If the smallest meaningful time interval is greater than zero, will the lines in Figure below ever meet?

Cosmology is the study of the character and evolution of the universe. The two most important features of the universe are the cosmological red shifts of its galaxies being proportional to distance and its cosmic microwave background (CMBR).

As the lines are following an exponential scale, So they will never meet.

(Assuming the question refers to lines that represent the size of the universe and if they will meet to the left of the figure)

The extrapolations of general relativity state that the universe was initially in a state of infinite density and temperature - a singularity. Let's set\(t = 0\)as the time when the universe was singular. If we assume that the smallest meaningful interval is some\(t = 0\), the lines would never meet because the universe would be expanding for every \(t > 0\)and have nonzero "volume". A little bit more formally, the universe expanding means that for every\(t > {t^\prime } \to V(t) > V\left( {{t^\prime }} \right)\).

Since \(t > 0\)we have \(V(t) > V(0) = 0 \Rightarrow V(t) \ne 0\) so the lines will never meet.