Pith. sign in

REVIEW 3 major objections 5 minor 25 references

Boundary terms in cosmology

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Enforcing the vanishing of the spacetime boundary term in the cosmological action yields an emergent stiff-matter fluid that decays as the sixth power of the scale factor.

desk verdict Clear but derivative: the claimed stiff-matter prediction rests on an imposed ODE, not on the boundary variation. read the letter →

arxiv 2505.23679 v2 pith:2BUU4BTU submitted 2025-05-29 gr-qc hep-thmath-phmath.MP

Ángel Cuevas , Javier Chagoya , C. Ortiz This is my paper
classification gr-qchep-thmath-phmath.MP
keywords boundarytermsEinstein-HilbertactionFriedmannequationsstiffmatterkinationLagrangemultipliersFLRWcosmologycosmologicalconstant
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes replacing the usual Gibbons-Hawking-York boundary term in the Einstein-Hilbert action with a Lagrange-multiplier constraint that forces the boundary contribution to vanish throughout cosmic evolution. Worked out in a flat FLRW universe, the constraint turns the boundary contribution into an extra term in the first Friedmann equation proportional to $a^{-6}$, which behaves exactly like a stiff-matter fluid ($\omega=1$) or a kination scalar field. The standard Friedmann equations are preserved, with the new component emerging from the boundary condition rather than from an added matter Lagrangian. A relaxed version of the constraint, allowing terms that die at the boundary, produces a cosmological-constant term in the same way. The authors argue that this shows stiff matter can be an emergent consequence of how boundary terms are handled in general relativity.

What carries the argument

The central object is the cosmological component $B^0$ of the geometric boundary vector in Eq. (5), evaluated for a flat FLRW metric at a fixed radial boundary, together with the exact-variation condition that turns $\partial_0(\sqrt{-g}B^0)$ into a total variation. That condition is implemented through the semi-holonomic constraint $f(a,\dot a,\ddot a)=a^{-3}(2a\dot a^2+a^2\ddot a-D_0)=0$, added to the Lagrangian as $\lambda(t)f$. Varying with respect to $\lambda$ enforces the constraint, while variation with respect to $a$ yields the modified Friedmann equations whose integration introduces the $\rho_{0s}a^{-6}$ stiff-matter term.

What would settle it

Compute the surface variation of the Einstein-Hilbert action in FLRW without the ansatz $\dot a = \dot a(a)$, keeping a general lapse $N(t)$ and spatial curvature $k$; if $\partial_\sigma(\sqrt{-g}B^\sigma)=0$ does not reproduce Eq. (22), the stiff matter is an artifact of the ansatz. Alternatively, a stiff-matter era changes the expansion rate before nucleosynthesis, so published light-element-abundance and CMB-damping constraints can bound $\rho_{0s}$; the paper does not supply such a comparison.

Watch

Extended reading notes

Core claim

The central claim is that imposing the vanishing of the gravitational boundary term, treated as a semi-holonomic constraint $f(a,\dot a,\ddot a)=0$ via a Lagrange multiplier, modifies the Friedmann equations so that part of the effective energy density is $\rho_{0s}a^{-6}$. Because $\rho\propto a^{-3(1+\omega)}$, this is the signature of a stiff fluid with $\omega=1$, the stiffest causal equation of state, which can be realized as a kinetic-energy-dominated scalar field known as kination. The derivation rests on writing the FLRW boundary term as an exact variation, which forces the power-law relation $\dot a = a^{2/E}$ and leads to $2a\dot a^2+a^2\ddot a=D_0$ as the constraint; solving it gives $a(t)\propto(-c_1+D_0^2(t+c_2)^2)^{1/3}$ and a first Friedmann equation containing dust, stiff matter, and, in the relaxed case, a cosmological constant. The authors stress that the stiff component arises naturally from the boundary condition rather than from the matter sector, and that it does not resolve the Hubble tension.

Load-bearing premise

The whole result depends on assuming that the boundary term is a total time derivative, which forces the power-law condition $\dot a = a^{2/E}$; if that assumption is not a genuine consequence of the action, the derived constraint and the stiff-matter component evaporate.

Editorial extensions

If this is right

  • The standard Friedmann equations survive with the same form, but the effective density acquires a stiff-matter component $\rho_{0s}/a^6$ without adding a new matter Lagrangian.
  • Because $\omega=1$ is the maximal causal stiffness, the boundary-term origin predicts a component that dominates the earliest stages of expansion before radiation.
  • Requiring the boundary term to vanish exactly yields dust and stiff matter only; allowing terms that become negligible at the boundary adds a cosmological constant $\rho_{0\Lambda}$, recovering an accelerated expansion phase.
  • The model does not resolve the Hubble tension: the stiff component changes the early-time expansion rate but not the late-time discrepancy in $H_0$.
  • The Lagrange multiplier $\lambda(t)$ decouples from the scale factor: its free constants set initial conditions for the constraint but do not appear in $a(t)$.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A reader should read Eqs. (13)-(17) as an integrability ansatz: the stiff-matter prediction is only as strong as the claim that the boundary term must be an exact variation. Repeating the construction with a general lapse $N(t)$ or nonzero spatial curvature would show whether the constraint is covariant or a gauge artifact.
  • If the mechanism is physical, applying the same Lagrange-multiplier treatment to anisotropic metrics such as Bianchi or Kantowski-Sachs models should produce stiff-matter-like anisotropic stress, since a boundary term generically carries directional information.
  • A quantitative test would be to compare the predicted $\rho_{0s}$ with big-bang nucleosynthesis and cosmic microwave background limits, because a stiff-matter era shifts the expansion rate before matter-radiation equality; the paper does not perform that comparison.
  • The ambiguity in boundary counterterms becomes an ambiguity in the emergent fluid: the prediction is contingent on which boundary condition one declares to vanish, so the method translates a known ambiguity rather than eliminating it.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes an alternative treatment of the gravitational boundary term in a cosmological Friedmann-Lemaître-Robertson-Walker setting. Instead of cancelling the boundary term with a Gibbons-Hawking-York counterterm, the authors impose its vanishing throughout the evolution by adding a Lagrange-multiplier constraint to the action. From the resulting constrained dynamics they derive modified Friedmann equations that, in addition to dust, contain a component scaling as a^{-6}, which they identify with stiff matter (kination). They then extend the constraint by hand with terms F1 a^3 and R2/a to reproduce a cosmological constant and radiation, and discuss the Hubble tension and early-universe dynamics.

Significance. If the central derivation were valid, the claim that a boundary term in the Einstein-Hilbert action generically produces an emergent stiff-matter component would be an interesting and testable result for early-universe cosmology, and the paper's explicit demonstration that this component does not resolve the Hubble tension is a useful negative check. However, the main physical prediction is not derived from the surface variation of the action; it follows from a constraint ODE that is introduced by hand. The later inclusion of Λ and radiation by adding terms to the same constraint shows that the framework is flexible enough to reproduce any desired fluid inventory, so the stiff-matter result is a relabeling of integration constants rather than a falsifiable prediction. The manuscript therefore does not support its central claim.

major comments (3)
  1. [§2.2, Eq. (18)] The equation 2a\dot a^2 + a^2\ddot a = D0 is introduced with the phrase 'For the vanishing of the boundary term,' but it is not derived from the boundary variation. Equation (12) expresses ∂0(√−g B^0) as a total time derivative of a combination of metric variations; the condition that the boundary term vanishes should involve B^σ n_σ evaluated on the boundary, not a bulk ODE that holds at all times. Setting the argument of the time derivative equal to a constant D0 is an additional assumption, and the variational quantity δ(a^2\dot a) is not the same as the ordinary time derivative a^2\ddot a + 2a\dot a^2. This step is load-bearing because every subsequent result, including the a^{-6} term in Eq. (30), follows from this ODE.
  2. [§3, Eq. (22)] The constraint f(a, \dot a, \ddot a)=0 is imposed as a Lagrange-multiplier constraint rather than derived from the variation of the action or from the surface term. A Lagrange multiplier can enforce any semiholonomic constraint; the physical content lies in why f=0 should hold. Since Eq. (18) is hand-imposed, the constraint in Eq. (22) is an ad hoc assumption. Consequently, solving that constraint and substituting into Eq. (28) yields 3H^2 = 2D0/a^3 + 3c1/a^6 (Eq. (30)); the stiff-matter coefficient c1 is an integration constant of the imposed ODE. Identifying it with ρ0s is a relabeling, not a derivation, and the claim in §3.1 that the boundary term 'predicts the existence of a stiff matter fluid' is therefore unsupported.
  3. [§3.2 and §3.2.1, Eqs. (35) and (44)] The terms F1 a^3 and R2/a are added to the constraint 'under the same considerations' to reproduce a cosmological constant and radiation, respectively. The stated criterion in the footnote, that ∂σ(√−gB^σ)/√−g → 0 at large a, is extremely weak and is satisfied by many other functions of a, including negative powers such as R2/a. The selection of exactly F1 a^3 and R2/a is guided by the known Friedmann fluid inventory, not by the boundary-term formalism. This demonstrates that the framework postdicts rather than predicts the cosmic fluid content, and it further undermines the claim that stiff matter arises naturally while other fluids must be inserted by hand.
minor comments (5)
  1. [Eq. (3) and Appendix A, Eq. (A.12)] The definition of the energy-momentum tensor is written as Tαβ = −2√−g [∂(√−gLM)/∂g^αβ − ∂σ(...)], which has the wrong power of √−g; the standard definition is Tαβ = −(2/√−g)[∂(√−gLM)/∂g^αβ − ∂σ(...)]. This appears to be a typographical error but should be corrected.
  2. [§2.2, Eqs. (13)–(17)] The derivation of the power-law relation \dot a = a^{2/E} relies on the assumption that \dot a can be written as a function of a and that the boundary term can be expressed as an exact variation; these assumptions are not physically motivated and are coordinate-dependent (N=1, k=0, boundary at constant r). The constant E is arbitrary, and Eq. (17) is not shown to be the unique consequence of the exact-variation requirement.
  3. [§3.1, Eq. (33)] Equation (33) contains a factor ordering and dimensionally mixed expression (−4ρ0s + 3κρ0d^2 (t+c2)^2)^{1/3} \ddot λ(t)=0; as written, the differential equation for λ(t) is not presented in a transparent dimensionless form, and the reader must infer that the prefactor is multiplied by \ddot λ.
  4. [Figures 1–4] The figures would be clearer if the axis labels and legends explicitly stated the values of the constants used and the normalization convention (3H0^2=1); in particular, the legend lines in Fig. 1 do not match the order of the curves described in the caption.
  5. [General presentation] There are numerous typographical issues, including 'FLR W' instead of 'FLRW' or 'FRW', 'kρef f' instead of 'κρ_eff', and inconsistent notation for the lapse function; these should be corrected in a revision.

Circularity Check

2 steps flagged · score 8.0 of 10

The stiff-matter 'prediction' is an integration constant of a hand-imposed ODE, not a consequence of the boundary term.

  1. fitted input called prediction [Sec. 2.2, Eq. (18) and Sec. 3.1, Eqs. (30)-(32)]
    "For the vanishing of the boundary term, 2a ˙a2 + a2ʨa = D0, (18) where D0 is a constant. ... By using Eq. (19) into Eq. (28) we get 2/3 D0/a3 + c1/a6 = κ/3 ρef f. (30) ... This dependence predicts the existence of a stiff matter fluid as an emergent consequence of including a boundary term in GR."

    Equation (18) is asserted as the vanishing of the boundary term, but it is a bulk ODE with a free constant D0; it does not follow from the surface variation computed in Eqs. (8)-(12). Equation (19) is the general solution of this imposed ODE and contains an arbitrary integration constant c1. Substituting Eq. (19) into Eq. (28) yields Eq. (30), in which c1/a6 is simply the homogeneous integration constant of the chosen ODE. The paper then renames this constant as a stiff-matter density. The 'prediction' therefore reduces to the choice made in Eq. (18): if that ODE is modified or omitted, the 1/a6 term disappears. No boundary-condition input selects c1.

  2. self definitional [Sec. 3.1, Eq. (32)]
    "3 ˙a2/a2 = κρef f = κ(ρ0d/a3 + ρ0s/a6), (32), where we have rewritten D0 and c1 in terms of the present day densities of dust and stiff matter, respectively, D0 = κρ0d/2 for dust, and c1 = κρ0s/3 for stiff."

    The identification is purely by matching the a−6 scaling to the continuity equation ρ = ρ0 a−3(1+ω) with ω = 1. Since c1 is an integration constant of the ODE imposed in Eq. (18), the 'emergent' stiff fluid is the homogeneous solution of that ODE under a new name. This is reinforced by Sec. 3.2, where the cosmological constant and radiation are inserted by adding F1 a3 and R2/a to the same constraint by hand, showing that each fluid is put in through the chosen right-hand side rather than derived from the boundary term.

full rationale

The paper is self-contained and does not rely on self-citations, so the circularity is not a citation-chain problem. The central claim that a boundary term in GR predicts stiff matter rises or falls on Eq. (22), which is the constrained form of Eq. (18). That ODE, d(a2 ˙a)/dt = D0, is introduced with the phrase 'For the vanishing of the boundary term', but the preceding variation of Bσ gives a condition on boundary variations, not this bulk second-order ODE with a free constant D0. Once Eq. (18) is imposed as a semi-holonomic constraint, the general solution contains an integration constant c1, and substituting that solution into the Friedmann equation produces the 1/a6 term. That term is therefore an artifact of the imposed ODE, not an emergent consequence of the boundary term. The subsequent addition of Λ and radiation by adding F1a3 and R2/a to the right-hand side of the same ODE confirms that the method encodes each fluid as a chosen term in the constraint. The stiff-matter 'prediction' is thus equivalent to the choice made in Eq. (18); if that choice is removed, the prediction disappears. This is a reduction by construction, so the circularity score is high.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central derivation relies on a hand-chosen constraint f = 0 rather than on the unmodified variational principle. The resulting dust and stiff matter densities are integration constants, so the model imports the known perfect fluid content rather than predicting it.

free parameters (5)
  • D0 = kappa * rho0d / 2
    Integration constant in Eq. (18) that becomes the dust density; its value is not predicted by the boundary term.
  • c1 = kappa * rho0s / 3
    Integration constant in Eq. (19) that becomes the stiff matter density; can be set to zero, so the stiff component is not forced.
  • F1 = kappa * rho0Lambda
    Hand-added term in Eq. (35) to reproduce the cosmological constant; not derived from the boundary term.
  • R2
    Hand-added term in Eq. (44) to reproduce radiation; not derived from the boundary term.
  • A and E proportionality constants
    Introduced in Eqs. (13) to (17) to force the boundary term to be a total variation; E sets the power law dot a = a^(2/E), but this assumption is not physically motivated and is later abandoned.
assumptions (6)
  • standard math Standard variational principle and Stokes' theorem for the Einstein-Hilbert action
    Used in Sec. 2.1 and Appendix A to derive Eq. (2).
  • domain assumption FLRW metric with k = 0 and N = 1 is the cosmological spacetime
    Eq. (7) and Sec. 2.2; restricts the boundary term analysis to homogeneous isotropic flat cosmology.
  • domain assumption Matter is a perfect fluid whose Lagrangian does not depend on metric derivatives, so G^sigma = 0
    Stated after Eq. (4); standard for minimally coupled perfect fluids.
  • ad hoc to paper The boundary term can be made to vanish by imposing f(a, dot a, ddot a) = 0 via Lagrange multiplier
    Eqs. (22) to (24); this is the central constraint and is not derived from the action's surface term.
  • ad hoc to paper The boundary term can be written as an exact variation only if dot a is a function of a, leading to dot a = a^(2/E) or sums of powers
    Eqs. (13) to (17); an integrability assumption imposed to obtain Eq. (18).
  • ad hoc to paper Additional terms F1 a^3 and R2/a can be added to the constraint because they become negligible at the late-time boundary
    Eqs. (35) and (44); used to recover cosmological constant and radiation, chosen by hand.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Boundary terms in cosmology." pith.science (2026). https://pith.science/paper/2BUU4BTU

@misc{pith2026250523679,
  author       = {Pith},
  title        = {Pith review of: Boundary terms in cosmology},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2BUU4BTU}},
  note         = {Machine review of arXiv:2505.23679}
}
read the original abstract

In the derivation of the Einstein field equations via Hamilton's principle, the inclusion of a boundary term is essential to render the variational problem well-posed, as it addresses variations that do not vanish at the boundary of the spacetime manifold. Typically, this term is chosen as the Gibbons-Hawking-York boundary term. In this work, we propose an alternative treatment of the boundary term within a cosmological framework by employing the Lagrange multiplier method. This approach enforces the vanishing of the boundary term throughout the evolution of the Universe, leading to the prediction of a fluid component that decays as the sixth power of the scale factor. This type of fluid has been studied in the context of the early universe under the name of stiff matter, and it can be related to a scalar field known as kination.

Figures

Figures reproduced from arXiv: 2505.23679 by the authors.

Figure 1
Figure 1. From Eq.(19) we set c2 = √c1/D0. In this qualitative analysis, 3H2 0 = 1. The dashed blue line corresponds to c1 = 0.05, D0 = 0.95, while the black line is for c1 = 0, D0 = 1. For the second constrained Friedmann equation, substituting Eq. (19) into Eq. (29) we obtain  −4ρ0s + 3κρ2 0d (t + c2) 2 1/3 λ¨(t) = 0, (33) with solution λ(t) = c3 + c4t, (34) where c3 and c4 are integration constants that determine the ini… view at source ↗
Figure 2
Figure 2. From the Eq.(36) we set c2 = log D0 + √ 3F1c1  / √ 3F1. Again for this qualitative anal￾ysis, 3H2 0 = 1. The dashed blue line corresponds to c1 = 0.03, D0 = 0.3 and F1 = 0.67, while the black line is for D0 = 0.3 and F1 = 0.7 [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. The dashed blue line and the black line are set at [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: In this qualitative analysis, 3H2 0 = 1. The dashed blue line corresponds to R2 = 0.03, D0 = 0.3 and F1 = 0.62, while the black line is for R2 = 0.03, D0 = 0.3 and F1 = 0.67. becomes √ −g (L + λ(t)f) = 3 κN a 2 a¨ − 3 N˙ κN2 a 2 a˙ + 3 κN aa˙ 2 + a 3Nλ(t) [PITH_FULL_I…

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

25 extracted references · 23 canonical work pages

  1. [1]

    A neumann boundary term for gravity

    Chethan Krishnan and Avinash Raju. A neumann boundary term for gravity. Journal of High Energy Physics, 8, 2017. arXiv:1608.06223

    arXiv 2017

  2. [2]

    Bound- ary conditions for constraint systems in variational principle

    Keisuke Izumi, Keigo Shimada, Kyosuke Tomonari, and Masahide Yamaguchi. Bound- ary conditions for constraint systems in variational principle. Journal of High Energy Physics, 9, 2023

    work page 2023

  3. [3]

    Noether’s theorems and energy in general relativity

    Sebastian De Haro. Noether’s theorems and energy in general relativity. Foundations of Physics, 66, 2021

    work page 2021

  4. [4]

    D. Hilbert. Die grundlagen der physik. Nachrichten von der Gesellschaft der Wis- senschaften zu G¨ ottingen, Mathematisch-Physikalische Klasse, pages 395–407, 1915

    work page 1915

  5. [5]

    C. Lanczos. The Variational Principles of Mechanics. Dover Books On Physics. Dover Publications, 1986

    work page 1986

  6. [6]

    Goldstein, C.P

    H. Goldstein, C.P. Poole, and J.L. Safko. Classical Mechanics. Addison-Wesley Series in Physics. Addison-Wesley, 3rd edition, 2002

    work page 2002

  7. [7]

    Grøn and S

    Ø. Grøn and S. Hervik. Einstein ’s General Theory of Relativity: With Modern Appli- cations in Cosmology. Springer New York, 2007

    work page 2007

  8. [8]

    Sean M. Carroll. Spacetime and Geometry: An Introduction to General Relativity. Cambridge University Press, 7 2019

    work page 2019

Show all 25 references
  1. [9]

    Padmanabhan

    Krishnamohan Parattu, Sumanta Chakraborty, and T. Padmanabhan. Variational principle for gravity with null and non-null boundaries: A unified boundary counter- term. Journal of High Energy Physics, 5, 2016

    2016

  2. [10]

    Boundary Terms of the Einstein–Hilbert Action

    Sumanta Chakraborty. Boundary Terms of the Einstein–Hilbert Action. Fundam. Theor. Phys., 187:43–59, 2017

    2017

  3. [11]

    Ya. B. Zel’dovich. The equation of state at ultrahigh densities and its relativistic limitations. Soviet Physics JETP, 7:1163–1167, 1961. September 4, 2025 18:21 WSPC/INSTRUCTION FILE ws-ijmpd 16 A. Cuevas, J.Chagoya, C.Ortiz

    1961

  4. [12]

    Electroweak Baryogenesis and the Expansion Rate of the Universe

    Michael Joyce. Electroweak Baryogenesis and the Expansion Rate of the Universe. Phys. Rev. D, 55:1875–1878, 1997

    1997

  5. [13]

    Sur les probl` emes aux d´ eriv´ ees partielles et leur signification physique

    Jacques Hadamard. Sur les probl` emes aux d´ eriv´ ees partielles et leur signification physique. Princeton university bulletin, pages 49–52, 1902

    1902

  6. [14]

    Boundary terms in the action principles of general relativity

    James York. Boundary terms in the action principles of general relativity. Found. Phys., 16:249–257, 1986

    1986

  7. [15]

    G. W. Gibbons and S. W. Hawking. Action Integrals and Partition Functions in Quantum Gravity. Phys. Rev. D, 15:2752–2756, 1977

    1977

  8. [16]

    Chru´ sciel and H.F

    P.T. Chru´ sciel and H.F. Friedrich. The Einstein Equations and the Large Scale Be- havior of Gravitational Fields: 50 Years of the Cauchy Problem in General Relativity. Birkh¨ auser, Basel, 2004

    2004

  9. [17]

    On the well-posedness of the vacuum einstein’s equations, 2009

    Lavi Karp. On the well-posedness of the vacuum einstein’s equations, 2009. arXiv:0906.0137

    2009 arXiv

  10. [18]

    The initial value problem in general relativity

    James Isenberg. The initial value problem in general relativity. In Springer Handbook of Spacetime, pages 303–321. Springer, 2014

    2014

  11. [19]

    J. A. Peacock. Cosmological physics. Cambridge university press, 1999

    1999

  12. [20]

    Methods of Mathematical Physics, volume 1

    Richard Courant and David Hilbert. Methods of Mathematical Physics, volume 1. Wiley, New York, 1989

    1989

  13. [21]

    A. G. Riess, W. H. Press, and R. P. Kirshner. Type ia supernovae and the accelerating universe: A new approach. The Astronomical Journal, 116(3):1009–1026, 1998

    1998

  14. [22]

    Schmidt, Adam G

    Saul Perlmutter, Brian P. Schmidt, Adam G. Riess, et al. Supernovae, dark energy, and the accelerating universe. The Astrophysical Journal, 517(2):565–586, 1999

    1999

  15. [23]

    Planck 2018 results

    Planck Collaboration. Planck 2018 results. vi. cosmological parameters. Astron- omy & Astrophysics, 641:A6, 2020. Erratum: https://doi.org/10.1051/0004-6361/ 201833910e

    2018 doi

  16. [24]

    Riess, Stefano Casertano, Wenlong Yuan, Lucas M

    Adam G. Riess, Stefano Casertano, Wenlong Yuan, Lucas M. Macri, and Dan Scolnic. Large magellanic cloud cepheid standards provide a 1 foundation for the determi- nation of the hubble constant and stronger evidence for physics beyond λcdm. The Astrophysical Journal, 876(1):85, 2019

    2019

  17. [25]

    Can stiff matter solve the hubble tension? Axioms, 13:526, 08 2024

    Øyvind Grøn. Can stiff matter solve the hubble tension? Axioms, 13:526, 08 2024

    2024

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.