Is there any reputable published source on expected elemental abundances at the end of the era of stellar fusion? I am here interested in the contents of galaxies; much of intergalactic gas will be lost and remain primordial.
Adams & Laughlin mention estimates of Timms that the final chemical composition will be $X\sim 0.2, Y \sim 0.6, Z \sim 0.2$ but does not analyse the composition in much detail beyond the chemical evolution of white dwarfs (which mostly happens in the later degenerate era). Fukugita and Peebles also make use of a very approximate estimate.
It seems entirely doable to run an IMF model, add some intergalactic gas infall assumpptions, add some recycling assumptions for different mass classes, generate a composition and iterate until a limiting value. But it also seems to be a lot of work that I strongly suspect somebody has already done somewhere far better than I could do.
Another, very crude, approach might be to argue that since we know the cosmic element abundances today after 13.6 billion years of stellar activity we can rescale them to a limiting value: $A(t)=A(\infty)(1-e^{-t/\tau})$ where $\tau$ is the timeconstant of stellar elemental conversion. That would give the desired $A(\infty)=A(t_\mathrm{now})/(1-e^{-t_\mathrm{now}/\tau})$ (at least for metals; hydrogen and helium would be depleted). This assumes that the rate of conversion does not change (highly doubtful, since it will be more red dwarf conversion of hydrogen to just helium in the future than in the past where many more heavy stars formed due to the peak of SFR). If we use the estimate that $Z$ will increase by a factor of 10 from the current $Z\approx 0.02$ we get $\tau=1.3097\cdot 10^{11}$ years which seems reasonable, and of course just $A(\infty)=10A(t_\mathrm{now})$. That would for example make 10% of the mass oxygen and 4.6% carbon. But it would be underestimating the r-elements produced in neutron star collisions (since these were more rare in the past) and cosmic ray spallation elements.
