arXiv subjects

Eleonora Di Valentino

Publications and source records attributed to Eleonora Di Valentino.

At least 19 recordsLinked to original sources

arXiv2026

When, Why, and How CMB Compression Fails

We test when compressed CMB likelihoods can be reliably used to constrain new physics beyond $Λ$CDM, formulating concrete criteria for \textit{when}, \textit{why}, and \textit{how} CMB compression fails. We derive our conclusions by exploring a broad set of models that modify different aspects of the cosmological evolution, including late-time dark-energy dynamics, non-standard late-time dark-matter evolution through interactions or decay, and dark-matter models with persistently non-standard redshift evolution. For each case, we compare the results obtained from data combinations based on the full Planck-CMB likelihood with their counterparts based on a compressed CMB likelihood calibrated in $Λ$CDM. We find that the compression remains accurate for late-time dark-energy extensions that preserve the dark-matter background evolution and do not introduce significant additional perturbative effects. By contrast, modifying the dark-matter evolution breaks the mapping between the present-day matter density and the matter density at the epochs relevant to the CMB, causing the compressed constraints to fail even when the modification acts exclusively at late times. In these cases, the compressed likelihood can drastically alter the geometry of the multidimensional posterior distributions, shifting their centers, producing strongly anisotropic deformations, reordering principal modes, and generating genuine mixing and rotation of their eigendirections. These multidimensional distortions propagate into substantially incorrect marginalized constraints on cosmological parameters, with differences between the full and compressed analyses reaching nearly an order of magnitude in some of the cases studied here.

astro-ph.CO↗

arXiv2026

Testing cosmic acceleration from thermogravity without vacuum energy

We present a first background-level observational test of a thermogravity theory in which the Einstein equations are clipped to a trace-free version, the cosmological constant $Λ$ does not gravitate, and controlled violations of energy conservation obstruct the usual reinstatement of $Λ$ as an integration constant. We therefore set $Λ=0$ and ask whether late-time acceleration can instead be generated solely by energy non-conservation, with no extra background parameter relative to flat $Λ\mathrm{CDM}$. We contrast a minimal universal implementation with a model in which only CDM partakes in non-conservation. The universal model is strongly disfavored when combining Supernovae and BAO distances, with the inclusion of DESI BAO worsening the fit by $Δχ^2\simeq 51$ relative to $Λ\mathrm{CDM}$, because matter creation ties the intermediate-redshift normalization of $H(z)$ too rigidly to the present acceleration. This conclusion, however, should be interpreted with caution, since universal non-conservation would modify the observational dictionary itself. By contrast, restricting non-conservation to CDM leaves baryonic and photon observables unaffected at the background level and therefore allows a self-contained analysis. The resulting $ξ\mathrm{CDM}$ model, which can be thought of as a one parameter extension of $Λ\mathrm{CDM}$, provides an improved fit relative to $Λ\mathrm{CDM}$ for the background dataset combinations considered, with improvements reaching $Δχ^2=-4.85$ and a maximum Bayesian preference of $\ln\mathcal{B}=2.77$. However, when the BAO ruler is calibrated using BBN or CMB information, the reduced effective early-time CDM density increases the sound horizon and drives $H_0$ towards lower values, thereby increasing rather than alleviating the tension with the distance-ladder calibration.

astro-ph.CO↗

arXiv2026

When One-Parameter Dark Energy Makes Neutrinos Physical Again

A puzzling implication of current data interpreted in the $Λ$-Cold Dark Matter cosmology is the preference for a negative sum of neutrino masses. Moving to $w_0w_a$CDM brings an appreciable fraction of the neutrino mass posterior back to positive values, while the constant equation-of-state dark energy case $w$CDM does not. We investigate a variety of one-parameter dynamical dark energy equations of state (DE EoS) whose redshift evolution is controlled by a single free parameter, each representing distinct physical properties, to understand whether a two-parameter DE EoS is required to bring the neutrino mass into the positive region. The conclusion is that certain one-parameter DE EoS can suffice, implying that the data are pointing toward physical characteristics rather than a broad degeneracy. This behavior effectively lowers the dark energy density at high redshift, allowing the sum of neutrino masses to shift toward the physical region. The required characteristics are identified as phantom dark energy at high redshift, crossing $w=-1$ at lower redshift.

astro-ph.CO↗

arXiv2026

Hunting Thermal Relics in the DESI DR1 Ly$α$ Forest

We investigate constraints on additional relativistic species and thermal sterile neutrinos using the DESI DR1 one-dimensional Lyman-$α$ forest power spectrum, combined with Planck 2018 CMB and DESI DR2 BAO measurements. We consider both the $Λ$CDM+$N_{\rm eff}$ extension and a thermal with a different-temperature sterile-neutrino (DTS) scenario, in which the sterile relic can be colder than the standard neutrino background. We first validate the DESI two-parameter $P_{\rm 1D}$ compression for the DTS model, finding that the residual cosmological dependence not captured by the compressed parameters remains below 0.15%. No significant evidence for additional radiation or a sterile component is found. For $Λ$CDM+$N_{\rm eff}$, we obtain $N_{\rm eff}<3.41$ at 95% credibility from CMB+DESI-BAO+DESI-$P_{\rm 1D}$. In the DTS scenario, the full CMB+DESI-BAO+DESI-$P_{\rm 1D}$ combination yields the stringent bound $m_s^{\rm eff}<0.061\,{\rm eV}$, highlighting the complementarity of BAO and Lyman-$α$ information in constraining the massive sterile abundance. We further interpret the allowed $ΔN_{\rm eff}$ in terms of thermal light relics, deriving lower limits on their decoupling temperatures that reach the QCD epoch.

astro-ph.CO↗

arXiv2026

Cosmological anatomy of interacting dark energy

Interacting dark energy (IDE) models, featuring interactions between dark matter (DM) and dark energy (DE), have received significant renewed interest. However, little attention has been devoted to understanding their genuine cosmological signatures, with comparisons against $Λ$CDM often carried out at fixed cosmological parameters. Considering the widely studied model with energy exchange rate proportional to the DE density, we carry out a three-level sequence of comparisons, starting from the naïve fixed-parameter comparison, then compensating for shifts in $θ_s$ and $z_{\text{eq}}$, and then removing effects due to the modified background. We show that fixing $θ_s$ and $z_{\text{eq}}$ leads to pre-recombination evolutions of the Weyl potential, photon monopole, and baryon velocity which are nearly identical to their $Λ$CDM counterparts, and hence virtually indistinguishable Cosmic Microwave Background (CMB) temperature power spectra. Comparing IDE to a non-interacting $w$CDM model with the same background, we find small scale-dependent signatures in CMB lensing. We find larger differences in the matter power spectrum, reflecting the different values of $Ω_m$ resulting from the different partition of the dark sector into DM and DE, with only percent-level differences remaining once we compare $Ω_m^2P_m(k)$, indicating the importance of high-fidelity determinations of $Ω_m$. Our controlled comparison strategy can be a powerful tool for a wide range of models beyond $Λ$CDM.

astro-ph.CO↗

arXiv2026

Peering Beyond the Veil of Last Scattering: A View of the Universe with CMB Spectral Distortions

The frequency spectrum of the cosmic microwave background is the most precise blackbody ever measured in nature, with deviations constrained at the level of almost one part per million from the COBE satellite. Nevertheless, departures away from a perfect blackbody are present in standard $Λ$CDM cosmology, lurking just beneath the surface of our current observational bounds. These spectral distortions provide invaluable information on our thermal history in both the post- and pre-recombination epochs, allowing us to peer beyond last scattering and into the primordial Universe. Here, we present an overview of the underlying physics responsible for generating CMB spectral distortions at all epochs. As an illustration of this rich physics, we review a comprehensive set of mechanisms capable of generating distortions both within and beyond the standard $Λ$CDM paradigm. We also discuss the information that can be gleaned by going beyond the monopole (sky-averaged) spectrum and exploiting the spatial information present in anisotropic spectral distortions. To supplement our discussion of the diverse science of spectral distortions, we provide an overview of the upcoming and proposed experimental landscape. We highlight that the combination of the TMS, COSMO, and BISOU experiments will provide the first discovery of a monopole $y$-type distortion within the coming decade. From space, the proposed FOSSIL experiment is forecasted to improve upon the original COBE/FIRAS measurement by roughly three orders of magnitude in sensitivity, bringing with it the detection of the $Λ$CDM $μ$-type distortion sourced by the dissipation of small scale acoustic modes in the pre-recombination plasma. With transformational measurements on the horizon, CMB spectral distortions offer a uniquely sensitive probe of the thermal history of the Universe at redshifts $z \lesssim 2 \times 10^6$.

astro-ph.CO↗

arXiv2026

One-parameter dynamical dark energy: Hints for oscillations

There is mounting evidence from multiple cosmological probes that dark energy may be dynamical, with an equation of state that evolves over cosmic time. While this evidence is typically quantified using the Chevallier-Polarski-Linder (CPL) parametrization, based on a linear expansion of $w(a)$ in the scale factor, non-parametric reconstructions frequently suggest non-linear features, particularly at late times. In this work, we investigate four minimal one-parameter models of dark energy with non-linear dependence on the scale factor. These models are constrained using Cosmic Microwave Background (CMB) data from Planck, lensing reconstruction from ACT-DR6, Baryon Acoustic Oscillation (BAO) measurements from DESI-DR2, and three Type-Ia supernovae (SNe) samples (PantheonPlus, DESY5, and Union3), considered independently. Although our conclusions depend on the choice of SNe sample, we consistently find a preference, as measured by the chi-squared statistic and the Bayesian evidence, for these dynamical dark energy models over the standard $Λ$CDM model. Notably, with the PantheonPlus dataset, one model shows strong Bayesian evidence ($Δ\ln B \simeq 4.5$) against CPL, favoring an equation of state that peaks near $a \simeq 0.7$ and oscillates near the present day. These results highlight the impact of SNe selection and contribute to the growing collection of evidence for late-time deviations from $Λ$CDM.

astro-ph.CO↗

arXiv2026

Late-Time Emergence of Dark Energy and Its Interaction with Dark Matter

We present an interacting scenario between dark energy (DE) and dark matter (DM), where DE has an emergent nature, that means, DE was absent in the early universe but it becomes effective only at late times. We consider two specific emergent DE models, one with no free parameters and the other featuring two parameters describing the speed and epoch of the transition. We constrain both scenarios using the cosmic microwave background (CMB) measurements from the Planck 2018 release, baryon acoustic oscillations from DESI DR2, and three different compilations of Type Ia supernovae (PantheonPlus, DES-Dovekie, and Union3). Our analysis indicates that current cosmological probes are not able to tightly constrain the speed of the transition. For both scenarios, the posterior distribution of the interaction parameter is shifted away from zero at more than 95\% CL whenever the CMB data are combined with any of these additional probes, with the preferred direction corresponding to a transfer of energy from DE to DM. While CMB alone yields a high value of $H_0$, in agreement with local determinations, this effect is reduced when DESI is added and disappears once supernova data are included. In contrast, the clustering parameter $S_8$ is consistently shifted toward lower values in the combined datasets, and it is correlated with the preference for a negative interaction. However, according to the $Δχ^2_{\rm min}$ and Bayesian evidence, none of the interacting models is favored over $Λ$CDM or $w_0w_a$CDM, indicating that the interaction does not rescue these emergent DE models. Our results therefore highlight the limitations of these scenarios in addressing current cosmological tensions, while pointing to the crucial role of future data in further assessing their viability.

astro-ph.CO↗

arXiv2026

Are Cosmological Data Excluding Sterile Neutrinos or Only the Fully Thermalized Limit?

We present a cosmological reassessment of light sterile-neutrino scenarios, examining whether current observations exclude sterile neutrinos as a class or primarily constrain the fully thermalized case. We consider three distinct realizations: (i) a fully thermalized sterile species (FTS), (ii) a different-temperature sterile-neutrino thermal relic (DTS) relative to the active neutrino background and (iii) a Dodelson--Widrow-like (DW) sterile neutrino with reduced phase-space normalization. Constraints are derived within both $Λ$CDM and the CPL dynamical dark-energy framework using combinations of Planck-CMB data, DESI DR2 BAO measurements, and the PantheonPlus and Union3 Type Ia supernova samples. For baseline data combinations without a local $H_0$ prior, the FTS scenario is strongly disfavored in both cosmological models. Adding the local $H_0^{\rm DN}$ prior allows $Λ$CDM+FTS to accommodate the high local $H_0$ value and become statistically competitive with standard $Λ$CDM once SNIa data are included, although the sterile-neutrino mass remains consistent with zero. By contrast, partially populated sterile-neutrino scenarios remain viable: the DW realization is broadly compatible with current observations, while the DTS scenario yields the least cosmological pressure among the cases considered. Overall, cosmological data mainly require a strongly suppressed effective sterile abundance, leading to tight constraints on \textbf{$m_s^{\rm eff}$} while allowing substantially weaker bounds on the physical sterile mass. We conclude that current observations do not generically exclude sterile neutrinos, but rather place strong pressure on fully thermalized or highly populated scenarios, highlighting the importance of production history and phase-space distribution when interpreting cosmological constraints.

astro-ph.CO↗

arXiv2026

Testing Matter Diffusion with Late-Time Cosmological Observations

We investigate a class of late-time cosmological models derived from the phenomenological framework of variable matter diffusion. In these scenarios, energy-momentum conservation requires a continuous energy exchange between matter and an effective scalar-field dark-energy component, $ϕ$. We consider a baseline constant-diffusion scenario alongside four non-linear power-law parametrizations, in which the diffusion coefficient evolves as a function of the scale factor, matter density, scalar-field density, or Hubble expansion rate. To assess their cosmological viability, we implement these models within \texttt{SimpleMC} and constrain them using late-time observations, including cosmic chronometers, baryon acoustic oscillation measurements, Type Ia supernovae with and without the local SH0ES calibration. In the absence of the local calibration, the diffusion models yield only modest improvements in the fit ($Δχ^2 \approx -4$), performing comparably to the CPL parametrization while exhibiting negative Bayesian log-evidence differences relative to $Λ$CDM. In contrast, including SH0ES leads to a dramatic reduction in the minimum $χ^2$ ($Δχ^2 \approx -22$) and decisive Bayesian evidence in favor of the diffusion framework ($Δ\ln\mathcal{Z} \approx 9$). Remarkably, the single-parameter constant-diffusion model accounts for virtually all the statistical improvement, outperforming the CPL parametrization by more than 10 units in $χ^2$ and more than 8 units in $Δ\ln\mathcal{Z}$. The four non-linear extensions provide only negligible additional improvements ($Δχ^2 \approx -1$), indicating that current late-time background observations favor the presence of a non-vanishing matter-diffusion interaction over $Λ$CDM, while providing no statistically significant evidence for a specific time-dependent functional form of the diffusion coefficient.

astro-ph.CO↗

arXiv2026

Intertwined Constraints in Extended Cosmologies: Dark Energy, Curvature, Neutrinos, and Inflation

We present a systematic reassessment of cosmological constraints beyond $Λ$CDM by progressively relaxing the assumptions underlying Dark Energy (DE), Curvature, Neutrinos, and Inflation. Using the latest CMB data together with DESI BAO and different SN catalogues, we show that the preference for dynamical DE persists across all the extended cosmologies considered. $Ω_k$ remains compatible with flatness, despite a mild $2.2σ$ preference for $Ω_k>0$ that is substantially degraded in dynamical DE extensions. Constraints on $N_{\rm eff}$ are broadly consistent with $N_{\rm eff}=3.04$, while cosmological upper limits on the total neutrino mass vary substantially across the cosmologies explored, ranging from $\sum m_ν\lesssim 0.06$ eV to $\lesssim 0.2$ eV. We quantify both the preference for the mass ordering and the apparent tension between cosmology and oscillation experiments, showing that they are strongly framework dependent. We find no evidence for inflationary tensor modes, with $r\lesssim 0.035$. Constraints on the spectral index $n_s$ show significant model dependence. Allowing for the scalar runnings produces a mild shift toward $α_s>0$ and $β_s>0$ that can reabsorb the preference for larger $n_s$ found in small-scale CMB data, although both $α_s$ and $β_s$ remain consistent with zero at $\sim 1.5σ$. We highlight the implications for slow-roll inflation and benchmark models. None of the extensions considered here can resolve the $H_0$ tension. We discuss the implications for $Ω_m$ and $S_8$. Overall, dynamical DE is the only significant deviation from $Λ$CDM and has the strongest impact on the inferred conclusions in the other sectors of the model.

astro-ph.CO↗

arXiv2026

Evolving Dark Energy Is Vacuum Energy After All

We investigate a physically motivated model of dynamical dark energy arising from the non-perturbative topological structure of the Quantum Chromodynamics (QCD) vacuum. The model introduces no new fundamental field or propagating degree of freedom: the dark energy (DE) density emerges as a global vacuum response to an expanding spacetime. We develop the first comprehensive cosmological implementation of this QCD-DE scenario and confront it with current observations, including Planck, ACT and SPT-3G cosmic microwave background data, DESI DR2 baryon acoustic oscillation measurements, and Type Ia supernova samples from Pantheon+ and DES-Dovekie. We compare the model with $Λ\mathrm{CDM}$ and $w_0w_a\mathrm{CDM}$ cosmologies. The model provides an excellent fit to the data and reproduces the late-time DE evolution preferred by DESI. The model naturally predicts effective phantom crossing behaviour at intermediate redshifts ($z\sim0.67$) while avoiding the instabilities associated with phantom scalar fields. Using goodness-of-fit statistics and Bayesian model-selection tools, including Akaike and Deviance Information Criteria and Bayesian evidence estimated from Markov-Chain Monte Carlo chains, we find that the QCD-induced model is consistently favoured over $Λ\mathrm{CDM}$ for the full combination of early and late-time datasets. Unlike the conventional descriptions of dynamical DE, support for QCD-DE in Bayesian evidence remains more consistent across datasets, suggesting that a physically motivated departure from a cosmological constant may provide a more economical description of the expansion history preferred by current observations.

astro-ph.CO↗

arXiv2026

General Relativistic Entropic Acceleration at the perturbation level: a CLASS implementation and first Boltzmann-code constraints

General Relativistic Entropic Acceleration (GREA) attributes the late-time acceleration of the Universe to the entropy growth of the causal cosmological horizon, without a cosmological constant, with a phenomenology fixed by the single $\mathcal{O}(1)$ parameter $α$. The model has so far been confronted with data only at the background level. We present its first implementation within an Einstein-Boltzmann solver: the GREA background is integrated directly into CLASS, while the entropic component is evolved as an effective fluid regulated by the parametrized-post-Friedmann scheme, giving access to the full CMB and matter power spectra. A Markov-chain Monte Carlo analysis with COBAYA against the full primary-CMB likelihoods, DESI DR2 BAO and Type Ia supernovae constrains the coupling $α\sim 1$, in excellent agreement with the theoretical prediction, with a fit matching $Λ$CDM to within $|Δχ^2| \lesssim 6$ despite the addition of a single free parameter. The equation of state inferred from the data agrees with binned, model-independent reconstructions and exhibits a second crossing of the phantom divide at $z \simeq 2$, a distinctive prediction of the thermodynamic dynamics rather than of an imposed parametrization.

gr-qc↗

arXiv2026

Constraining the axiverse with reionization

Axions that couple to electromagnetism are produced in the early Universe by, among other channels, freeze-in via the Primakoff process. For sufficiently large axion masses, the same coupling causes the axions to decay into two photons, which subsequently ionize the intergalactic medium. If this decay occurs in the redshift range $20 \lesssim z \lesssim 1100$, then the contribution to the cosmic microwave background optical depth $τ_{\rm reio}$ can lead to a conflict with observations, excluding models with sufficiently strongly coupled, heavy axions and high reheating temperatures, $T_{\rm reh}$. Using large ensembles of explicit type IIB string theory models with up to $h^{1,1} = 100$ axions, we compute the full cosmic reionization history caused by the decays of multiple axions. We compare this to the posterior on the high-$z$ component of $τ_{\rm reio}$ derived from parametric-independent constraints on the ionization state of the Universe, obtained in a full \textit{Planck} analysis presented in a companion paper. For $h^{1,1} = 20, 50, 100$, we find that approximately 15\%, 15\%, and 10\% of the models in the ensemble prefer $T_{\rm reh} \lesssim 10^{10}\,\text{GeV}$ at 95\% CL. We provide a publicly available code at:~\href{https://github.com/ZiwenYin/Reionization-with-multi-axions-decay}{github.com/ZiwenYin/Reionization-with-multi-axions-decay}, which computes the reionization history for arbitrary ensembles of decaying axions. Our analysis opens the door for future large-scale work studying the preference for low-temperature reheating in models with multiple axions.

hep-ph↗

arXiv2026

Robust Preference for Dark Sector Interactions

Recent DESI baryon acoustic oscillation data reveal deviations from $Λ$CDM cosmology, conventionally attributed to dynamical dark energy (DE). We demonstrate that these deviations are equally, if not better, explained by interactions between dark matter and dark energy (IDE), without requiring a time-varying DE equation of state. Using a unified framework, we analyze two IDE models - coupled quintessence and coupled fluid - against the latest CMB (Planck, ACT, SPT), DESI BAO, and SN (including DES-Dovekie recalibrated) data. Both IDE scenarios show robust evidence for non-vanishing interactions at the 3-5$σ$ level, with marginalized constraints significantly deviating from the $Λ$CDM limit. This preference persists even under DES-Dovekie SN recalibration, which weakens dynamical DE evidence. Crucially, for the same number of free parameters, IDE models provide fits to low- and high-redshift data that match or exceed the performance of the CPL dynamical DE parametrization. Our results establish IDE as a physically motivated alternative to dynamical DE, highlighting the necessity of future cosmological perturbation measurements (e.g., weak lensing, galaxy clustering) to distinguish between these paradigms.

astro-ph.CO↗

arXiv2026

Model-Independent Indication for a Localized Anomaly in the Late-Time Expansion History

We investigate the late-time expansion history of the Universe using a model-independent spline reconstruction of cosmological distances based on the latest DESI DR2 baryon acoustic oscillation (BAO) measurements and the DES Dovekie Type Ia supernova compilation. Comparing the reconstructed expansion history with the prediction of the Planck 2018 $Λ$CDM model, we identify a localized deviation over the redshift interval $0.3\lesssim z\lesssim0.6$, reaching a maximum significance of approximately $3.5σ$ at $z\simeq0.47$. We demonstrate that this feature persists under substantial variations of the reconstruction methodology, dataset composition and sound-horizon calibration. Mock analyses further show that the reconstruction is unbiased and that the observed anomaly is unlikely to arise from reconstruction bias or miscalibrated uncertainties. If confirmed by future observations, this localized feature could point to previously unrecognized late-time physics or reveal subtle inconsistencies between early and late Universe cosmological probes.

astro-ph.CO↗

arXiv2026

A New Window on Dynamical Dark Energy: Combining DESI-DR2 BAO with future Gravitational Wave Observations

Baryon acoustic oscillation (BAO) data from the Dark Energy Spectroscopic Instrument (DESI) appear to indicate the first evidence for dynamical dark energy (DDE), with a present-day behavior resembling quintessence. This evidence emerges when the Chevallier-Polarski-Linder (CPL) parameterization of the dark energy equation of state, $w_{\textrm{de}} = w_0 + w_a (1-a)$, is considered, and persists across other functional forms of $w_{\textrm{de}}$. In this work, we investigate how the inclusion of future gravitational wave (GW) standard siren data impacts the uncertainties in cosmological parameters when combined with DESI measurements. Specifically, we analyze the expected contributions from upcoming GW observatories such as the Einstein Telescope (ET) and the Deci-hertz Interferometer Gravitational-wave Observatory (DECIGO), as well as the current Laser Interferometer Gravitational-Wave Observatory (aLIGO). We find that the addition of GW data, particularly from DECIGO, significantly reduces the uncertainties in cosmological parameters, with the extent of the improvement depending on the specific form of $w_{\textrm{de}}$ and being more expressive for the $Ω_m$ and $H_0$ parameters for all models studied. Our results highlight both the constraining power of future GW observations and the importance of considering a range of cosmological models in the data analysis.

astro-ph.CO↗

arXiv2026

Cosmological Viability of Exponential Infrared $f(T)$ Gravity

We investigate the cosmological viability of exponential infrared $f(T)$ teleparallel gravity using current cosmological observations. This framework realizes late-time cosmic acceleration through torsional modifications of gravity without enlarging the six-parameter cosmological parameter space of spatially flat $Λ$CDM, and admits two distinct solution branches: a phantom-like model (Model I) and a model featuring a negative-to-positive transition in the effective torsional dark-energy density (Model II). We constrain both branches using CMB observations from Planck, ACT, and SPT together with DESI BAO and Pantheon+ Type Ia supernovae. We find that the principal branch (Model I) alleviates the Hubble tension relative to $Λ$CDM, but remains statistically disfavoured by the combined dataset. The secondary branch (Model II) is decisively ruled out. We show that the failure of Model II originates from the interplay between background and perturbation constraints: once late-time distance measurements constrain the expansion history, the model becomes overconstrained, forcing correlated shifts in $Ω_{\rm m}h^2$, $A_s$, $n_s$, and $τ_{\rm reio}$, degrading the fit to the CMB damping tail and driving the optical depth to unphysical values. Our results demonstrate that perturbation observables provide stringent and complementary tests of teleparallel gravity beyond the background expansion history.

astro-ph.CO↗