The issue here is: what's the nature of time? Is it a reality independent of the universe, or just a feature of it?

1. Substantival theory:

1. a moment is a real entity in its own right.
2. time is the series of all moments ordered by relations of “earlier” and “later”.

NOTE: hence, time does not presuppose events.
NOTE: the above account needn't take time as a totum syntheticum (i.e. a totality composed of its parts, that is, such that the parts are ontologically prior to the whole, as bricks to a house).

1. Start with an actual event e (if constructing actual time) and the tenseless (or tensed) temporal relation R of “being earlier (or in the past) at a temporal distance d.”
2. A moment is the collection of all (possible) events having the relation R to e.
3. Time is the series of all moments, i.e. these collections of events, ordered by relation R.

NOTE: hence, time presupposes events.  So, no events, no time.  In other words, time presupposes change.
NOTE: temporal relations are prior to time (time is constructed out of them).

3. Criticism of the relational theory.
The relational theory has the important advantage of leading to ontological simplification.  However, there are some criticisms which have been raised against the relational theory of time:

1. The awareness of time passing in the absence of any awareness of change in events shows that time doesn't depend on change.

Replies:
• passing moments are not observable, and the alleged awareness of time passing without awareness of change in events questionable.
• At any rate, the argument makes a questionable move from epistemology to metaphysics.
2. Two counterfactual-arguments:
1. “Nothing might have happened now” is true.  Hence, the moment identified by “now” cannot be a collection of events.

Reply: Three possible replies:
• “nothing might have happened now” is false.
• “nothing might have happened now” must be understood as “the present time might not have existed”.
•   “nothing might have happened now” must be understood as referring to the empty collection of events.

    NOTE: this requires that merely possible events be admitted in the construction of moments.
 
2. “Now Joe is asleep, but might have been awake” could be true.  But if Joe's being asleep is a member of the collection constituting “now”, then Joe's being awake could not be a member of the collection constituting “now”, i.e. the identical moment at which he is asleep.

NOTE: if this is right, then there are interesting consequences for possible worlds.  A possible world is a complete way in which things might have been.  Possible worlds are useful in dealing with counterfactuals.  For example,  I'm now typing, but I could have been walking. Then, there's a possible world W at which  now I'm walking.   Individuals are world-bound if they can exist in only one possible world.  If individuals are world bound, then the person walking at W is someone very similar to me but not numericallly identical to me (he isn't me).  If the world I am at is the only possible world, then there's no other way things could have been, and all that happens happens necessarily.
If criticism (2) is right, then relational time entails world bound individuals (individuals exists only in one possible world) or necessitarianism (the actual world is the only possible one)
3. The 'Time without change argument':

Imagine a world in which many things cease and restart to exist at regular intervals gradually turning white before they cease, and gradually regaining their color after they restart existence.  Suppose that we can calculate that at 4 each object in our world ceases for 20 minutes.  Then, suppose that today at 4 everything is white.  The next thing everybody notices is lots of white things gradually regaining their color.  One could reasonably conclude that between 4 and 4:20 no event took place but time went by.  Hence, time doesn't presuppose change, and the relational theory is wrong.
Replies:
• Is the story coherent?
• Assuming that the argument is good, all it shows is that empty time preceded and followed by non-empty time is possible.  But this can be accounted for in two ways:
1. by a relational theory allowing the events out of which moments are constructed to be merely (metaphysically or physically) possible.
2. by holding that time is substantival in some worlds but not in the actual world.

Reply: But if relational theory true, it would give the nature of time, which would be the same in all possible worlds.

1. Moments, which go by in time, are unobservable.  Hence, it's possible for a change to occur in the sense that all events speed up with respect to the rate of passage of moments.  This speeding up, however, would be unobservable and unknowable.  But a change which is in principle unobservable and unknowable is no change at all.   By contrast, if relational theory is true, then no such speeding up is possible.
2. If an event occurs now, there must be an explanation why, even if we might not know it.  But if absolute time exists and it stretches beyond the existence of the universe, then there's no possible explanation why the universe occupies this stretch of time because each stretch of time is indiscernible from any other.  Hence, there's no absolute time (Leibniz).

Reply: Is the global question of why the universe exists when it does a proper one?
3. Two internally identical possible worlds occurring at different dates would be indiscernible.  Hence, if one accepts the principle of the Identity of Indiscernibles (if two things are qualitatively identical, then they are numerically identical), then the two world would not be two.  So, the principle of the Identity of Indiscernibles entails that there is no absolute time (Leibniz).

Reply: deny the principle of the Identity of Indiscernibles, or that at any rate it's applicable to the case.
 

Appendix: A relational modal view of time

1. Construction from an event e plus a metrication given by the distance relation R and a number n:

(Et) [Rn (t, e)] <-> Possible (Ex)[ Event x & Rn (x, e)], that is,
[there is a time t with a temporal distance relation Rn to a given event e if and only if there is a possible event x which has the temporal distance relation Rn to e].
So, a time t located at n units from an event e is a collection (or  alternatively the set) of actual or possible events located n units from  e.

2. by varying “R”, “n”, “e”, “possible”, one gets different topologies.

a. Varying R:

1.   R = “before”, then time one-dimensional.
2.   R globally asymmetric, then no closed time (no loop).
3.   R globally symmetric, then closed time (every event “before” and  “after” any other).

1.   n ranging on integers, rational or real, then time discrete, dense, or continuous.
2.   n ranging over a closed interval, then first and last moment.
3.   n ranging over a semiclosed (open) interval, then no first or last (neither first nor last) moment.

d. Varying range of “possible” (actual, physically possible, metaphysically possible), then possibility of differently structured times.