Cosmology at the End of Time
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsDear editor and author,
The manuscript on cosmology at the end of time is an interesting exploration of alternative cosmological frameworks in which differences from ΛCDM arise only in the future. While this does not affect observations along our past lightcone, it does have interesting philosophical implications, especially when considering the likelihood of observers finding themselves at various epochs in cosmic history. This is an interesting idea that deserves further consideration, so I am recommending only a few minor revisions, described below and in the attachment.
Figure 1 could helpfully have another curve drawn at some intermediate value of ΩM, e.g. at 0.31, to better match the observational constraints. In the text, the author should then use this information to predict the quantity H0tU, where H0 is the Hubble constant and tU is the age of the Universe. This will help readers to assess the model in light of observational constraints on the age of the Universe and the present expansion rate. I feel this would be important information to include in the manuscript, given that the proposed model works reasonably well with a nearly standard ΩM.
The author mentions the negative correlation coefficient of -0.8 between w0 and wa. The source for this should be mentioned, or the author should clarify if this is just a rough estimate to get the contour to look about right.
When discussing the DESI evidence for evolving dark energy density, the author should mention that the underlying BAO observables deviate from expectations in the Planck ΛCDM cosmology at close to 3σ significance:
https://arxiv.org/abs/2506.20707
The author is however not necessarily correct that these deviations are due to an evolving dark energy density. These studies must be mentioned instead, showing that the deviations were predicted in advance in the scenario where the locally observed KBC void solves the Hubble tension:
https://academic.oup.com/mnras/article/499/2/2845/5939857
https://academic.oup.com/mnras/article/540/1/545/8129689
The reason is that the extra outward peculiar velocity and gravitational redshift due to our location on a potential hill would inflate the redshifts of distant galaxies, distorting the relation between the observed redshift and the BAO angular scale and redshift depth. In the above model, there is a Planck ΛCDM cosmology at the background level, with a pure cosmological constant. Therefore, as shown in the latter study mentioned above, it is quite possible that the BAO anomaly is not due to evolving dark energy. This possibility must be mentioned to give a more complete discussion.
In summary, the manuscript is novel and interesting, so it should be published after the minor revisions discussed above.
Yours sincerely,
Referee
Comments for author File: 
Comments.pdf
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for Authors19 Sep 2025 - universe-3888260 report on
Cosmology at the End of Time by Meir Shimon
The paper starts with a discussion of a few modern day paradoxes and mind bending puzzles in cosmology, such as the enormous discrepancy of the vacuum energy density based on QFT and the apparently small observed cosmological constant Lambda and the ‘why now?’ problem related to the observation that according to the popular LCDM we are at the beginning of the Lambda epoch where matter and cosmological constant are of the same order. Then after a brief background on the FRW (FLRW) spacetime, which is the cornerstone of the LCDM, the papers continues with a few more paradoxes and mind bending puzzles like Cosmological Arrow of Time, Boltzmann Brains, Freak Observers, BH Evolution and Information Paradox, Time Travel, and Simulation Hypothesis. Then all these problems are apparently addressed by the hypothesis that the universe may be subject to a finite conformal life time spam as well as a finite cosmic life time as well. Then life as we know it is a random sampling observer that should be located towards the end of this finite time. To support this idea a model with a nontrivial lapse function that can be transformed into a conformal and traditional FLRW metric form is introduced in eq (5). Historically there are many other approaches to the cosmological constant and its value but it seems that a popular paper on the subject is missing from the references [1].
The details of the argument on the sampling probability are discussed in section 5 pointing to the need of finite interval to make sense of non-zero likelihood estimates. It seems that choosing a reasonable probability measure is a hard problem but some reasonable progress has been made, in my opinion among the good papers is [2].
The metric in (5) however has a time coordinate that is infinite from -infinity to +infinity but helps one see that such metric suggests H0η0 = π. The paper also points out that other metric choices will not result in the observed 69% & 31% matter content because they will produce a different value for H0η0 while the observed values can be justified by matching π to the LCDM observed value as discussed after (9). The author admits that the choice of the lapse function is very much justified on its ability to make the argument work. In particular in mapping the time tau to z=0 to infinity and obtaining H0η0 being near π within LCDM. This is essentially their argument about the value of the cosmological constant energy density and against any other models. Finally the paper also adds w0waCDM model indicating the deviation away from w0=-1 case. All these arguments could be argued based on the success of LCDM and its value for H0η0 excluding models that do not come anywhere close to it. Thus, the form (5) is important only if one would utilize the relevant probability distribution to compute something interesting. Say the averaged size or age of the Universe?
I don't consider most of the paradoxes and mind bending puzzles to be actually true, for example the dimensionally estimated value of Lambda based on H0, c and G is in good agreement with observations; thus, QFT has a problem with vacuum expectation value not cosmology. Next, the ‘why now?’, well for an observation to detect and effect the signal has to exceed the background or the "previous" signal without the inclusion of a new phenomenon, so naturally we should be after the transition from matter into Lambda driven expansion where Omega_m=1-Omega_L given that Omega_L has been related to H0, c and G. Finally, there are models that resolve the eternal inflation, for example the scale invariant vacuum paradigm [3] has a graceful exit from inflation, so eternal inflation is not a true problem either.
My conclusion is that this is an interesting paper but may need some clarifications that will make its revision publishable. Below are some of my suggestions to improve the paper.
I) Along with H0η0 = π in the LCDM there is also H0(ηf-η0)=1. Thus, we are at 3/4 of the life spam based on conformal time and LCDM but the choice (5) for tau covers only up tp now, so it seams to be incomplete.
II) Thus, more needs to be done to justify the choice (5) and to extend it beyond the z in [0, Infinity]. That is, what is the meaning of tau and why this form and not anything else that would have the same results as H0η0 = π.?
III) Clearly past and future horizons can provide limits on the cosmological time for an observer. After all as observers we are confined between our past and future horizons. Apparently, extending z from 0 to -1 and further -> -2.3 may result in unbound η which makes the finite conformal spam invalid, so what is the role and relevance of the future horizon and it size?
IV) in section (6) it will be interesting to see what matter plus w_DE=-2/3 will predict for Omega_m.
V) Adding a graph of Omega_m and w_DE as alternative to the w_DE=w0+wa*(1-a) parametrization.
VI) How would the proposed measure (10) could quantitatively improve on the results in [2]?
Minor changes/suggestions and typos to be fixed:
1) Upon giving the LCDM parameter values after (9) the author should also provide the value H0η0=3.2 for the LCDM.
2) in section (6) it will be useful to have the values of w0 and wa with their uncertainty intervals from the indicated w0waCDM studies, By the way, the green ellipse in Fig. 1 corresponding to DESI+CMB+DESY5 (green) shows as the same color as Omega_m=0.35 (pink on my pdf).
[1] https://doi.org/10.48550/arXiv.astro-ph/0004075
[2] https://doi.org/10.48550/arXiv.hep-th/0702115
[3] https://doi.org/10.48550/arXiv.2104.09314
If the authors are to modify the paper, it will be best to use \color{blue} or any other suitable color to indicate the more substantial changes in the next version no need to show what was the old text, only where are the new substantial changes beyond a few words or major formula modifications.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
Comments and Suggestions for Authors10 Oct 2025 - universe-3888260 second report on
Cosmology at the End of Time by Meir Shimon
The manuscript has been changed but needs some more improvements.
The paper states "Crucially, the model predicts no future in cosmic or conformal time – the Universe effectively ends at the present in these coordinates – while the time coordinate τ is defined along an infinite timeline." But such claims are clearly unreasonable unless one can show that there is a big-crunch happening at the end of time! Do we see it happening or coming from where are we now?
I) The meaning of the new time coordinate is problematic! It seems to put the car before the horse because there is no any predictive power to suggest something new that could be tested. Such metric is only valid if the end of time is here! But it is not, we are 3/4 on our way and there is 1/4 more to go according to LCDM! (see my previous remark I and II)
II) My suggestion for comparison of the probability distributions and expectation values of non-trivial observables like in hep-th/0702115 has been discussed in the cover letter but did not resulted in any text added in the paper to show such comparison.
III) Even my simple suggestion to explore w=-2/3 dark component with this approach to show whether it will or not agree with geometric selection rule was ignored. Perhaps this can be rectified by showing the LCDM accepted range of values of Omega_m and what this indicates about the range of w in Fig 1. Note that DESI+CMB+Union3 and DESI+CMB+DESY5 data supports such w=-2/3!
Author Response
Please see the attachment
Author Response File: Author Response.pdf
