Interacting dark energy after the latest Planck, Des, and measurements: an excellent solution to the and cosmic shear tensions
Abstract
We examine the most wellstudied model featuring nongravitational interactions between dark matter and dark energy in light of the latest cosmological observations. Our data includes Cosmic Microwave Background (CMB) measurements from the Planck 2018 legacy data release, galaxy clustering and cosmic shear measurements from the Dark Energy Survey Year 1 results, and the 2019 local distance ladder measurement of the Hubble constant from the Hubble Space Telescope. We find that the presence of interactions among the two dark sectors can bring the significance level of the longstanding tension below the level. The very same model also significantly reduces the tension between CMB and cosmic shear measurements. Interactions between the dark components of our Universe remain therefore as an extremely promising solution to these persisting cosmological tensions. The results presented in this paper are among the first constraints on exotic physics from the Planck 2018 legacy dataset. In a companion paper, we will further investigate these tensions when allowing for more freedom in the dark energy sector.
pacs:
Introduction — The concordance CDM cosmological model has been incredibly successful at describing cosmological observations at high and low redshift Riess:1998cb; Perlmutter:1998np; Ade:2015xua; Alam:2016hwk; Troxel:2017xyo. Yet, as uncertainties on cosmological parameters keep shrinking, a number of weaknesses have emerged: one of the most intriguing ones is the “ tension”, referring to the mismatch between the value of the Hubble constant inferred from Planck Cosmic Microwave Background (CMB) data and direct local distance ladder measurements Freedman:2017yms; DiValentino:2017gzb. In the past decade we have witnessed the tension between these two values grow in significance level from to : the latest determinations from the Planck 2018 results and from the observations of Large Magellanic Cloud Cepheids by the Hubble Space Telescope (HST; measurement denoted as R19 hereafter) give Aghanim:2018eyx and Riess:2019cxk respectively, with the reduced Hubble constant. A very appealing possibility is that the discrepancy might be a hint of physics beyond the canonical CDM model. The most economic possibilities in this direction involve phantom dark energy or some form of dark radiation DiValentino:2016hlg; Bernal:2016gxb; Vagnozzi:2019ezj, but a number of more complex scenarios have been studied, e.g. QingGuo:2016ykt; Ko:2016uft; Karwal:2016vyq; Chacko:2016kgg; Zhao:2017cud; Vagnozzi:2017ovm; Agrawal:2017rvu; Benetti:2017gvm; Feng:2017nss; Zhao:2017urm; DiValentino:2017zyq; Gariazzo:2017pzb; Dirian:2017pwp; Feng:2017mfs; Renk:2017rzu; Yang:2017alx; BuenAbad:2017gxg; Raveri:2017jto; DiValentino:2017rcr; DiValentino:2017oaw; Khosravi:2017hfi; Peirone:2017vcq; Benetti:2017juy; Mortsell:2018mfj; Vagnozzi:2018jhn; Nunes:2018xbm; Poulin:2018zxs; Kumar:2018yhh; Banihashemi:2018oxo; DEramo:2018vss; Guo:2018ans; Graef:2018fzu; Yang:2018qmz; Banihashemi:2018has; Aylor:2018drw; Poulin:2018cxd; Kreisch:2019yzn; Pandey:2019plg; Vattis:2019efj; Colgain:2019pck; Agrawal:2019lmo; Li:2019san; Yang:2019jwn; Keeley:2019esp; DiValentino:2019exe; Archidiacono:2019wdp; Nesseris:2019fwr; Yang:2019nhz; Cai:2019bdh; Schoneberg:2019wmt; Pan:2019hac; Visinelli:2019qqu; Panpanich:2019fxq.
On the other hand, tensions between cosmic shear surveys (such as Kohlinger:2017sxk; Hildebrandt:2016iqg; Joudaki:2016kym) and CMB measurements have also emerged Hildebrandt:2016iqg; Joudaki:2017zdt; DiValentino:2018gcu. For instance, the quantity as measured by the KiDS weak lensing survey was shown to be in tension with the same quantity as measured by Planck Joudaki:2017zdt; Hildebrandt:2016iqg (see also Refs. Kilbinger:2012qz; Heymans:2013fya for previous analyses of CFHTLenS data). Focusing on the joint galaxy clustering and lensing likelihoods from the Dark Energy Survey (DES) Troxel:2017xyo; Abbott:2017wau; Krause:2017ekm, the Planck collaboration found modest tension with the DES results when galaxy clustering measurements are included, as the latter prefer an lower value of Aghanim:2018eyx. A number of exotic scenarios have been advocated in the past to alleviate the tension, see for instance Joudaki:2016kym; Ko:2016uft; Chacko:2016kgg; BuenAbad:2017gxg; DiValentino:2017oaw; Benetti:2017juy; Gariazzo:2017pzb; Poulin:2018zxs; Kreisch:2019yzn; Keeley:2019esp.
Within the CDM model, dark matter (DM) and dark energy (DE) behave as separate fluids not sharing interactions beyond gravitational ones. However, from a microphysical perspective it is hard to imagine how nongravitational DMDE interactions can be avoided, unless forbidden by a fundamental symmetry. This has motivated a large number of studies based on models where DM and DE share interactions other than gravitational, usually referred to as interacting dark energy (IDE) models (see e.g. Farrar:2003uw; Barrow:2006hia; Amendola:2006dg; He:2008tn; Valiviita:2008iv; Gavela:2009cy; CalderaCabral:2009ja; Majerotto:2009np; Abdalla:2009mt; Honorez:2010rr; Clemson:2011an; Pan:2012ki; Salvatelli:2013wra; Yang:2014vza; Yang:2014gza; Nunes:2014qoa; Faraoni:2014vra; Pan:2014afa; Ferreira:2014cla; Tamanini:2015iia; Li:2015vla; Murgia:2016ccp; Nunes:2016dlj; Yang:2016evp; Pan:2016ngu; Sharov:2017iue; An:2017kqu; Santos:2017bqm; Mifsud:2017fsy; Kumar:2017bpv; Guo:2017deu; Pan:2017ent; An:2017crg; Costa:2018aoy; Wang:2018azy; vonMarttens:2018iav; Yang:2018qec; Costa:2019uvk; Martinelli:2019dau; Li:2019loh; Yang:2019vni; Bachega:2019fki; Li:2019ghw, for a recent comprehensive review see Wang:2016lxa). Several studies in the literature have been devoted to exploring whether DMDE interactions may help resolve the enduring tension, see e.g. Salvatelli:2014zta; Kumar:2016zpg; Xia:2016vnp; Kumar:2017dnp; DiValentino:2017iww; Yang:2017ccc; Feng:2017usu; Yang:2018ubt; Yang:2018xlt; Yang:2018uae; Li:2018ydj; Kumar:2019wfs; Pan:2019jqh; Yang:2019uzo; Pan:2019gop.
In this Letter we (re)assess whether IDE cosmologies still provide a viable solution to the tension in light of the latest Planck and HST measurements. We find that IDE provides an extremely compelling solution to the tension, which is brought below the level. Intriguingly, when combining the latest Planck and HST measurements we find very strong indications for an interaction between the two dark components. We find that IDE also provides a compelling solution to the tension between Planck and DES.
Interacting dark energy — We consider a nongravitational DMDE interaction with energy exchange proportional to the DM fourvelocity, extensively studied in Valiviita:2008iv; delCampo:2008jx; Gavela:2009cy; Honorez:2010rr. We assume a pressureless cold DM component and a DE component with equation of state (EoS) , and denote the DM and DE energy densities by and respectively. At the background level, the DMDE coupling modifies the continuity equations for the two dark fluids as follows Gavela:2009cy:
(1)  
(2) 
where the dot denotes derivative with respect to conformal time , and is the conformal Hubble rate. In the notation of Eqs. (1,2), and indicate energy transfer from DE to DM and viceversa. We choose to focus on one of the most wellstudied IDE models, wherein the coupling takes the following form Valiviita:2008iv; Gavela:2009cy:
(3) 
where is a dimensionless coupling governing the strength of the DMDE interaction.
The presence of the DMDE coupling also modifies the evolution of perturbations. In synchronous gauge, the linear perturbation equations for the evolution of the DM and DE density perturbations and velocity divergences are given by Valiviita:2008iv; Gavela:2009cy; Gavela:2010tm:
(4)  
(5)  
(6)  
(7) 
We appropriately modify the initial conditions for and following Gavela:2010tm; Salvatelli:2013wra; DiValentino:2017iww.
In the presence of DMDE interactions, care must be given to the stability of the interacting system. For (i.e. interacting vacuum), IDE models can suffer from gravitational instabilities Valiviita:2008iv; He:2008si. However, even when , one has to worry about earlytime instabilities, leading to curvature perturbations blowing up on superhorizon scales. For IDE models in which , these instabilities are absent if the signs of and are opposite Valiviita:2008iv; He:2008si; Jackson:2009mz; Gavela:2010tm; Clemson:2011an (see also Li:2014eha; Li:2014cee; Guo:2017hea; Zhang:2017ize; Guo:2018gyo; Yang:2018euj; Dai:2019vif for alternative approaches to avoiding these instabilities).
Methodology and Cosmological Observations— We consider an IDE model characterized by the coupling given by Eq. (3). The model is described by the usual six cosmological parameters of CDM (, , , , , and ), in addition to the DMDE coupling . To circumvent the instability problem, we fix the DE EoS to . The rationale behind this approach (already followed in Salvatelli:2013wra; DiValentino:2017iww) is that for sufficiently close to the effect of DE perturbations in Eqs. (6,7) is basically unnoticeable: consequently, these equations are essentially only capturing the effect of the DMDE coupling , while at the same time ensuring the absence of gravitational instabilities present when . Such a model provides therefore a rather accurate surrogate for a CDM+ cosmology, and we shall refer to this model as CDM. In order to avoid earlytime instabilities, we need to impose , implying that we are considering a model where energy flows from DM to DE.
Datawise, we first consider measurements of CMB temperature and polarization anisotropies, as well as their crosscorrelations, from the Planck 2018 legacy data release Aghanim:2018eyx; Aghanim:2018oex. This dataset is referred to as Planck TT,TE,EE+lowE in Aghanim:2018eyx, whereas we refer to it simply as Planck. In addition to CMB data, we also consider a Gaussian prior on the Hubble constant , consistent with the latest measurement by HST in Riess:2019cxk. We refer to this prior as R19. Finally, we include galaxy clustering and cosmic shear measurements from the Dark Energy Survey combinedprobe Year 1 results Troxel:2017xyo; Abbott:2017wau; Krause:2017ekm, and refer to this dataset as DES.
We modify the Boltzmann solver CAMB Lewis:1999bs to incorporate the effect of the DMDE coupling as in Eqs. (4,7). We sample the posterior distribution of the cosmological parameters by making use of Markov Chain Monte Carlo (MCMC) methods, through a modified version of the publicly available MCMC sampler CosmoMC Lewis:2002ah. We monitor the convergence of the generated MCMC chains through the GelmanRubin parameter Gelman:1992zz, requiring for our MCMC chains to be considered as converged. We impose flat priors on all cosmological parameters unless otherwise stated. In particular, as required by stability considerations, we impose at the prior level.
Finally, we use our MCMC chains to compute the Bayesian evidence for the IDE model (for different choices of datasets) using the MCEvidence code Heavens:2017afc. We then compute the (logarithm of the) Bayes factor with respect to CDM, , with a value indicating that the IDE model is preferred. We qualify the strength of the obtained values of using the modified version of the Jeffreys scale provided in Kass:1995loi.
Parameter  Planck  Planck+R19 














Results — Our main results are shown in Tab. 1 and Fig. 1. As shown in Tab. 1, from the Planck dataset alone, the value of the Hubble constant inferred within the CDM model is . While the uncertainty is larger than that reported in Ref. Aghanim:2018eyx within the standard CDM scenario, the central value has significantly shifted upwards. Indeed, this value is perfectly consistent with the HST measurement of Riess:2019cxk, showing an agreement well below the level. Therefore, within this IDE model, the tension is compellingly solved.
The reason for such a high value of from CMB measurements alone can be found in the strong degeneracy between and , as depicted in the left panel of Fig. 1. The origin of this degeneracy resides in the fact that for the IDE model considered here, the background evolution of the DM energy density has an extra contribution proportional to the absolute value of and growing with . Due to the presence of this extra term, the amount of DM today, , must be smaller. However, the acoustic peak structure of the CMB (and in particular the relative height of odd and even peaks, as well as the overall height of all peaks) accurately fixes the value of : in order to accommodate a lower value of , a higher value of is required. An inverse correlation between and is therefore expected, which is perfectly reflected in the contours in the left panel of Fig. 1.
Note that even if the Planck dataset alone shows a preference for a nonzero negative at C.L., this is likely due to a volume effect, i.e. more models with are compatible with Planck than models with . This explanation is supported by the fact that the bestfit for is almost the same as the bestfit for CDM. Computing the Bayes factor for the IDE model with respect to CDM for the Planck dataset we find . According to the modified Jeffreys scale of Kass:1995loi, this indicates a positive preference for the IDE model.
As the Planck and R19 datasets are now consistent, it is possible to combine them. When considering the Planck+R19 combination, we find an even stronger indication for nonzero , inferring . Computing the Bayes factor, we find the extremely high value , indicating a very strong preference for the IDE model.
The solution to the tension due to a lower intrinsic value for at present within the CDM model implies a much larger degeneracy in the plane, reflected in the right panel of Fig. 1: the allowed contours from the Planck dataset follow a band, rather than reproducing the small region usually singled out. The reason is that once a coupling is switched on, the required DM energy density must be smaller as we have seen, implying that the clustering parameter must be larger to have a proper normalization of the (lensing and clustering) power spectra. This effect can be perfectly understood from the scatter plot in the plane depicted in Fig. 2: as the absolute value of is increased, the allowed region bends towards larger (smaller) values of ().
The DES contours follow the expected behavior Aghanim:2018eyx . Notice that the DES and Planck contours overlap for a very large fraction of the parameter space in the plane, implying that the tension between Planck and DES is alleviated. Notice that this is not merely an effect due to the larger uncertainties in the Planck contours, but rather is due to the strong overlap between the two contours.
Conclusions — In this Letter, we have examined the persisting tension in light of the Planck 2018 legacy data release and the latest determination of from HST. We find that within a wellstudied interacting dark energy model, the value of inferred by Planck is consistent with the latest local distance measurement well within , representing an extremely compelling solution to the tension. Bayesian evidence considerations show that combining the Planck and HST measurements leads to a very strong preference for the interacting dark sector scenario explored here with respect to the baseline CDM model. This finding reinforces the idea that the tension might be truly pointing towards new physics in the dark sector. The model at hand also appears extremely promising in terms of alleviating the tensions between CMB and cosmic shear measurements. In particular, we observe a considerably improved overlap between the Planck and DES contours in the plane.
To conclude, it is extremely intriguing that the interacting dark sector model we have considered provides not only one of the most compelling solutions to the tension to date, but at the same time can alleviate the tension between CMB and cosmic shear measurements. We shall further investigate several related issues, for instance the inclusion of lowredshift Baryon Acoustic Oscillation and Supernovae distance measurements. It is also worth exploring interacting scenarios with more freedom in the dark energy sector, for instance treating the dark energy equation of state as a free parameter (possibly timedependent). We shall report on these and other issues in a companion paper to appear shortly.