Cosmic Microwave Background Data Research Articles

Constraining constant and tomographic coupled dark energy with low-redshift and high-redshift probes

We consider coupled dark energy (CDE) cosmologies, where dark matter particles feel a force stronger than gravity, due to the fifth force mediated by a scalar field which plays the role of dark energy. We perform for the first time a tomographic analysis of coupled dark energy, where the coupling strength is parametrized and constrained in different redshift bins. This allows us to verify which data can better constrain the strength of the coupling and how large the coupling can be at different epochs. First, we employ cosmic microwave background data from Planck, the Atacama Cosmology Telescope (ACT) and South Pole Telescope (SPT), showing the impact of different choices that can be done in combining these datasets. Then, we use a range of low redshift probes to test CDE cosmologies, both for a constant and for a tomographic coupling. In particular, we use for the first time data from weak lensing (the KiDS-1000 survey), galaxy clustering (BOSS survey), and their combination, including 3x2pt galaxy-galaxy lensing cross-correlation data. We do not find evidence for nonzero coupling, either for a constant or tomographic case. A nonzero coupling is however still in agreement with current data. For CMB and background datasets, a tomographic coupling allows for $\ensuremath{\beta}$ values up to one order of magnitude larger than in previous works, in particular at $z<1$. The use of 3x2pt analysis then becomes important to constrain $\ensuremath{\beta}$ at low redshifts, even when coupling is allowed to vary: for 3x2pt we find, at $0.5<z<1$, $\ensuremath{\beta}={0.018}_{\ensuremath{-}0.011}^{+0.007}$, comparable to what CMB and background datasets would give for a constant coupling. This makes upcoming galaxy surveys potentially powerful probes to test CDE models at low redshifts. We find a smaller tension in ${H}_{0}$ and ${S}_{8}$ when the coupling is allowed to vary, although this is rather due to an increase in their uncertainties. We also see that our model is penalized by a Bayesian ratio model comparison with respect to $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$, which is still favored by current data.

Constraining dark matter decay with cosmic microwave background and weak-lensing shear observations

From observations at low and high redshifts, it is well known that the bulk of dark matter (DM) has to be stable or at least very long-lived. However, the possibility that a small fraction of DM is unstable or that all DM decays with a half-life time (τ) significantly longer than the age of the Universe is not ruled out. One-body decaying dark matter (DDM) consists of a minimal extension to the ΛCDM model. It causes a modification of the cosmic growth history as well as a suppression of the small-scale clustering signal, providing interesting consequences regarding theS8tension, which is the observed difference in the clustering amplitude between weak-lensing (WL) and cosmic microwave background (CMB) observations. In this paper, we investigate models in which a fraction or all DM decays into radiation, focusing on the long-lived regime, that is,τ ≳ H0−1(H0−1being the Hubble time). We used WL data from the Kilo-Degree Survey (KiDS) and CMB data fromPlanck. First, we confirm that this DDM model cannot alleviate theS8difference. We then show that the most constraining power for DM decay does not come from the nonlinear WL data, but from CMB via the integrated Sachs-Wolfe effect. From the CMB data alone, we obtain constraints ofτ ≥ 288 Gyr if all DM is assumed to be unstable, and we show that a maximum fraction off = 0.07 is allowed to decay assuming the half-life time to be comparable to (or shorter than) one Hubble time. The constraints from the KiDS-1000 WL data are significantly weaker,τ ≥ 60 Gyr andf < 0.34. Combining the CMB and WL data does not yield tighter constraints than the CMB alone, except for short half-life times, for which the maximum allowed fraction becomesf = 0.03. All limits are provided at the 95% confidence level.

Study on the filters of atmospheric contamination in ground based CMB observation

The atmosphere is one of the most significant sources of contamination in ground-based Cosmic Microwave Background (CMB) observations. Atmospheric emission increases the additional optical loading on the detector, resulting in higher photon noise. Additionally, atmospheric fluctuations cause spatial and temporal variations in detected power, leading to additional correlations between detectors and in the time stream of individual detectors. This correlated signal, known as the 1/f noise, can interfere with the detection of CMB signals, severely hindering the probing of CMB signals. In this paper, we study three types of filters: the polynomial fitting, high-pass filter, and Wiener filter. We evaluate the filters based on their ability to remove atmospheric noise, and investigate the impact of the filters on the data analytic process through end-to-end simulations of CMB experiments. We track their performance by analyzing the response of different components of the data, including both signal and noise. In the time domain, the high-pass filter is found to have the smallest root mean square error and achieves high filtering efficiency, followed by the Wiener filter and polynomial fitting. We adopt two map making methods, namely naive map making and Minimum Variance map making, to study the effects of filters on the map level. The results show that the polynomial fitting gives a high noise residual at low frequency, resulting in significant leakage to small scales in the map domain, while the high-pass and Wiener filters do not have significant leakage. We compare the filters' effects on the power spectra domain by estimating the angular power spectra of residual noise and input signal, and estimating the standard deviation of the signal recovered power spectra. At low noise level, the three filters give almost comparable standard deviations on medium and small scales. However, at high noise level, the standard deviation of the polynomial fitting is significantly larger. These studies can be used for reducing atmospheric noise in future ground-based CMB data processing.

The reconstructed CMB lensing bispectrum

Weak gravitational lensing by the intervening large-scale structure (LSS) of the Universe is the leading non-linear effect on the anisotropies of the cosmic microwave background (CMB). The integrated line-of-sight mass that causes the distortion — known as lensing convergence — can be reconstructed from the lensed temperature and polarization anisotropies via estimators quadratic in the CMB modes, and its power spectrum has been measured from multiple CMB experiments. Sourced by the non-linear evolution of structure, the bispectrum of the lensing convergence provides additional information on late-time cosmological evolution complementary to the power spectrum. However, when trying to estimate the summary statistics of the reconstructed lensing convergence, a number of noise-biases are introduced, as previous studies have shown for the power spectrum. Here, we explore for the first time the noise-biases in measuring the bispectrum of the reconstructed lensing convergence.We compute the leading noise-biases in the flat-sky limit and compare our analytical results against simulations, finding excellent agreement. Our results are critical for future attempts to reconstruct the lensing convergence bispectrum with real CMB data.

Phantom scalar-tensor models and cosmological tensions

We study three different extended scalar-tensor theories of gravity by also allowing a negative sign for the kinetic term for the scalar field in the Jordan frame. Our scope is to understand how the observational constraints for these models cope with the volume of the parameter space in which the theory is healthy. Models with a negative kinetic term lead to decreasing effective gravitational constant with redshift and behave as an effective relativistic component with a negative energy density as opposite to their corresponding version with a standard kinetic term. As a consequence, we find that the extended branch with a negative sign for the kinetic term correspond in general to lower H 0 and σ 8 compared to ΛCDM. We find that in all the cases with a negative sign for the kinetic term studied here, cosmological observations constrain these models around GR and prefer a volume of the parameter space in which the theory is not healthy since the scalar field behave as a ghost also in the related Einstein frame. We show that also in the phantom branch early modify gravity with a quartic coupling can substantially reduce the H 0 tension fitting the combination of cosmic microwave background data from Planck, baryon acoustic oscillations from BOSS and eBOSS, and Supernovae from the Pantheon sample with calibration information by SH0ES.

Probing the interaction between dark energy and dark matter with future fast radio burst observations

Interacting dark energy (IDE) scenario assumes that there exists a direct interaction between dark energy and cold dark matter, but this interaction is hard to be tightly constrained by the current data. Fast radio bursts (FRBs) will be seen in large numbers by future radio telescopes, and thus they have potential to become a promising low-redshift cosmological probe. In this work, we investigate the capability of future FRBs of constraining the dimensionless coupling parameter β in four phenomenological IDE models. If we fix the FRB properties, about 105 FRB data can give constraints on β tighter than the current cosmic microwave background data in the IDE models with the interaction proportional to the energy density of dark energy. In all the IDE models, about 106 FRB data can achieve the absolute errors of β to less than 0.10, providing a way to precisely measure β by only one cosmological probe. Jointly constraining the FRB properties and cosmological parameters would increase the constraint errors of β by a factor of about 0.5–2.

Beyond – ΛCDM constraints from the full shape clustering measurements from BOSS and eBOSS

ABSTRACT We analyse the full shape of anisotropic clustering measurements from the extended Baryon Oscillation Spectroscopic Survey quasar sample together with the combined galaxy sample from the Baryon Oscillation Spectroscopic Survey. We obtain constraints on the cosmological parameters independent of the Hubble parameter h for the extensions of the Lambda cold dark matter (ΛCDM) models, focusing on cosmologies with free dark energy equation of state parameter w. We combine the clustering constraints with those from the latest cosmic microwave background data from Planck to obtain joint constraints for these cosmologies for w and the additional extension parameters – its time evolution wa, the physical curvature density ωK and the neutrino mass sum ∑mν. Our joint constraints are consistent with a flat ΛCDM cosmological model within 68 per cent confidence limits. We demonstrate that the Planck data are able to place tight constraints on the clustering amplitude today, σ12, in cosmologies with varying w and present the first constraints for the clustering amplitude for such cosmologies, which is found to be slightly higher than the ΛCDM value. Additionally, we show that when we vary w and allow for non-flat cosmologies and the physical curvature density is used, Planck prefers a curved universe at 4σ significance, which is ∼2σ higher than when using the relative curvature density ΩK. Finally, when w is varied freely, clustering provides only a modest improvement (of 0.021 eV) on the upper limit of ∑mν.

New cosmological constraints on f(T) gravity in light of full Planck-CMB and type Ia supernovae data

We investigate two new observational perspectives in the context of torsional gravitational modification of general relativity, i.e., the $f(T)$ gravity: i) We use Pantheon data of type Ia supernovae motivated by a time variation of the Newton's constant on the supernovae distance modulus relation, and find that a joint analysis with Baryon Acoustic Oscillations (BAO) and Big Bang Nucleosynthesis (BBN), i.e., Pantheon+BAO+BBN, provides constraints on the effective free parameter of the theory to be well compatible with the $\Lambda$CDM prediction; ii) We present the framework of $f(T)$ gravity at the level of linear perturbations with the phenomenological functions, namely the effective gravitational coupling $\mu$ and the light deflection parameter $\Sigma$, which are commonly used to parameterize possible modifications of the Poisson equation relating the matter density contrast to the lensing and the Newtonian potentials, respectively. We use the available Cosmic Microwave Background (CMB) data sets from the Planck 2018 release to constrain the free parameters of the $f(T)$ power-law gravity and $\Lambda$CDM models. We find that CMB data, and its joint analyses with Pantheon and BAO data constrain the $f(T)$ power-law gravity scenario to be practically indistinguishable from the $\Lambda$CDM model. We obtain the strongest limits ever reported on $f(T)$ power-law gravity scenario at the cosmological level.

Quintessential cosmological tensions

Several cosmological tensions have emerged in light of recent data, most notably in the inferences of the parameters ${H}_{0}$ and ${\ensuremath{\sigma}}_{8}$. We explore the possibility of alleviating both these tensions simultaneously by means of the Albrecht-Skordis ``quintessence'' potential. The field can reduce the size of the sound horizon ${r}_{s}^{*}$ while concurrently suppressing the power in matter density fluctuations before it comes to dominate the energy density budget today. Interestingly, this rich set of dynamics is governed entirely by one free parameter that is of $\mathcal{O}(10)$ in Planck units. We find that the inferred value of ${H}_{0}$ can be increased, while that of ${\ensuremath{\sigma}}_{8}$ can be decreased, both by $\ensuremath{\approx}1\ensuremath{\sigma}$ compared to the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ case. However, ultimately the model is disfavored by Planck and BAO data alone, compared to the standard $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model, with a $\mathrm{\ensuremath{\Delta}}{\ensuremath{\chi}}^{2}\ensuremath{\approx}+6$. When including large scale structure and supernova data we find $\mathrm{\ensuremath{\Delta}}{\ensuremath{\chi}}^{2}\ensuremath{\approx}+1$. We note that historically much attention has been focused on preserving the three angular scales ${\ensuremath{\theta}}_{D}$, ${\ensuremath{\theta}}_{\mathrm{EQ}}$, and ${\ensuremath{\theta}}_{s}^{*}$ to their $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ values. Our work presents an example of how, while doing so indeed maintains a relatively good fit to the cosmic microwave background data for an increased number of ultrarelativistic species, it is a priori insufficient in maintaining such a fit in more general model spaces.

Observational constraints on warm natural inflation

Warm natural inflation is studied for the case of the original cosine potential. The radiation bath during inflation induces a dissipation (friction) rate in the equation of motion for the inflaton field, which can potentially reduce the field excursion needed for an observationally viable period of inflation. We examine if the dissipation thus provides a mechanism to avoid the large decay constant f ≳ M pl of cold cosine natural inflation. Whereas temperature independent dissipation has previously been shown to alleviate the need for a trans-Planckian decay constant f, we illustrate here the difficulties of accommodating a significantly sub-Planckian decay constant (f < 10-1 M pl) for the case of a temperature dependent dissipation rate in the form Γ ∝ Tc , with c = {1,3}. Such dissipation rates represent physically well-motivated constructions in the literature. For each model, we map its location in the r-ns plane and compare with cosmic microwave background (CMB) data. For c = 1 (c = 3), we find that agreement with CMB data requires that dissipation be in the weak (moderate) regime and that the minimum allowed value of the decay constant in the potential is f min = 0.3 (0.8) M pl, respectively.

Testing Cosmic Microwave Background Anomalies in E-mode Polarization with Current and Future Data

In this paper, we explore the power of the cosmic microwave background (CMB) polarization (E-mode) data to corroborate four potential anomalies in CMB temperature data: the lack of large angular-scale correlations, the alignment of the quadrupole and octupole (Q–O), the point-parity asymmetry, and the hemispherical power asymmetry. We use CMB simulations with noise representative of three experiments—the Planck satellite, the Cosmology Large Angular Scale Surveyor (CLASS), and the LiteBIRD satellite—to test how current and future data constrain the anomalies. We find the correlation coefficients ρ between temperature and E-mode estimators to be less than 0.1, except for the point-parity asymmetry (ρ = 0.17 for cosmic-variance-limited simulations), confirming that E-modes provide a check on the anomalies that is largely independent of temperature data. Compared to Planck component-separated CMB data (smica), the putative LiteBIRD survey would reduce errors on E-mode anomaly estimators by factors of ∼3 for hemispherical power asymmetry and point-parity asymmetry, and by ∼26 for lack of large-scale correlation. The improvement in Q–O alignment is not obvious due to large cosmic variance, but we found the ability to pin down the estimator value will be improved by a factor ≳100. Improvements with CLASS are intermediate to these.

Warm beta -exponential inflation and the swampland conjectures

We investigate theoretical and observational aspects of a warm inflation scenario driven by the beta -exponential potential, which generalizes the well-known power law inflation. In such a scenario, the decay of the inflaton field into radiation happens during the inflationary phase. In our study, we consider a dissipation coefficient (varGamma ) with cubic dependence on the temperature (T) and investigate the consequences in the inflationary dynamics, focusing on the impact on the spectral index n_s, its running n_{run} and tensor-to-scalar ratio r. We find it possible to realize inflation in agreement with current cosmic microwave background data in weak and strong dissipation regimes. We also investigate theoretical aspects of the model in light of the swampland conjectures, as warm inflation in the strong dissipation regime has been known as a way to satisfy the three conditions currently discussed in the literature. We find that when varGamma propto T^3, the beta -exponential model can be accommodated into the conjectures.

Primordial lepton asymmetries in the precision cosmology era: Current status and future sensitivities from BBN and the CMB

Using a new sample of extremely metal poor systems, the EMPRESS survey has recently reported a primordial helium abundance that is $3\sigma$ smaller than the prediction from the standard big bang nucleosynthesis (BBN) scenario. This measurement could be interpreted as a hint for a primordial lepton asymmetry in the electron neutrino flavor. Motivated by the EMPRESS results, we present a comprehensive analysis of the lepton asymmetry using measurements of the abundances of primordial elements, along with cosmic microwave background (CMB) data from Planck. Assuming that there is no dark radiation in our Universe, we find an electron neutrino chemical potential $\xi_{\nu_e} = 0.043 \pm 0.015$, which deviates from zero by $2.9\sigma$. If no assumption is made on the abundance of dark radiation in the Universe, the chemical potential is $\xi_{\nu_e} = 0.046 \pm 0.021$, which deviates from zero by $2.2\sigma$. We also find that this result is rather insensitive to the choice of nuclear reaction rates. If the true helium abundance corresponds to the EMPRESS central value, future CMB observations from the Simons Observatory and CMB-S4 will increase the significance for a nonzero lepton asymmetry to $4\sigma$ and $5\sigma$ respectively, assuming no dark radiation, or to $3\sigma$ when no assumption is made on the abundance of dark radiation.

Cosmological Constant from Boundary Condition and Its Implications beyond the Standard Model

Standard cosmology has long been plagued by a number of persistent problems. The origin of the apparent acceleration of the cosmic expansion remains enigmatic. The cosmological constant has been reintroduced as a free parameter with a value in energy density units that “happens” to be of the same order as the present matter energy density. There is an internal inconsistency with regards to the Hubble constant, the so-called H0 tension. The derived value of H0 depends on the type of data that is used. With supernovae as standard candles, one gets a H0 that is 4–5 σ larger than the value that one gets from CMB (Cosmic Microwave Background) data for the early universe. Here we show that these problems are related and can be solved if the cosmological constant represents a covariant integration constant that arises from a spatial boundary condition, instead of being a new type of hypothetical physical field, “dark energy”, as assumed by standard cosmology. The boundary condition only applies to the bounded 3D subspace that represents the observable universe, the hypersurface of the past light cone.

Inference of gravitational lensing and patchy reionization with future CMB data

We develop an optimal Bayesian solution for jointly inferring secondary signals in the cosmic microwave background (CMB) originating from gravitational lensing and from patchy screening during the epoch of reionization. This method is able to extract full information content from the data, improving upon previously considered quadratic estimators for lensing and screening. We forecast constraints using the marginal unbiased score expansion method, and show that they are largely dominated by CMB polarization, and depend on the exact details of reionization. For models consistent with current data which produce the largest screening signals, a detection ($3\text{ }\ensuremath{\sigma}$) of the cross-correlation between lensing and screening is possible with SPT-3G and a detection of the autocorrelation is possible with CMB-S4. Models with the lowest screening signals evade the sensitivity of SPT-3G but are still possible to detect with CMB-S4 via their lensing cross-correlation.

The Atacama Cosmology Telescope: limits on dark matter-baryon interactions from DR4 power spectra

Diverse astrophysical observations suggest the existence of cold dark matter that interacts only gravitationally with radiation and ordinary baryonic matter. Any nonzero coupling between dark matter and baryons would provide a significant step towards understanding the particle nature of dark matter. Measurements of the cosmic microwave background (CMB) provide constraints on such a coupling that complement laboratory searches. In this work we place upper limits on a variety of models for dark matter elastic scattering with protons and electrons by combining large-scale CMB data from the Planck satellite with small-scale information from Atacama Cosmology Telescope (ACT) DR4 data. In the case of velocity-independent scattering, we obtain bounds on the interaction cross section for protons that are 40% tighter than previous constraints from the CMB anisotropy. For some models with velocity-dependent scattering we find best-fitting cross sections with a 2σ deviation from zero, but these scattering models are not statistically preferred over ΛCDM in terms of model selection.

Joint analysis of Dark Energy Survey Year 3 data and CMB lensing from SPT andPlanck. I. Construction of CMB lensing maps and modeling choices

Joint analyses of cross-correlations between measurements of galaxy positions, galaxy lensing, and lensing of the cosmic microwave background (CMB) offer powerful constraints on the large-scale structure of the Universe. In a forthcoming analysis, we will present cosmological constraints from the analysis of such cross-correlations measured using Year 3 data from the Dark Energy Survey (DES), and CMB data from the South Pole Telescope (SPT) and Planck. Here we present two key ingredients of this analysis: (1) an improved CMB lensing map in the SPT-SZ survey footprint and (2) the analysis methodology that will be used to extract cosmological information from the cross-correlation measurements. Relative to previous lensing maps made from the same CMB observations, we have implemented techniques to remove contamination from the thermal Sunyaev Zel’dovich effect, enabling the extraction of cosmological information from smaller angular scales of the cross-correlation measurements than in previous analyses with DES Year 1 data. We describe our model for the cross-correlations between these maps and DES data, and validate our modeling choices to demonstrate the robustness of our analysis. We then forecast the expected cosmological constraints from the galaxy survey-CMB lensing auto and cross-correlations. We find that the galaxy-CMB lensing and galaxy shear-CMB lensing correlations will on their own provide a constraint on S8=σ8Ωm/0.3 at the few percent level, providing a powerful consistency check for the DES-only constraints. We explore scenarios where external priors on shear calibration are removed, finding that the joint analysis of CMB lensing cross-correlations can provide constraints on the shear calibration amplitude at the 5% to 10% level.13 MoreReceived 31 March 2022Accepted 12 December 2022DOI:https://doi.org/10.1103/PhysRevD.107.023529© 2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCosmic microwave backgroundCosmological parametersDark matterEvolution of the UniverseGravitational lensesLarge scale structure of the UniverseGravitation, Cosmology & Astrophysics

Restoring cosmological concordance with early dark energy and massive neutrinos?

ABSTRACT The early dark energy (EDE) solution to the Hubble tension comes at the cost of an increased clustering amplitude that has been argued to worsen the fit to galaxy clustering data. We explore whether freeing the total neutrino mass Mν, which can suppress small-scale structure growth, improves EDE’s fit to galaxy clustering. Using Planck Cosmic Microwave Background and BOSS galaxy clustering data, a Bayesian analysis shows that freeing Mν does not appreciably increase the inferred EDE fraction fEDE: we find the 95 per cent C.L. upper limits fEDE &amp;lt; 0.092 and $M_{\nu }\lt 0.15\, {\rm eV}$. Similarly, in a frequentist profile likelihood setting (where our results support previous findings that prior volume effects are important), we find that the baseline EDE model (with $M_{\nu }=0.06\, {\rm eV}$) provides the overall best fit. For instance, compared to baseline EDE, a model with $M_\nu =0.24\, {\rm eV}$ maintains the same H0(km/s/Mpc) = (70.08, 70.11, respectively) whilst decreasing S8 = (0.837, 0.826) to the ΛCDM level, but worsening the fit significantly by Δχ2 = 7.5. For the datasets used, these results are driven not by the clustering amplitude, but by background modifications to the late-time expansion rate due to massive neutrinos, which worsen the fit to measurements of the BAO scale.

Robustness of cosmic birefringence measurement against Galactic foreground emission and instrumental systematics

The polarization of the cosmic microwave background (CMB) can be used to search for parity-violating processes like that predicted by a Chern-Simons coupling to a light pseudoscalar field. Such an interaction rotates E modes into E modes in the observed CMB signal through an effect known as cosmic birefringence. Even though isotropic birefringence can be confused with the rotation produced by a miscalibration of the detectors' polarization angles, the degeneracy between both effects is broken when Galactic foreground emission is used as a calibrator. In this work, we use realistic simulations of the High-Frequency Instrument of the Planck mission to test the impact that Galactic foreground emission and instrumental systematics have on the recent birefringence measurements obtained through this technique. Our results demonstrate the robustness of the methodology against the miscalibration of polarization angles and other systematic effects, like intensity-to-polarization leakage, beam leakage, or cross-polarization effects. However, our estimator is sensitive to the EB correlation of polarized foreground emission. Here we propose to correct the bias induced by dust EB by modeling the foreground signal with templates produced in Bayesian component-separation analyses that fit parametric models to CMB data. Acknowledging the limitations of currently available dust templates like that of the Commander sky model, high-precision CMB data and a characterization of dust beyond the modified blackbody paradigm are needed to obtain a definitive measurement of cosmic birefringence in the future.

Observational constraints on interacting vacuum energy with linear interactions

We explore the bounds that can be placed on interactions between cold dark matter and vacuum energy, with equation of state w = -1, using state-of-the-art cosmological observations. We consider linear perturbations about a simple background model where the energy transfer per Hubble time, Q/H, is a general linear function of the dark matter density, ρc , and vacuum energy, V.We explain the parameter degeneracies found when fitting cosmic microwave background (CMB) anisotropies alone, and show how these are broken by the addition of supernovae data, baryon acoustic oscillations (BAO) and redshift-space distortions (RSD). In particular, care must be taken when relating redshift-space distortions to the growth of structure in the presence of non-zero energy transfer. Interactions in the dark sector can alleviate the tensions between low-redshift measurements of the Hubble parameter, H0 , or weak-lensing, S8 , and the values inferred from CMB data. However these tensions return when we include constraints from supernova and BAO-RSD datasets. In the general linear interaction model we show that, while it is possible to relax both the Hubble and weak-lensing tensions simultaneously, the reduction in these tensions is modest (reduced to less slightly than 4σ and 2σ respectively).