoms to form, as spacetime itself would be expanding faster than any binding forces could hold things together.

• This scenario is not supported by observations, as the real universe has a much slower expansion rate.

According to me in Conclusion:

If the expansion rate were in such that the recession velocity reached the speed of light at very small distances , the universe would be expanding so rapidly that known physics would break down. In reality, the Hubble constant is much smaller, and the expansion only reaches light speed at cosmological distances (~14 billion light-years).

Based on my research and analysis, with support from various online sources, I have arrived at the following conclusion.

The universe expands with c at the edge. See Article Expansion, Topology and Entropy