{"id":"c8d55643-ddd6-4e15-a45e-57e4143fab6b","arxiv_id":"2501.11103","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":13,"one_line_summary":"Constraining nDGP, k-mouflage, and phenomenological modified gravity with JWST high-redshift data yields preferred parameters, but no model fully reproduces the observed z~12 star formation rate density.","lead":"This paper tests several modified gravity models against JWST observations of early galaxies and finds preferred parameter values, but the analysis relies on visual inspection of model curves. The study is a first exploration of how high-redshift JWST data can narrow the space of viable gravity theories.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central k-mouflage claim depends on treating LCDM-calibrated baryonic physics as gravity-independent and on visual, not statistical, agreement with JWST data.","rationale":"The reader's weakest-assumption analysis identifies the same load-bearing issue: baryonic prescriptions calibrated in LCDM are assumed unchanged in modified gravity. My reading of the paper confirms this, and I add that the paper itself explicitly acknowledges the approximation in Secs. 5.2 and 8. This is a genuine threat to the central claim because the only place k-mouflage enters the observable predictions is through the halo mass function and Mmin; the mapping from halos to stars and ionizing photons is entirely fixed by LCDM-calibrated relations. If those relations are gravity-dependent, the claimed success of k-mouflage could be an artifact of the assumed baryonic model. A second, compounding issue is the absence of any statistical goodness-of-fit: 'satisfy' is judged by eye, so even within the assumed model there is no quantitative support for the headline. These are not minor caveats; they bear directly on whether the paper's central conclusion is established. I therefore agree with the reader's reject-level concern, although I would frame the path forward as a concrete joint fit rather than an immediate falsification of the physical idea. The proposed MCMC test would settle whether the baryonic assumptions are actually load-bearing or whether the k-mouflage preference survives a proper likelihood analysis. The paper does provide useful exploratory machinery and a reproducible pipeline, but the strength of the conclusion is not matched by the strength of the analysis.","tokens_in":48653,"tokens_out":4550,"duration_ms":47377,"concrete_test":"Run a joint MCMC for the k-mouflage double-power-law case with free parameters (beta, K0, epsilon_star,0, fesc, log10 Nion, and the SMHR slopes gamma_lo, gamma_hi), fitting the JWST SMD data (Labbé et al. 2023, Wang et al. 2024) and EoR constraints (QHII and tau_reion) with full error bars. If the posterior keeps beta ~ 0.1 and K0 >= 0.9 while baryonic parameters stay at their LCDM-calibrated values, the claim survives; if the fit instead requires shifting epsilon_star,0 or fesc outside their quoted ranges, the baryonic assumption is load-bearing and the headline conclusion is unsupported. A cheaper first check: recompute the SMD and QHII curves at fixed (beta, K0) = (0.1, 0.9) while varying epsilon_star,0 within [0.15, 0.3] and fesc within [0.1, 0.3]; if the curves shift by more than the data error bars, the central claim is not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The headline result in Sec. 8 is that k-mouflage with the double-power-law SMHR can satisfy both reionization and high-redshift SMD constraints up to M_star ~ 1e11 solar masses. For this to be supported, the analysis must assume that all baryonic prescriptions calibrated within LCDM remain exactly valid in modified gravity: the double-power-law stellar-mass-to-halo relation of Eq. (68), the UV/dust scatter of Eqs. (86)-(88), and the reionization inputs fesc=0.25, CHII=3.0, log10 Nion=53.14 from Sec. 6. The MG physics enters only through the halo mass function and Mmin; no baryonic ingredient is re-derived for k-mouflage. The paper itself flags this: Sec. 5.2 states that the UV scatter parameters 'were derived on the basis of LCDM cosmology. Clearly, this is an approximation', and Sec. 8 admits that parameters such as epsilon_star,0 'are not bounded at all' and that an LCDM value was assumed. Since SMD and QHII are sensitive to epsilon_star,0, fesc, and Nion, a modest gravity-induced change in star-formation efficiency or ionizing escape would be degenerate with (beta, K0). Moreover, preferred regions in Fig. 23 are determined by visual inspection of figures, with no likelihood and no propagated error bars, so the claim that k-mouflage 'can satisfy' both datasets is not quantitatively established.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper explores several modified gravity (MG) models—phenomenological gravity, wγCDM, the normal branch of DGP (nDGP), and k-mouflage—as potential explanations of JWST observations at z ≲ 17. The author implements the halo mass function and spherical collapse in MG, then applies fixed baryonic prescriptions to compute the stellar mass function (SMF), stellar mass density (SMD), UV luminosity function (UVLF), star formation rate density (SFRD), and reionization quantities Q_HII and τ_reion. The main claimed results are that nDGP prefers r_c ≳ 10^3.5 Mpc, k-mouflage prefers β ~ 0.1 with K_0 ≳ 0.9, and phantom-like w_Λ is preferred; the central conclusion is that k-mouflage with a double-power-law SMHR can simultaneously satisfy both reionization and high-redshift JWST SMD constraints up to M_* ~ 10^11 M_sun.","tokens_in":49101,"tokens_out":5146,"duration_ms":53775,"significance":"If the central claim were quantitatively established, the paper would provide a concrete modified-gravity candidate that explains JWST's early massive galaxies and the epoch of reionization, with falsifiable predictions for future surveys. The manuscript has strengths: it covers a broad landscape of MG models, uses a consistent MG-CLASS-based pipeline, includes recent JWST data, and states that the code is available. However, the analysis as presented is exploratory: constraints are drawn by visual inspection of overlaid model curves, baryonic prescriptions are calibrated within ΛCDM and assumed unchanged in MG, and the paper itself acknowledges that several key parameters are unconstrained. These issues are load-bearing for the paper's main conclusion, so the significance is currently limited to a proof-of-concept under strong assumptions.","major_comments":[{"comment":"The parameter constraints and the central conclusion that k-mouflage 'can satisfy' the JWST constraints are based on visual inspection of model curves overlaid on data, with no likelihood, no MCMC exploration, no parameter uncertainties, and no goodness-of-fit statistic. Statements such as 'preferred values', 'excluded', and 'best-fit parameters' in Sections 7.1–7.5 and Figure 23 are therefore not quantitatively supported. This is not a minor presentational issue: the paper's main claim depends on distinguishing models that 'satisfy' the data from those that 'fail', and that distinction cannot be made reliably without a statistical comparison that accounts for the error bars on the data points and the scatter prescriptions.","section":"Section 7 and Figure 23"},{"comment":"The baryonic prescriptions are calibrated within ΛCDM and then assumed to remain exactly valid in modified gravity. This applies to the double-power-law SMHR of Eq. (68), the UV scatter parameters in Eq. (88), the reionization inputs f_esc = 0.25, C_HII = 3.0, and log10 N_ion = 53.14 from Section 6, and the peak star formation efficiency ϵ_*,0. The paper itself notes in Section 5.2 that the UV scatter parameters 'were derived on the basis of ΛCDM cosmology. Clearly, this is an approximation', and in Section 8 that ϵ_*,0 is 'not bounded at all' and an ΛCDM value was assumed. Since SMD, UVLF, and Q_HII depend sensitively on these parameters, a modest gravity-induced change in star formation efficiency or escape fraction would be degenerate with the fitted MG parameters (β, K_0, r_c). The preferred regions in Figure 23 could therefore shift substantially if the baryonic prescriptions were re-derived or marginalized within each MG model.","section":"Section 5.2 and Section 8"},{"comment":"There is a potential circularity in testing the MG models against observables that were used, at least in part, to calibrate the baryonic ingredients of the same pipeline. The Rodríguez-Puebla SMHR (Eqs. 64–70) is calibrated on SMF and SMD data, the double-power-law SMHR is calibrated on UVLF data, the UV scatter model (Eq. 88) is calibrated on UVLF data, and log10 N_ion is derived from HUDF data. The paper then uses SMF, SMD, UVLF, and reionization observations from Section 7 as constraints. If the calibration data overlap with the 'test' datasets, then the claim that k-mouflage 'satisfies' the JWST constraints is not an independent validation; at minimum, the effective number of degrees of freedom is decreased and the comparison is biased. This should be quantified or the analysis reframed as a consistency test under a stated calibration scheme.","section":"Sections 4.1, 5.2, 6 and 7"},{"comment":"The paper's statements about the preferred dark energy equation of state are internally inconsistent. The abstract states that 'phantom-like dark energy EoS w_Λ ≲ −1 is preferred over the quintessence', but Section 7.1 reports that Model II prefers the range −1 ≲ w_Λ < ∞, Section 7.4 says that 'w_Λ ≤ 1 ... makes quintessence cosmology a viable choice', and Section 8 states that wγCDM 'prefers w_Λ ≳ −1 instead of quintessence'. These statements cannot all be correct, and the abstract's strong phantom preference is not supported by the body text. This needs to be corrected and the conclusion about w_Λ made consistent with the actual results.","section":"Abstract, Section 7.1, Section 7.4, Section 8"},{"comment":"The central claim in Section 8—that k-mouflage with the double-power-law SMHR can satisfy both reionization and high-redshift SMD constraints up to M_* ~ 10^11 M_sun—is qualified by the paper's own finding in Section 7.4 that 'for any model and any scatter value, it is still not possible to produce the nearly constant SFRD, required by JWST at z ≳ 12'. The title and abstract claim to 'explain JWST star formation history at z ~ 17', but the SFRD at z ≳ 12 is not reproduced. The paper should either soften the claim to the specific observables and mass range that are actually reproduced, or provide quantitative evidence that the remaining SFRD discrepancy is within the observational and modeling uncertainties.","section":"Section 7.4 and Section 8"}],"minor_comments":[{"comment":"The Christoffel symbol in Eq. (43) has a typo: the first two terms are both written as ∂_ν g_{βμ}; the standard expression is Γ^α_{μν} = (1/2)g^{αβ}(∂_μ g_{βν} + ∂_ν g_{βμ} − ∂_β g_{μν}).","section":"Equation (43)"},{"comment":"The text in Section 7.1 says 'first model suggests higher deviation from the fiducial cosmology than the second one', and Section 8 says 'the double power-law best-fit values are noticeably closer to the ΛCDM than Rodriguez-Puebla'. These are consistent, but the phrasing 'closer to the ΛCDM than Rodriguez-Puebla' is missing an explicit comparison object and should be reworded.","section":"Section 7.1 and Section 8"},{"comment":"There are repeated typographical issues, e.g. 'di fferent', 'it’s power spectrum', 'can easily be implement', and 'JDB' instead of 'JBD' in Section 2.4. A careful proofread is needed.","section":"Throughout"},{"comment":"The caption of Figure 23 says 'Arrow signs signify an upper limit' and uses circles/squares for degenerate solutions, but the marker codes are not explained in the figure caption; please define the symbols explicitly.","section":"Figure 23"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is an interesting exploratory study, but in its current form the main constraints are not quantitative. The absence of a statistical analysis, the adoption of ΛCDM-calibrated baryonic prescriptions, and the potential overlap between calibration and test datasets all affect the headline claim. These issues are fixable in principle, but would require a substantial revision that reframes the claims and adds a likelihood-based comparison. If the author is not able to add such an analysis, the paper may be better positioned as a methods/consistency study rather than as a constraints paper."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First, what you should know: this is real work, not a crank. The author builds a consistent pipeline from MG-CLASS power spectra, through modified spherical collapse and HMFs, to SMF/SMD/UVLF/SFRD/EoR predictions, and applies it to nDGP, k-mouflage, and several phenomenological models. That scope is genuinely new. The code is on GitHub, and the paper is fairly transparent about its own limitations.\n\nThe soft spots are where the conclusions live. The headline result—k-mouflage with the double power-law SMHR can satisfy both reionization and high-redshift SMD up to ~1e11 Msun—comes from visual inspection of Figure 23. There is no likelihood, no MCMC, no error propagation. The paper admits in Section 8 that epsilon_star,0 is not bounded and an LCDM value was assumed. The baryonic recipes are all LCDM-calibrated: the Rodriguez-Puebla SMHR is fit to SMF/SMD data, the UV scatter parameters are explicitly stated in Section 5.2 to be derived on the basis of LCDM, and fesc=0.25, CHII=3, log10 Nion=53.14 come from simulations or observations within LCDM. If any of those shift under modified gravity, the (beta, K0) preference changes. That is load-bearing, not cosmetic.\n\nThe title also overstates. Section 7.4 admits that no model in the paper can reproduce the nearly constant SFRD required by JWST at z>12. So “explaining the star formation history” is not what the paper does. There is also a confusing internal inconsistency about wLambda: the abstract says phantom-like w<-1 is preferred, while Section 8 says w≳-1 is preferred “instead of quintessence,” which reads as self-contradictory.\n\nWhat holds up: the spherical collapse derivations for screened theories look plausible, the comparison to existing rc constraints from Raccanelli et al. and Barreira et al. is sensible, and the paper is honest about degeneracies and missing constraints. This is not a paper with a load-bearing logical contradiction; it is a paper with an overinterpreted, under-sampled analysis.\n\nWho is this for? Someone working on modified gravity and high-z JWST data might use this as a map of where parameters could go, but only as a starting point. I would not cite the parameter constraints as established.\n\nMy recommendation: do not desk-reject. A referee who knows both modified gravity and galaxy formation could push the author to add a real statistical analysis—even a simple chi-square grid with bootstrapped errors would be a big improvement—and to marginalize over the baryonic nuisance parameters. As it stands, I would accept only after major revision.","headline":"A serious but statistically unfinished attempt to constrain modified gravity with JWST high-z data; the headline k-mouflage claim rests on visual inspection and LCDM-calibrated baryonic physics.","tokens_in":49638,"tokens_out":3116,"would_cite":false,"duration_ms":32179,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that k-mouflage gravity, a modified theory with a screening scalar field, can simultaneously explain JWST's surprisingly massive early galaxies and the completion of reionization, while six other cosmologies tested fail…","keywords":["modified gravity","JWST high-redshift galaxies","star formation history","halo mass function","reionization","k-mouflage gravity","nDGP braneworld","cosmological tensions"],"falsifier":"Re-calibrate the double power-law stellar mass-to-halo relation and the UV scatter from hydrodynamic simulations run inside k-mouflage gravity and repeat the fits: if the JWST stellar mass density and reionization constraints no longer overlap for $\\beta \\approx 0.1$ and $K_0 \\gtrsim 0.9$, the central claim is falsified. A simpler observational check is new JWST spectroscopy showing that the $z \\gtrsim 10$ galaxies assigned $M_\\star \\sim 10^{11}\\,M_\\odot$ actually have lower stellar masses, which would relax the tension that k-mouflage is invoked to resolve.","tokens_in":48460,"feed_emoji":"🌌","tokens_out":9508,"duration_ms":90553,"temperature":0.7,"pith_summary":"The paper argues that JWST's surprisingly massive, early galaxies and the requirement that reionization finish on schedule can be explained together if gravity is modified in a specific way. It builds galaxy observables—stellar mass functions, stellar mass densities, star formation rate densities, UV luminosity functions, and reionization histories—from halo mass functions computed in several beyond-ΛCDM theories, then asks which parameter choices survive. The answer it reaches is that only k-mouflage gravity, a scalar-field theory with a screening mechanism, combined with a double power-law stellar mass-to-halo relation, satisfies both the high-redshift JWST stellar mass density and the reionization constraints up to stellar masses around $10^{11}\\,M_\\odot$. The other tested theories—phenomenological modifications, varying-growth-index cosmologies, and the normal-branch DGP braneworld—fail at least one of these probes. If true, this narrows the modified-gravity landscape and suggests the early-galaxy excess is a gravitational, not a baryonic, effect.","feed_headline":"One gravity model fits JWST's early massive galaxies and reionization","feed_subtitle":"k-mouflage gravity passes both reionization and JWST stellar-mass constraints up to 10^11 solar masses.","key_machinery":"The machinery is an analytic chain that converts a theory of gravity into galaxy observables. Modified gravity enters through the functions $\\mu(a,k)$ and $\\gamma(a,k)$ that rescale the gravitational coupling and the Bardeen potentials; these feed a modified Einstein-Boltzmann solver that produces linear matter power spectra. From those spectra, spherical collapse gives the linear density threshold $\\delta_c$ and virial quantities, and the extended Press-Schechter formalism yields the halo mass function. Abundance matching with two stellar mass-to-halo relations converts halos into stars, producing the stellar mass function, stellar mass density, and—through a star-formation-rate-to-UV luminosity conversion with dust attenuation—the UV luminosity function and star formation rate density. Reionization is modeled with $Q_{\\rm HII}$ and $\\tau_{\\rm reion}$, using escape fraction $f_{\\rm esc}=0.25$, clumping factor $C_{\\rm HII}=3.0$, and photon production rate $\\log_{10} N_{\\rm ion}=53.14$. The load-bearing identity is that only the halo mass function is changed by gravity; all baryonic conversion recipes are carried over from ΛCDM unchanged.","core_discovery":"The central claim is that k-mouflage gravity with scalar-field parameters $\\beta \\approx 0.1$, $K_0 \\gtrsim 0.9$ and the double power-law stellar mass-to-halo relation can simultaneously account for the JWST stellar mass density at $z \\sim 8$–$16$ and the epoch of reionization constraints on the ionized hydrogen filling fraction $Q_{\\rm HII}$ and the CMB optical depth $\\tau_{\\rm reion}$, up to stellar masses of roughly $10^{11}\\,M_\\odot$. No other model considered—ΛCDM, the phenomenological parameterizations, the varying-growth-index $w\\gamma$CDM model, or the nDGP braneworld—passes both sets of constraints. The paper also derives new parameter preferences: nDGP favors a crossover scale $r_c \\gtrsim 10^{3.5}\\,{\\rm Mpc}$, and in the $w\\gamma$CDM case phantom-like dark energy with $w_\\Lambda \\lesssim -1$ is preferred over quintessence. The result is presented as using JWST to narrow the landscape of viable modified gravity theories.","pith_inferences":["The same pipeline could test other screened theories, such as symmetron or chameleon models, because the paper shows the discriminating power comes from the high-mass end of the halo mass function.","If the gravity-dependence of baryonic recipes is small, the JWST excess is evidence for enhanced small-scale structure formation; if it is large, the k-mouflage preference may be an artifact of using ΛCDM-calibrated star-formation physics, and a hydrodynamic simulation in k-mouflage gravity would settle which.","The reionization analysis fixes $f_{\\rm esc}$ and $N_{\\rm ion}$; treating them as free parameters would likely widen the allowed $\\{\\beta, K_0\\}$ region and could remove the single-model victory, so the claimed success is conditional on those fiducial values.","A direct observational extension is to measure the UV luminosity function at $z \\sim 14$–$17$ with future JWST observations: k-mouflage predicts a specific bright-end excess relative to ΛCDM that the current UVLF data constrain only weakly."],"forward_implications":["If k-mouflage gravity is correct, JWST's excess of massive galaxies at $z > 10$ is a prediction of the modified halo mass function rather than an anomaly requiring extreme star-formation efficiency.","The combined reionization and stellar mass density constraints single out $\\beta \\approx 0.1$, $K_0 \\gtrsim 0.9$ for k-mouflage, a parameter region that future galaxy surveys can either confirm or exclude.","nDGP is driven to $r_c \\gtrsim 10^{3.5}\\,{\\rm Mpc}$, meaning a viable braneworld must have a very large crossover scale, nearly returning to ΛCDM on observable scales.","Phenomenological modified gravity and $w\\gamma$CDM cannot fix the JWST high-redshift tension because their halo mass functions barely deviate from ΛCDM at $z \\gtrsim 4$; only screened theories with an enhanced small-scale gravitational force succeed.","The strong dependence of the constraints on the choice of stellar mass-to-halo relation means modified gravity parameters are degenerate with baryonic feedback assumptions, so joint fits are needed before concluding that gravity is modified."],"supporting_citations":[{"why":"Supplies the modified Einstein-Boltzmann solver and the $\\mu$–$\\Sigma$–$\\gamma$ parameterizations used for all the gravity models.","marker":"Sakr & Martinelli (2022)"},{"why":"Provides the analytic framework connecting the halo mass function to stellar mass function and stellar mass density.","marker":"Dayal & Giri (2023)"},{"why":"Supplies the observationally calibrated stellar mass-to-halo relation used as Model I.","marker":"Rodríguez-Puebla et al. (2017)"},{"why":"Supplies the double power-law stellar mass-to-halo relation with redshift-dependent efficiency used as Model II.","marker":"Mirocha et al. (2017)"},{"why":"Provides the screened spherical-collapse formalism and Vainshtein-radius treatment for nDGP gravity.","marker":"Schmidt et al. (2010)"},{"why":"Provides the k-mouflage background equations, $\\mu(a,k)$, and screening treatment that the central claim rests on.","marker":"Brax & Valageas (2014)"},{"why":"Provides the JWST stellar mass density measurements at $z \\sim 8$–$10$ that drive the tension and the k-mouflage preference.","marker":"Labbé et al. (2023)"},{"why":"Provides JWST star formation rate density and UV luminosity function data up to $z \\sim 16$–$17$ used for comparison.","marker":"Harikane et al. (2023)"},{"why":"Supplies the reionization inputs for the ionizing photon production rate and temperature used in $Q_{\\rm HII}$ and $\\tau_{\\rm reion}$.","marker":"Robertson et al. (2015)"},{"why":"Provides the UV luminosity function code and the dust attenuation and scatter treatment used to model UVLF predictions.","marker":"Shen et al. (2023)"}],"fun_headline_variants":["k-mouflage gravity passes JWST and reionization tests","Only k-mouflage fits JWST galaxies and reionization","JWST and reionization data favor k-mouflage gravity","k-mouflage beats ΛCDM on JWST and reionization","k-mouflage gravity explains early galaxies and reionization"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The star-formation efficiencies, UV scatter and dust corrections, and reionization parameters ($f_{\\rm esc}=0.25$, $C_{\\rm HII}=3.0$, $\\log_{10} N_{\\rm ion}=53.14$) were calibrated inside ordinary ΛCDM and are assumed to remain correct when gravity is modified, so only the halo mass function changes.","fun_headline_variants_meta":{"raw":{"variants":["k-mouflage gravity passes JWST and reionization tests","Only k-mouflage fits JWST galaxies and reionization","JWST and reionization data favor k-mouflage gravity","k-mouflage beats ΛCDM on JWST and reionization","k-mouflage gravity explains early galaxies and reionization"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000817,"raw_usage":{"total_tokens":3673,"prompt_tokens":1133,"completion_tokens":2540,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":749,"completion_tokens_details":{"reasoning_tokens":2462}},"tokens_in":749,"tokens_out":2540,"duration_ms":21177,"temperature":1.0,"reasoning_tokens":2462,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T18:38:33.260338+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-calibrate the double power-law stellar mass-to-halo relation and the UV scatter from hydrodynamic simulations run inside k-mouflage gravity and repeat the fits: if the JWST stellar mass density and reionization constraints no longer overlap for $\\beta \\approx 0.1$ and $K_0 \\gtrsim 0.9$, the central claim is falsified. A simpler observational check is new JWST spectroscopy showing that the $z \\gtrsim 10$ galaxies assigned $M_\\star \\sim 10^{11}\\,M_\\odot$ actually have lower stellar masses, which would relax the tension that k-mouflage is invoked to resolve.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the modified Einstein-Boltzmann solver and the $\\mu$–$\\Sigma$–$\\gamma$ parameterizations used for all the gravity models."},{"cited_title":"Warm dark matter constraints from the JWST","cited_arxiv_id":"2303.14239","evidence_quote":"Provides the analytic framework connecting the halo mass function to stellar mass function and stellar mass density."},{"cited_title":"R., & Sun, G","cited_arxiv_id":null,"evidence_quote":"Supplies the double power-law stellar mass-to-halo relation with redshift-dependent efficiency used as Model II."},{"cited_title":"2010, Phys","cited_arxiv_id":null,"evidence_quote":"Provides the screened spherical-collapse formalism and Vainshtein-radius treatment for nDGP gravity."},{"cited_title":"E., Ellis, R","cited_arxiv_id":null,"evidence_quote":"Supplies the reionization inputs for the ionizing photon production rate and temperature used in $Q_{\\rm HII}$ and $\\tau_{\\rm reion}$."}],"review_version":1}