How long will the Universe's hydrogen reserves last for? I recently became really interested in learning about physics and cosmology, but I still know very little. Hopefully someone with more knowledge will be able to shed some light on my questions.
Here are my presumptions (please correct me if I'm mistaken):


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*$t_{0}$: Big Bang.

*The Universe expands (and thus cools) sufficiently to allow the formation of atoms.

*The early Universe mostly consists of Hydrogen and is not uniform in its geometry.

*Gravity pushes lumps of matter together until their density (temperature) is so high that nuclear fusion kicks off. The first giant stars are born.

*Some heavy elements are created in these stars and when they explode, sufficient temperatures are reached to form heavier elements still.

*All of the successive stars and planets are the product of these original stars.


My questions:


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*If the amount of Hydrogen is finite in the Universe and each successive generation of stars use up most of their Hydrogen, what is the theoretical maximum number of generations of stars that our Universe can support? A ballpark figure in terms of years is fine too. ;)

*Are there some special physical processes that occur in the Universe on a large enough scale that are able to break up heavy elements (i.e., Helium) into lighter elements (i.e., Hydrogen)? Kind of like a cosmic recycling operation.

*If we discount the possibility of a Big Crunch, is the Universe pretty much headed into a time when there will be no more stars and only a bunch of black holes, planets, and other debris?
 A: Tis, a good question. Two related questions arise from it. The first one is, will the hydrogen all be used up in finite time? The second related one is, will star formation completely stop in finite time? They sound related, but the first result doesn't necessarily imply the same result for the second, or vice versa. I.E. a low but nonzero gas density might possibly not allow further star formation, and maybe we could have no hydrogen, but have other types of gas (or even solid objects) still collect into stellar mass objects.
I don't know for sure the answers. The rate of star formation (and hydrogen consumption) could decline slowly enough as to never formally reach zero. Or not.
We do know that a lot of gas gets blown out of galaxies by massive stars, supernova, and black hole activity, and becomes intergalactic gas -usually staying within the galaxy cluster. On a long time scale this should eventually fall back into the cluster's galaxies. So I would think the star formation rate would have a very long tail.
A: The vast majority of hydrogen in the universe is in hot gas in galaxy clusters, or cold, extremely diffuse atomic hydrogen in the intergalactic medium (Lyman alpha absorbers). Neither population is likely to ever form stars, so I think the safe answer is "forever."
A: This is really a comment but is too long.
A simpler, but related question is "How much of the primordial hydrogen has been used up so far?"   or "Can we measure a difference between the percentage of primordial hydrogen (~75% H-1) or the percentage of primordial Helium (~25% He-4) and the percentages today.  Short answer - no.
Well, how about a gradient of helium-4 from the galactic center to the outer arms.   I think the answer is yes but it's hard for me to tell.    Well, can we see a metallicity gradient (all elements heavier than He)?  Yes, we can.  See http://nedwww.ipac.caltech.edu/level5/Sept04/Henry/Henry2_1.html, fig 1.
Conclusion, you have asked an experimental question in astronomy, and I would like to see astronomical evidence in any answer given.
A: One can estimate the primordial abundance of He using the Planck/WMAP parameters derived from the cosmic microwave background to get the baryon/photon ratio and a standard big-bang nucleosynthesis model. The result can be checked by estimating the He abundance in very low-metallicity galaxies and there is reasonable concordance between the two (see for example Why is hydrogen the most abundant element in the Universe? ).
Next you can estimate how the He mass-fraction $Y$ varies as a function of the increase in metallicity $Z$(elements heavier than He) as the pristine gas is processed through stars. One can also cross-calibrate this with an estimate for the initial He abundance of the Sun and Galactic chemical evolution models (see Serenelli & Basu 2010) to infer that $\Delta Y/\Delta Z \simeq 2$. That is for every (absolute) 1% increase by mass in heavy elements, we deduce an absolute increase of 2% in the He mass fraction.
The current metallicity of the Galactic disk interstellar medium is $Z \sim 0.015$, indicating that the mass fraction of He (in our Galaxy) has increased from about 25% after the big bang, to 28% now. The mass fraction of H has therefore decreased from about 75% after the big bang, to $100-28-1.5 = 70.5$%. In other words a relative fraction of 6% of the initial hydrogen (by mass) has been processed inside stars, been converted into heavier elements and been returned to the ISM. A further $\sim 20-30$% of the hydrogen atoms in our Galaxy are still locked inside (low-mass) stars.
However, we cannot conclude from this that $\sim 30$% of the hydrogen in the universe has been used up or captured in stars. It is estimated that only 10% of hydrogen is actually in stars. The vast majority is expected to exist in the form of ionised protons in the intergalactic or intracluster medium (e.g. see the second slide of this presentation).
In conclusion, about 10% of the H is incorporated into stars and if our Galaxy is a typical residing place for those stars then only a few per cent of the hydrogen has actually been processed into heavier elements.
What happens in the future depends on the (uncertain) future star formation rate. This is already in steep decline in our own Galaxy and in the universe in general. However, if gas continues to cool radiatively and fall into potential wells and is not re-energised by new supernovae explosions, then we might expect it to eventually form stars. The cooling time for hot intracluster gas as sparse as the average H atom density in the universe is about $10^{11}$ years (see here) and this is also about the freefall timescale of a large cluster of galaxies (even larger structures will likely be pulled apart by the accelerating cosmic expansion). After a few of these timescales then it is likely that most hydrogen will have cooled, collapsed and been recycled to heavier elements or incorporated into long-lived low-mass stars.
Most of the stars that are born presently are low-mass, with a median of around $0.3M_\odot$. These have life times of order $10^{12}$ years, so stars are going to be around for a long time after the star formation rate becomes negligible.
