Modified Gravity Approaches to the Cosmological Constant Problem

Round 1

Reviewer 1 Report

This paper presents an interesting review of modified gravity approaches to the cosmological constant problem.   I have some comments about physics and presentation that the authors should address before publication.   The authors argue that a key reason for considering modified gravity models involves theoretical issues with separation of scales. The discussion presented in the present paper is too simplified on this point, e.g., starting from the first paragraph line 73+, that it may be misleading for understanding various of the rest of the presentation.   Recent LHC data has shown that the particle physics Standard Model, if extrapolated up to the Planck scale, sits very close to the border of stable and metastable, see e.g. G. Degrassi et al. JHEP 08 (2012) 098, F. Jegerlehner Acta Physica Polon B 45 (2014) 1167 and Foundations of Physics 49 (2019) 9,915 which includes related discussion of the cosmological constant, AV Bednyakov et al, Phys Rev Lett 115 (2015) 210802. Small changes in the values of Standard Model parameters can have large effects on the stability of the Standard Model vacuum with the Higgs self coupling perhaps crossing zero in the ultraviolet and also with the sign of radiative corrections to the Higgs mass (the so called Higgs mass "hierarchy problem"). That is, within the Standard Model the physics of the IR and UV are strongly correlated so that if the Standard Model is taken as a low energy effective theory then it should be supplemented with some IR-UV correspondence connected to the stability of the vacuum.   One interpretation is the Standard Model as an emergent theory where new symmetry appears in the infrared that dissolves in the ultraviolet. In this scenario, the cosmological constant scale 0.002 eV comes out with same order of size as what one expects for (Majorana) light neutrino masses, see e.g., Bass+Krzysiak Phys Lett B 803 (2020) 135351, Bass, PTRSA 380 (2021) 2216, 202110059 and early work by Bjorken, Phys Rev D64 (2001) 085008 and hep-th/0111196. This is consistent with phenomenology based on fits to neutrino oscillations with a lightest mass neutrino coming out with mass ~0.001 eV (see e.g., H. Fritzsch, Universe 6 (2020) 2, 29).   Some mention of this phenomenology and related theory should be included when the authors discuss possible IR-UV connections and the role of spacetime translation invariance in connection with the cosmological constant problem.   It is important to note that the measured cosmological constant is independent of any particle physics renormalization scales, e.g., how someone tried to calculate QCD, Higgs... contributions to the vacuum energy. The \mu in line 165, the "weight of the vacuum" discussion, is not a physical mass scale. There is some confusion on this in the literature. E.g., in the authors reference 24, there is a comment in Section IX of that paper about maybe relating the renormalization scale \mu to the measured Hubble constant and energies of photons coming from supernovae which is wrong.   Possible time dependence issues: It is an open question whether the DE might be time dependent or not, with connection to the quintessence ideas briefly mentioned in the paper. The authors should at least quote the key papers which initiated these ideas, e.g., Wetterich Nucl. Phys. B 302 (1988) 668 and Peebles+Ratra, Astro J Phys 325 (1988) L17 with short description of these ideas.    An important related question is the stability of de Sitter space which is not mentioned in the paper. See e.g., Dvali+Gomez, Fortsch Phys. 67 (2019) 1-2, Dvali in Symmetry 13 (2020) 3, and Polyakov, hep-th/1209.4135. This also has interesting consequences for the matter/radiation components of the Universe, see e.g. Fritzsch+Sola, Eur. Phys. J C (2017) 3, 193.   The Hubble tension is not mentioned in the paper. There are interesting related ideas involving an extra possible early DE component which should be mentioned. Also ideas exploring possible connections between primordial inflation and present DE might be briefly mentioned.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

In this paper the authors give a comprehensive review of some of the main approaches to solve the cosmological constant problem in the context of modified theories of gravity.

The paper is well organized and clearly written. It starts by presenting the CC problem and reviewing Weinberg's no go theorem. This allows the authors to give a systematic exposition of several classes of modified theories of gravity.

Although not including all the modified theories of gravity, the manuscript discusses the most studied and understood theories.

 

In summary the paper is clearly written and therefore I recommend the manuscript for publication in Universe.

One minor point, I recommend that the hand written text in figure 2 on page 30, should be replaced with a font.

 

Author Response

We would like to thank the reviewer for their positive and encouraging response. We have updated figure 2 as suggested by the referee.

Reviewer 3 Report

This is an excellent and topical article which addresses the issue of the cosmological constant and dark energy problems in modifications of general relativity. Such a review-type article is most welcome, and fills an impressive need in the literature. The article deserves to be published.

Author Response

We would like to thank the reviewer for their very positive and encouraging response.

Reviewer 4 Report

This is a well-organized review of possible modifications of Einstein's general relativity related to the presence of the cosmological constant and its phenomenology. The authors use modern and concise language to describe the problems associated with the cosmological constant's phenomenology and inspect no-go theorems and their loopholes to motivate some modified theories of gravity. They clearly show how such modifications of gravity cannot be arbitrary but need to respect no-go theorems and data constraints.

I have only a few minor comments to add:

(1) The sentence below eq. (18) "Here, T is a localised gravitational probe such as the Moon, light rays in the gravitational field of the Sun or one of the two masses in a torsion balance." is not clear. I suggest rewriting it.

(2) Before Eq. (19), the authors write:  "gives rise to the familiar exchange amplitude". I would suggest giving a bit more detail here.

(3) Since they extensively talk about Solar System checks, I would suggest including also the reference: https://arxiv.org/abs/1812.11181

(4) At the beginning of page 13, the authors introduce the ``fifth-force''. Perhaps a bit more explanation can be added at this point.

(5) Before Eq. (28) they say: ``We note that both frames violate the equivalence principle and refer the reader to [72] for a discussion. ''. I would suggest adding a bit more detail here to make it clear the motivation of the mentioned discussion. 

Author Response

We would like to thank the reviewer for their very positive and constructive response, which helped to improve the manuscript. We will answer to the referee’s suggestions and comments in turn below.

Comment 1: The sentence below eq. (18) "Here, T is a localised gravitational probe such as the Moon, light rays in the gravitational field of the Sun or one of the two masses in a torsion balance." is not clear. I suggest rewriting it.

Reply: We have re-written and simplified this sentence, hopefully making it more clear: “Here, $\bar{T}_{\mu\nu}$ is assumed to be a source that falls off asymptotically. Physically, it plays the role of a local mass distribution that is accessible to observations such as a finite set of point masses. Its counterpart ${T}_{\mu\nu} $ represents a generic source, which, in particular, is not assumed to fall off at infinity and will be later identified with vacuum energy.”

Comment 2: Before Eq. (19), the authors write:  "gives rise to the familiar exchange amplitude". I would suggest giving a bit more detail here.

Reply: We have made the statement more concrete and added a reference to the literature here: “gives rise to the familiar exchange amplitude between two localised sources after substituting the propagator for a massless graviton (for a detailed derivation of $G^{(2)}_{\alpha\beta\gamma\delta}(\mu)$ for $\mu=0$ and $\mu \neq 0 $ see for example Sec.~2.2 in [arXiv:1401.4173])”

Comment 3: Since they extensively talk about Solar System checks, I would suggest including also the reference: https://arxiv.org/abs/1812.11181

Reply: We have included this reference in the manuscript (and cited it together with arXiv:1403.7377). 

Comment 4: At the beginning of page 13, the authors introduce the ``fifth-force''. Perhaps a bit more explanation can be added at this point.

Reply:  We have reconsidered the paragraph and decided that it is adequately clear at that stage in the manuscript. Below Eq.31, we explicitly describe the effects of this fifth force. 

Comment 5:  Before Eq. (28) they say: ``We note that both frames violate the equivalence principle and refer the reader to [72] for a discussion. ''. I would suggest adding a bit more detail here to make it clear the motivation of the mentioned discussion. 

Reply: We have removed this sentence as it was out of context.

We would again like to thank the reviewer for improving the quality of this review, and we hope we have satisfied all concerns. 

Best regards,

FADE collaboration

 

Round 2

Reviewer 1 Report

In my first report I suggested various issues of direct relevance to the manscript that the authors should look at before publication. Very few of these referee requests have been implemented so I am sending the article back to the authors for an extra round of changes and review. The authors appear not to have looked at some of the papers I referenced. Otherwise, their response might very probably have been different.

My concerns are mainly with some of Sections 1 and 2. Sections 3 and 4 (on details of possible gravity modifications) read well. Topics like the Hubble tension and possible early dark energy, possible connections to inflation, and possible (in-)stability of de Sitter space could be mentioned briefly as an extra paragraph in the conclusions, Section 5, as relevant topics for future work, e.g. just after the mention of Quintessence ideas. 

The motivational comments in Sections 1,2 on ideas with effective theories and decoupling of scales as presented are severely challenged by results from the Large Hadron Collider at CERN. In particular, the stability of the electroweak vacuum depends on whether the Higgs self-couplings crosses zero in the deep ultraviolet which turns out very sensitive to the values of particle physics masses and couplings measured in collider experiments. Our own existence is connected to the value of the heavy top quark mass! For an excellent summary, see the opening paragraph in the left column of the first page of AV Bednyakov et al., Phys. Rev. Lett. 115 (2015) 210802.  

Perhaps one could cover this by something like a footnote or extra paragraph below line 64 (manuscipt opening paragraph): "This (in addition to the CCP) is also challenged by LHC data which suggest that the electroweak vacuum sits close to the border of stable and metastable. In the Standard Model vacuum stability is determined by whether the Higgs self coupling crosses  zero in the deep ultraviolet, which is very sensitive to the values of the Higgs boson and top quarks masses measured in the experiments [Refs. Bednyakov et al (PRL quoted above)., G. Degrassi et al. JHEP 08 (2012) 098, F. Jegerlehner Acta Physica Polon B 45 (2014) 1167]."

Then below line 196, add an extra paragraph something like "If one imposes vacuum global spacetime translational invariance as a renormalization condition at mass dimension four, then the cosmological constant, if finite, would appear as a higher dimensional term in the action. This scenario follows with a possible emergent Standard Model with the cosmological constant scale similar to the size of light Majorana neutrinos masses, see [Refs: SD Bass+ J Kryzsiak, PLB 803 (2020) 135351; JD Bjorken, Phys Rev D64 (2001) 085008] and [Ref: F Jegerlehner, Foundations of Physics 49 (2019) 8, 915] for connections with electroweak vacuum stability."

For the hierarchy puzzle, the authors' reference is a Ph D thesis. I suggest adding an extra reference [Ref. J.D. Wells, arXiv:0909.4541 [hep-ph]] - his  Section 9 gives an excellent discussion of the physics issues. 

Discussion of ideas about possible early dark energy in connection with the Hubble tension, connections to inflation and (in-)stability of de Sitter space could be included as a short extra paragraph on more open issues somewhere in the Conclusions section, e.g. below line 998. An excellent recent discussion of EDE ideas is M Kamionkowski and AG Riess, arXiv: 221104492 [astro-ph.CO].

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf