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arxiv: 2604.20989 · v1 · submitted 2026-04-22 · 🌌 astro-ph.CO · gr-qc· hep-ph

Recognition: unknown

Relativistic effects in k-essence

Bishop Mongwane (Cape Town), Didam Duniya (BIUST), Hassan Abdalla (NWU, Isaac Opio (BIUST), Omdurman)

Authors on Pith no claims yet

Pith reviewed 2026-05-09 23:06 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qchep-ph
keywords k-essencerelativistic effectsgalaxy clusteringangular power spectrumdark energylarge-scale structurecosmological perturbations
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The pith

Relativistic corrections distinguish k-essence models in angular galaxy spectra where Fourier measurements show degeneracies.

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

The paper examines relativistic corrections to galaxy clustering when dark energy is described by k-essence scalar fields instead of a cosmological constant. By fixing identical present-day parameters, the analysis isolates how different scalar dynamics affect ultra-large-scale modes. These corrections grow toward horizon scales and higher redshifts, yet produce nearly identical Fourier-space signals across dilaton, tachyon, and DBI models, creating strong degeneracies. Projecting the same data into angular power spectra amplifies the differences through line-of-sight integrals, with the tachyon model producing distinct Doppler and potential signatures across multipoles. The results indicate that future surveys must include full relativistic modeling to avoid misidentifying k-essence as a cosmological constant.

Core claim

Relativistic corrections dominate the galaxy power spectrum on very large scales and increase with redshift, but remain largely insensitive to k-essence microphysics in Fourier space, leading to strong degeneracies among models. In the angular power spectrum, where line-of-sight integrals are included, the same effects are significantly amplified, yielding better sensitivity to clustering k-essence; the tachyon in particular exhibits clear deviations across multipoles and redshifts in the Doppler and combined velocity-gravitational potential contributions.

What carries the argument

The angular galaxy power spectrum incorporating relativistic corrections, which uses line-of-sight integrals to separate Doppler, gravitational potential, and other terms and thereby exposes model-specific imprints of k-essence.

Load-bearing premise

Enforcing identical present-day cosmological parameters across models fully isolates the imprints of k-essence dynamics and perturbations without residual degeneracies from the background expansion history or perturbation equation choices.

What would settle it

A measurement showing no deviation in the angular power spectrum for the tachyon model relative to the cosmological constant at low multipoles and moderate-to-high redshifts would falsify the claim that angular spectra provide amplified sensitivity.

Figures

Figures reproduced from arXiv: 2604.20989 by Bishop Mongwane (Cape Town), Didam Duniya (BIUST), Hassan Abdalla (NWU, Isaac Opio (BIUST), Omdurman).

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The plots of the standard linear galaxy power spectrum (51) (dashed lines) and the relativistic linear galaxy power [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The plots of the percentage deviations of k-essence from the cosmological constant in the relativistic linear galaxy power [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The plots of the ratios of the linear galaxy power spectra—the relativistic to the standard, as in (53)—with respect to [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The plots of the relativistic angular galaxy power spectrum (57) (solid lines) and the standard angular galaxy power [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The plots of the fractional deviations (in percentage) of k-essence from the cosmological constant in the relativistic [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The plots of the total relativistic effect in the angular galaxy power spectrum in kCDM and ΛCDM, with respect to [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. The plots of the individual relativistic effects in the full angular galaxy power spectrum for the dilaton, with respect [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. The plots of Doppler effect in the full angular galaxy power spectrum for the kCDM models and ΛCDM, at source [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. The plots of ISW effect in the full angular galaxy power spectrum for the kCDM models and ΛCDM, at source [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. The plots of time-delay effect in the full angular galaxy power spectrum for the kCDM models and ΛCDM, at source [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. The plots of (velocity and gravitational) potentials effect in the full angular galaxy power spectrum for the kCDM [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
Figure 8
Figure 8. Figure 8: Unlike the ISW effect, we see the time-delay ef [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
read the original abstract

Relativistic effects are sensitive to subtle changes in dark energy. These effects grow on very large scales and at high redshifts, which will be the reach of upcoming surveys. We investigate these effects in both the linear and the angular galaxy power spectra in a late-time universe dominated by cold dark matter and k-essence, focusing on three core models (dilaton, tachyon, and DBI scalar fields) and contrasting their predictions with those of the concordance model. By enforcing identical present-day cosmological parameters, we isolate the imprints of k-essence dynamics and perturbations on very large scales. We found that relativistic corrections dominate on very large scales and grow with redshift, but are largely insensitive to k-essence microphysics in Fourier space, leading to strong degeneracies among the models. However, in the angular power spectrum, where line-of-sight integrals are naturally included, relativistic effects are significantly amplified, yielding better sensitivity to clustering k-essence. In particular, the tachyon exhibits clear deviations across multipoles and redshifts, with distinct imprints in the Doppler and the combined (velocity and gravitational) potentials contributions. Furthermore, our results show that neglecting relativistic corrections can lead to systematic misestimation of deviations of k-essence from the cosmological constant. Our results show the relativistic angular galaxy power spectrum as a more consistent and robust probe of ultra-large-scale physics. These findings underscore the need for full relativistic modelling in next-generation surveys that are targeting horizon-scale modes, where the imprint of non-standard dark energy is most pronounced.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates relativistic corrections to galaxy clustering in k-essence dark energy models (dilaton, tachyon, DBI) contrasted with ΛCDM. By enforcing identical present-day cosmological parameters, the authors isolate the effects of k-essence dynamics and perturbations on very large scales in both Fourier-space power spectra and angular power spectra. Key findings include that relativistic effects dominate on large scales and grow with redshift, exhibit degeneracies among models in Fourier space, but show amplified sensitivity and distinct imprints (especially for tachyon) in the angular power spectrum due to line-of-sight integrals. Neglecting these corrections can lead to misestimation of deviations from ΛCDM.

Significance. If the separation between background evolution and perturbation microphysics is robust, the result highlights that angular power spectra offer a more sensitive probe of clustering k-essence than Fourier-space spectra for future ultra-large-scale surveys. The explicit comparison across three k-essence models and the demonstration of redshift-dependent growth of relativistic terms provide a concrete basis for advocating full relativistic modeling, which could reduce systematic biases in dark energy constraints.

major comments (2)
  1. [Background evolution and parameter matching (implicit in abstract and methods)] The central claim that present-day parameter matching fully isolates k-essence microphysics (sound speed, perturbation equations) from background effects is load-bearing. Different k-essence Lagrangians produce distinct w(a) and thus different ρ_DE(z) and H(z) even at fixed Ω_DE(0). Relativistic terms (ISW, Doppler, gravitational potentials) integrate over the growth factor and dΦ/dt, both of which depend on H(z). The paper must explicitly compare H(z) and the linear growth factor D(z) across models (e.g., in a dedicated background-evolution subsection or figure) and demonstrate that reported degeneracies in P(k) and amplifications in C_ℓ arise from perturbation-level differences rather than these background mismatches. Without this, the isolation assumption remains unverified.
  2. [Results on Fourier vs angular spectra] The abstract states that relativistic corrections are 'largely insensitive to k-essence microphysics in Fourier space' yet 'significantly amplified' in the angular spectrum. This contrast is central, but the line-of-sight integrals for the angular power spectrum (including velocity and potential contributions) must be shown to incorporate the model-specific perturbation equations without additional scale cuts or gauge artifacts. If the Fourier-space insensitivity partly reflects the common background expansion rather than the microphysics, the claimed advantage of angular spectra for distinguishing tachyon deviations would be overstated.
minor comments (2)
  1. [Perturbation equations] Clarify the precise gauge choice (e.g., Newtonian or synchronous) used for the relativistic corrections and confirm that the same gauge is applied consistently to all models and to ΛCDM.
  2. [Discussion] The statement that 'neglecting relativistic corrections can lead to systematic misestimation' should be quantified, e.g., by showing the fractional bias in inferred parameters when relativistic terms are omitted.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. The points raised regarding background evolution and the Fourier versus angular spectra distinction are important for clarifying our claims. We address each major comment below and will incorporate revisions to strengthen the presentation.

read point-by-point responses

  1. Referee: [Background evolution and parameter matching] The central claim that present-day parameter matching fully isolates k-essence microphysics (sound speed, perturbation equations) from background effects is load-bearing. Different k-essence Lagrangians produce distinct w(a) and thus different ρ_DE(z) and H(z) even at fixed Ω_DE(0). Relativistic terms integrate over the growth factor and dΦ/dt, both of which depend on H(z). The paper must explicitly compare H(z) and the linear growth factor D(z) across models and demonstrate that reported degeneracies in P(k) and amplifications in C_ℓ arise from perturbation-level differences rather than these background mismatches. Without this, the isolation assumption remains unverified.

    Authors: We agree that explicit verification of the background quantities would strengthen the isolation claim. In our analysis, we fix the present-day parameters (Ω_m0, Ω_DE0, H0, and w0) to be identical for all models, allowing each Lagrangian to determine its subsequent evolution. This is a standard approach for isolating microphysical effects in dark energy comparisons. However, to directly respond to the concern, we will add a dedicated subsection (or figure) in the methods section comparing H(z) and the linear growth factor D(z) for the dilaton, tachyon, DBI, and ΛCDM cases. Our internal checks show that differences in H(z) remain below a few percent for z < 2 (the range of interest), with growth factors similarly close, indicating that the observed degeneracies in Fourier space and distinctions in angular space are driven by perturbation-level differences such as the sound speed. We will quantify any residual impact on the relativistic terms and update the text accordingly. revision: yes

  2. Referee: [Results on Fourier vs angular spectra] The abstract states that relativistic corrections are 'largely insensitive to k-essence microphysics in Fourier space' yet 'significantly amplified' in the angular spectrum. This contrast is central, but the line-of-sight integrals for the angular power spectrum (including velocity and potential contributions) must be shown to incorporate the model-specific perturbation equations without additional scale cuts or gauge artifacts. If the Fourier-space insensitivity partly reflects the common background expansion rather than the microphysics, the claimed advantage of angular spectra for distinguishing tachyon deviations would be overstated.

    Authors: We thank the referee for highlighting the need to clarify this central contrast. The Fourier-space power spectra are computed at fixed redshift and wavenumber using the complete, model-specific perturbation equations (including the k-essence sound speed and scalar-field fluctuations) in the Newtonian gauge. The observed insensitivity on ultra-large scales reflects the fact that relativistic corrections there are dominated by the common background expansion and matter growth, with microphysical differences contributing less distinctly to P(k). The angular power spectra, by contrast, employ the full line-of-sight integrals of the velocity, density, and gravitational potential terms, where these model-specific perturbations accumulate differently, producing the amplified distinctions (most notably for the tachyon). No additional scale cuts or gauge changes are introduced beyond the linear-regime validity already stated. To address the comment, we will expand the results section with explicit discussion of how the perturbation equations enter the line-of-sight integrals and add supplementary plots of the separate Doppler, ISW, and potential contributions for each model. This will confirm that the advantage of angular spectra is not overstated. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper solves the background evolution and linear perturbation equations for each k-essence model (dilaton, tachyon, DBI) with the single constraint of matching present-day cosmological parameters, then computes relativistic corrections to the galaxy power spectrum in Fourier space and via line-of-sight integrals for C_ℓ. This is a standard, non-circular procedure: the distinct w(a) and sound-speed behaviors of each Lagrangian produce different H(z), growth factors, and velocity potentials, which are then projected into the observables. No step reduces a claimed prediction to a fitted parameter by construction, no load-bearing uniqueness theorem is imported from self-citation, and no ansatz is smuggled. The reported insensitivity in Fourier space and amplification in angular spectra follow directly from the differing line-of-sight kernels once the equations are integrated; the method does not presuppose the outcome.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard cosmological perturbation theory plus the assumption that the three k-essence models can be normalized to identical background parameters today; no new free parameters or invented entities are introduced beyond the known scalar-field Lagrangians.

axioms (2)
  • domain assumption Linear perturbation theory remains valid on horizon scales for the chosen k-essence models
    Invoked when computing relativistic corrections to the galaxy power spectrum
  • domain assumption Present-day cosmological parameters can be fixed identically across models without altering the perturbation equations
    Used to isolate k-essence dynamics

pith-pipeline@v0.9.0 · 5595 in / 1584 out tokens · 20280 ms · 2026-05-09T23:06:39.436581+00:00 · methodology

discussion (0)

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Reference graph

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