Cosmological implications of DESI DR2 BAO measurements in light of the latest ACT DR6 CMB data

The current understanding of the expansion of the Universe has been built upon rapidly evolving observations from a variety of cosmological probes. Each cosmological dataset provides information about the Universe at different epochs. The Cosmic Microwave Background (CMB) data provide a description of the Universe at redshift $z\approx 1090$, a mere 400,000 years after the Big Bang. Baryon acoustic oscillations (BAO) from galaxy surveys constrain the expansion history of the Universe at $0.1<z<4.2$, exploring the matter dominated era and the recent era of cosmic acceleration. Type Ia Supernovae (SNe Ia) data were used to discover dark energy [1, 2] and constrain the expansion history at low redshifts. The combination of these cosmological probes across the evolving Universe provides quantitative information on the temporal evolution of the dark energy density.

The most precise BAO measurements to date come from the Dark Energy Spectroscopic Instrument (DESI). DESI is installed on the Mayall Telescope at the Kitt Peak National Observatory [3, 4, 5, 6], and uses robotically controlled fiber-optic cables [7, 8, 9, 10, 11] to simultaneously capture light from up to 5,000 pre-selected galaxies and quasars across an eight-square-degree field of view. By analyzing the spectra of collected light, DESI has obtained redshift information on over 30 million extragalactic objects during the first three years of observations [12, 13, 14]. BAO measurements from more than 14 million galaxies and quasars [15, 16], as well as from 820,000 Lyman-$\alpha$ forest spectra [17, 18, 19] have significantly contributed to current knowledge of cosmological parameters.

Recently, the DESI collaboration presented a cosmological analysis based on the latest BAO measurements from its Data Release 2 (DR2) [16]. This analysis points to discrepancies between datasets becoming more relevant within the $\Lambda$CDM model, highlighting evolving dark energy as a possible solution (or alternatively, unrecognized systematics in one or more datasets, or a rare statistical fluctuation), and also reporting updated constraints on the neutrino mass (with an extended analysis allowing an effective neutrino mass parameter that allows negative values [20]). In particular, while the DESI DR2 BAO results are broadly consistent with the picture of the $\Lambda$CDM cosmological model, they exhibit a 2.3$\sigma$ tension [16] with Planck CMB data (including external CMB lensing data from [21]) [14, 22, 23, 24, 25, 26]. On the other hand, a time evolving dark energy component is favored by the joint analysis of these datasets, a scenario in which the datasets are consistent. This behavior can be deduced through either a simple CPL parameterization ($w_{0}w_{a}\rm CDM$) [27, 28], or other dark energy reconstruction methods [29]. Using the $w_{0}w_{a}$CDM parameterization, DESI BAO DR2 combined with CMB temperature and polarization anisotropies, as well as CMB lensing, shows evolving dark energy is preferred at $3.1\sigma$, increasing up to $4.2\sigma$ when including SNe data [16] (this preference is also supported by the Dark Energy Survey BAO and SN combined analysis [30]).

Around the same time as the DESI DR2 results were published, the Atacama Cosmology Telescope (ACT) collaboration also presented their final results on the CMB power spectrum measurements and cosmological implications [31, 32, 33], based on their Data Release 6 (DR6) with five years of observations. The ACT results provide measurements on the small-scale region of the CMB spectrum, adding extra information to the damping tail of the CMB not covered by the Planck space-based mission. Conversely, Planck is able to resolve anisotropies in the temperature and polarization of the CMB maps at large scales not accessible to ACT ($\ell<600$), making the two CMB datasets complementary to each other.

Given the mild discrepancy between DESI BAO and Planck CMB (including ACT DR6 CMB lensing), it becomes important to evaluate the effect of the final ACT DR6 dataset in the context of DESI BAO, whether analyzed individually or combined with Planck. A conservative combination of ACT and Planck involves considering non-overlapping multipole ranges of each CMB spectrum. While in [31] the complete ACT dataset was complemented with CMB measurements from Planck up to $\ell=1000$ to provide a complete CMB picture, other combinations with different multipole cuts are of interest, notably combinations between ACT and Planck based on the multipole ranges where each CMB experiment is more precise. Different combinations may impact parameters such as the physical cold-dark-matter density $\Omega_{\mathrm{c}}h^{2}$, which can affect the discrepancy between DESI and CMB, and impact the evidence in favor of $w_{0}w_{a}$CDM. While ACT alone reports a higher $\Omega_{\mathrm{c}}h^{2}$ value compared to Planck [31] (a $\sim$1.5$\sigma$ shift), the P-ACT combination used by the ACT collaboration measures a slightly lower $\Omega_{\mathrm{c}}h^{2}$ (where $h$ is the hubble constant normalized to 100 km s^-1 Mpc^-1) with respect to Planck.

In addition, BAO helps break geometric degeneracies in CMB constraints on neutrino mass. DESI reported a 95% upper limit of $\sum m_{\nu}<0.064$ eV for the sum of neutrino masses in the $\Lambda$CDM model when combined with Planck CMB data, that changes to $\sum m_{\nu}<0.078$ eV with an alternative CMB likelihood [16]. The constraints on the neutrino mass is relaxed to $\sum m_{\nu}<0.16$ eV in a $w_{0}w_{a}$CDM model. These differences in the neutrino mass constraints further justify a joint DESI+ACT analysis that covers the neutrino sector.

The purpose of this work is to explore the cosmological implications of including the latest ACT power spectrum data and likelihoods within the BAO+CMB+SNe combination already analyzed by the DESI Collaboration, and assess the robustness of the conclusions made by DESI in light of the latest ACT data. We extend the analysis to different combinations of the ACT and Planck datasets based on other multipole cuts that can be more precise at measuring $\Omega_{c}h^{2}$ and other parameters.

In Section II, we describe the datasets, likelihoods, and methodology. In Section III, we test the consistency of DESI and CMB data within the $\Lambda$CDM model. In Section IV, we present the results of dark energy for different datasets, including ACT DR6 power spectra. In Section V, we present constraints on the neutrino masses. Finally, we present our conclusions in Section VI.

The purpose of this work is to explore the cosmological implications of incorporating the latest ACT power spectrum data [31] into a combined analysis with BAO, CMB, and SNe observations, as presented in [16]. We also consider the CMB data from Planck [44] and assess how the inclusion of ACT data affects the cosmological parameters. As reported in [31], ACT measures a higher $\Omega_{\mathrm{c}}h^{2}$ value compared to Planck (a 1.5$\sigma$ shift). Also, it was observed that the P-ACT combination defined in [31] favors a lower value of $\Omega_{\mathrm{c}}h^{2}$ compared to both Planck (0.4$\sigma$ lower) and ACT (1.9$\sigma$ lower). Since the CMB measurement of $\Omega_{\mathrm{c}}h^{2}$ is key for the DESI results as it can affect the discrepancy between DESI and CMB, the preference for $w_{0}w_{a}$CDM and the neutrino mass constraints, the exploration of these CMB datasets and how to combine Planck with ACT becomes relevant. Additionally, the results presented in [16] and [31] use a different version for the low-$\ell$ EE likelihood, which can have an impact on the neutrino mass constraints and deserves exploration.

The CMB high-$\ell$ power spectra from Planck and ACT are combined in a conservative way, without modeling a covariance between the surveys, but rather by applying simple data cuts. ACT resolves temperature anisotropies at smaller angular scales compared to Planck: its CMB spectra start at $\ell=600$ and extend up to $\ell=8500$. On the other hand, Planck can resolve the anisotropies well on large scales, even in the low-$\ell$ regime ($\ell<30$) where the distribution of the CMB spectra is non-Gaussian, while its high-$\ell$ spectra are measured up to $\ell=2500$. In our analysis, we consider the official Planck Release 3 (PR3) [37, 45, 38], as well as Planck Release 4 (PR4) [46], which is a reanalysis using the NPIPE processing pipeline and CMB lensing reconstruction of NPIPE maps [42]. Throughout this work, we focus on the PR4 CamSpec high-$\ell$ likelihood, which provides $\sim$8–10% tighter constraints than PR3 Plik [41] on relevant parameters for this work such as $\Omega_{\mathrm{c}}h^{2}$ and $\Omega_{\mathrm{m}}$, when analyzing CMB alone.

We summarize the datasets used in this work in Table 1 and define the variations under which we combine CMB datasets. Motivated by the ACT baseline data as defined in [31], we use the ACT DR6 high-$\ell$ spectra MFLike in combination with the low-$\ell$ EE Planck data analyzed through the SRoll2 likelihood code [39]¹¹1The inclusion of the low-$\ell$ EE data helps to break degeneracies between the optical depth parameter $\tau$ and the amplitude of primordial scalar fluctuations $A_{\rm s}$. (see also [47, 48] for works related to the SRoll2 maps) but with the inclusion of CMB lensing from the combination of Planck NPIPE and ACT DR6 as described in [43]. We label this combination simply as ACT ²²2Note that this would be equivalent to ACT-L, in the nomenclature used in [31].. Since the ACT data cannot fully constrain the first two CMB acoustic peaks, it is useful to complement it with data from other CMB surveys. We define an analogous combination to P-ACT as used in [31], based on a combination of ACT DR6 and PR3 (plik_lite)³³3The absolute calibration parameter $A_{Planck}$ is shared between the two CMB likelihoods., but with the addition of CMB lensing. We consider fits to the PR4 data only, matching the baseline CMB combination presented in [16]. Since Planck and ACT probe a common part of the CMB spectra, we test different combinations between the two by means of $\ell$ cuts. We consider combinations between PR4 and ACT DR6 with a baseline low-$\ell$ TT Commander and low-$\ell$ EE SimAll data from Planck ($\ell<30$) [37], CMB lensing, and mixed high-$\ell$ information from PR4 and ACT DR6 split by a multipole cut $\ell_{\text{TT}}$ and a common cut $\ell_{\text{TE,EE}}$. This cut uses PR4 TT information for $\ell<\ell_{\text{TT}}$ and then ACT DR6 information for higher values of $\ell$ up to $\ell=8500$. Similarly, the common TE and EE cut uses PR4 data for $\ell<\ell_{\text{TE,EE}}$ and ACT DR6 for the rest of the $\ell$ range up to $\ell=8500$. We define the explicit cuts we use below.

We construct a CMB combination that can be regarded as maximal in the information included from ACT DR6, using its full CMB spectra. However, since the ACT DR6 data are highly impacted by atmospheric noise in the range $600<\ell<1000$ [32], we increase the Planck TT coverage and use $\ell_{\mathrm{TT}}=1000$ and $\ell_{\text{TE,EE}}=600$, as done for P-ACT. This combination is analogous to P-ACT in this work but uses PR4 CamSpec. We label this combination as PR4_(1000,600)+ACT. We also test a combination with $\ell_{\text{TT}}=2000$ and $\ell_{\text{TE,EE}}=1000$ motivated by Figure 12 in [31]. This combination corresponds approximately to the multipole range where the precision of ACT DR6 in measuring the TT spectrum across frequency channels begins to become comparable to, or slightly exceed, that of Planck, around $\ell\sim$ 2000. Similarly, $\ell=1000$ is a point where ACT DR6 is roughly more precise in measuring TE compared to Planck, while $\ell=1000$ is also the scale at which approximately the white noise transition occurs for the ACT DR6 EE polarization data. We label this combination simply as PR4+ACT and consider it as our baseline CMB combination. We note that this choice of $\ell$ cuts may not correspond to the configuration that minimizes cosmological parameter uncertainties, but rather should provide a fair approximation. For the latter set of cuts, we also test the effect of the SRoll2 likelihood by defining an analogous variation where we replace the low-$\ell$ EE SimAll likelihood with the low-$\ell$ EE SRoll2 likelihood and label this PR4${}_{\text{(SRoll2)}}$+ACT. Table 1 summarizes the CMB variations used in this paper. We discuss the effect on the parameter space for some of these combinations with respect to ACT DR6 and PR4 in Appendix A.

We use DESI DR2 BAO data (see [16] for definitions of co-moving distances $D_{\mathrm{M}}$, $D_{\mathrm{H}}$, and $D_{\mathrm{V}}$) containing measurements of $D_{\rm V}/r_{\rm d}$ at redshifts $0.1<z<0.4$ for the BGS tracer, and measurements of $D_{\rm H}/r_{\rm d}$ and $D_{\rm M}/r_{\rm d}$ for the rest of the tracers, LRGs at $0.4<z<0.6$ and $0.6<z<0.8$, a combined tracer LRG+ELG at $0.8<z<1.1$, the ELG tracer at $1.1<z<1.6$, QSO at $0.8<z<2.1$ plus the Ly$\alpha$ forest and the correlation with QSO positions, at $1.8<z<4.2$. Here, $r_{\mathrm{d}}$ represents the sound horizon at the drag epoch, when acoustic waves stall in the primordial plasma as baryons cease to feel the ‘drag’ from the photons.

We also used SNe Ia data from Pantheon+ that consists of 1550 spectroscopically classified type Ia SNe [49]. Similarly, we use the Union3 sample that consists of 2087 SNe Ia and uses an alternative analysis framework based on Bayesian hierarchical modeling using Unity 1.5 [35]. We also include SNe Ia data from the DESY5 sample with 1635 photometrically classified SNe [36].

We test deviations from $\Lambda$CDM, corresponding to dynamical dark energy, by means of the $w_{0}w_{a}\rm CDM$ parameterization based on an equation of state of dark energy given by $w(a)=w_{0}+w_{a}(1-a)$, with $w_{0}$ and $w_{a}$ as free parameters. Finally, when performing constraints on the sum of neutrino masses, we adopt a physical prior $\sum m_{\nu}>0$ and assume 3 degenerate states. Throughout this work, we adopt the priors and tension metrics as described in [16].

In this section, we explore the consistency between DESI BAO data and CMB across the CMB combinations described in Section II, assuming the $\Lambda$CDM model. In [16] it was pointed out that DESI DR2 BAO data show a discrepancy of 2.3$\sigma$ with PR4. It is interesting to assess how this discrepancy stands with the latest CMB spectra from ACT, which provide precision measurements of the small-scale CMB anisotropies in temperature and polarization, as well as tight constraints on the CMB damping tail. At the cosmological parameter level, the quantitative comparison between BAO and CMB data is performed by analyzing the 2D posteriors on the combination $H_{0}r_{\mathrm{d}}$-$\Omega_{\mathrm{m}}$, which are the two cosmological parameters constrained by BAO data. The left panel of Figure 1 shows the comparison of two CMB combinations (ACT in green, and PR4+ACT in purple) with DESI BAO and DESY5 SNe data. We observe that the discrepancy between DESI and CMB occurs along the degeneracy direction of constant $\Omega_{\mathrm{m}}h^{3}=\text{const.}$ [50], roughly preserving the location of the first acoustic peak. This ensures that DESI is consistent with the acoustic angular scale $\theta_{*}$ predicted from CMB. In the following, we describe how the consistency between CMB and DESI changes across the various CMB combinations.

The base ACT combination (without CMB lensing) shown in [31] reports high values of $\Omega_{\mathrm{c}}h^{2}$ and $\Omega_{\mathrm{b}}h^{2}$ and a lower $H_{0}$ with respect to Planck. This further pushes the ACT (no CMB lensing) data away from DESI, leading to a moderate 3.2$\sigma$ tension. The inclusion of CMB lensing reduces this tension to 2.7$\sigma$. Interestingly, this is the opposite effect observed in [16], where excluding CMB lensing elongates the CMB contours reducing the discrepancy between DESI and PR4 data. The discrepancy persists even when the low-$\ell$ SRoll2 likelihood is replaced with low-$\ell$ SimAll and low-$\ell$ TT information is included. However, the combination of P-ACT with the CMB lensing included alleviates the discrepancy leading to a 1.6$\sigma$ difference with DESI. This pull of the CMB contours towards the DESI best-fit value is related to the higher values of $\Omega_{\mathrm{b}}h^{2}$ and the spectral index $n_{\rm s}$ measured by ACT with respect to Planck, as well as to parameter correlations, as explained in Appendix A.

We further explore how DESI compares with a combination of PR4 and ACT. While ACT is more consistent with PR3 as compared to PR4 as pointed out in [31], here we assess the consistency between ACT and PR4 under the assumed $\ell$ cuts before combining them and verify that the overall discrepancy is 2.0$\sigma$ or less in a six-parameter space under $\Lambda$CDM, and that individual parameters show discrepancies below this threshold. Our baseline CMB dataset labeled as PR4+ACT shows a 14% and 23% precision improvement in $n_{\rm s}$ and $\Omega_{\mathrm{b}}h^{2}$ parameters, respectively, with respect to PR4. Also, it shows only a mild discrepancy of 2.0$\sigma$ with DESI (or 1.9$\sigma$ for PR4${}_{(\texttt{SRoll2})}$+ACT). Applying a cut analogous to the one assumed in the P-ACT combination but using PR4, leads to a 1.4$\sigma$ discrepancy with DESI, for our PR4_(1000,600)+ACT combination. We also tested that removing the $600<\ell<1000$ TT data from Planck to avoid any overlaps in $\ell$ while still using a dataset that is “maximal” in ACT increases the discrepancy with DESI to 2.0$\sigma$.

We summarize the results in the right-hand-side panel of Figure 1 highlighting the three base CMB combinations for the rest of this work: ACT (the new CMB dataset), P-ACT (the official combination using PR3) and PR4+ACT (our baseline combination using PR4).

Finally, the left panel of Figure 1 also shows the SNe Ia data from DESY5 (for a more comprehensive comparison of all cosmological probes), which favors a high value of $\Omega_{\mathrm{m}}$ with respect to DESI and CMB. Other SNe Ia datasets (not shown in Figure 1), Pantheon+ and Union3, show a slightly better consistency with DESI. If we combine DESI with P-ACT, the $\Omega_{\mathrm{m}}$ tension between DESI+CMB and SNe Ia ranges from 1.6$\sigma$ for Pantheon+, to 2.0$\sigma$ for Union3, and to 3.0$\sigma$ for DESY5. We do not observe a significant change in these numbers using different CMB datasets. Overall, the combination between DESI and any CMB combination of Planck and ACT shows a mild to moderate discrepancy with the $\Omega_{\mathrm{m}}$ measurement from SNe Ia, under $\Lambda$CDM.

We proceed to explore how the constraints on dark energy as presented in [16] depend on the ACT results. We parameterize deviations from the cosmological constant using the $w_{0}w_{a}\rm CDM$ [27, 28] dark energy equation of state given by $w(a)=w_{0}+(1-a)w_{a}$. As demonstrated in [16], $w_{0}w_{a}$CDM provides enough flexibility to jointly fit current BAO, CMB, and SNe Ia data while preserving consistency between the datasets; thus, we combine all three datasets into our analysis for $w_{0}w_{a}$CDM constraints.

The combination of DESI DR2 BAO with ACT, P-ACT and PR4+ACT are shown in the $w_{0},w_{a}$ plane in the left-hand-side panel of Figure 2. We observe that DESI+ACT pulls the constraints away from the $(w_{0},w_{a})=(-1,0)$ limit, leading to a 2.9$\sigma$ preference in favor of $w_{0}w_{a}$CDM. Interestingly, ACT provides a CMB dataset that is well fit by $A_{\text{Lens}}\approx 1$, where the parameter $A_{\text{Lens}}$ can lead to an artificial smoothing of the CMB peaks [51]. Thus, it does not suffer from the so-called lensing anomaly. For DESI+P-ACT, the preference for a departure from $\Lambda$CDM diminishes to 2.4$\sigma$. On the other hand, the combination DESI+PR4+ACT shows a 3.0$\sigma$ preference in favor of $w_{0}w_{a}$CDM. For this combination, the errors on $w_{0}$ and $w_{a}$ remain unchanged compared to P-ACT. Since the PR4+ACT combination roughly chooses a sweet spot between Planck and ACT that provides more precise error bars on CMB parameters, we include more data from Planck compared to the P-ACT combination.

The difference between the evidence in favor of $w_{0}w_{a}$CDM when DESI is combined with ACT versus that when DESI is combined with P-ACT or PR4+ACT can be linked to the difference in the measured $\Omega_{\mathrm{c}}h^{2}$ in the $\Lambda$CDM model by these respective CMB datasets. For example, a high CMB measurement of $\Omega_{\mathrm{c}}h^{2}$ in $\Lambda$CDM would lead to a high $\Omega_{\mathrm{m}}$ and a low $H_{0}r_{\mathrm{d}}$ with respect to DESI, pulling the contours away from $w_{0}=-1$ and $w_{a}=0$ in a $w_{0}w_{a}$CDM model. In contrast, a lower measurement of $\Omega_{\mathrm{c}}h^{2}$ with respect to, e.g. PR4, would lead to more consistent results with DESI. This is also related to the importance of jointly matching physical density parameters like $\Omega_{c}h^{2}$ from the CMB with BAO, given the consistency of BAO with the CMB-predicted acoustic scale $\theta_{*}$ and that most of the significance in favor of $w_{0}w_{a}$CDM comes from CMB priors on ($\theta_{*}$, $\Omega_{b}h^{2}$, $\Omega_{bc}h^{2}$), as discussed in [16]. As shown in Appendix A, ACT alone shows a high value of $\Omega_{\mathrm{c}}h^{2}$ with respect to PR4, although with larger error bars. On the other hand, P-ACT shows the opposite behavior measuring a lower $\Omega_{\mathrm{c}}h^{2}$ compared to PR4, while in PR4+ACT the $\Omega_{\mathrm{c}}h^{2}$ measurement is still lower than the PR4 prediction but the constraint is 19% tighter than P-ACT. In terms of the ACT data, it was reported that there is a strong dependency on the inferred values of $\Omega_{\mathrm{c}}h^{2}$ and $H_{0}$ given the polarization efficiency calibration choices [31], which may impact the determination of these parameters.

The right-hand-side panel of Figure 2 shows the constraints for DESI+DESY5 in combination with the three CMB baseline datasets. We can see that once the background cosmology is set by BAO and SNe Ia data, the effect of assuming a different CMB variation leads to only minor changes. As summarized in Figure 3, we find that the significance in favor of $w_{0}w_{a}$CDM ranges from 2.5$\sigma$ to 4.2$\sigma$, depending on the SNe Ia dataset used, while the assumed CMB variation has little impact on it. Table 2 summarizes the results on the effective difference on the $\chi^{2}_{\text{MAP}}$, the corresponding significance in the frequentist representation, and the results for the deviance information criterion analysis, as presented in [29]. Once SNe Ia is included, the combination providing the mildest tension with $\Lambda$CDM is DESI+P-ACT+Pantheon+, with a 2.5$\sigma$ significance in favor of $w_{0}w_{a}$CDM. However, replacing Pantheon+ with Union3 and DESY5 increases the significance in favor of $w_{0}w_{a}$CDM to 3.5$\sigma$ and 4.0$\sigma$, respectively. The results from our baseline CMB variations provide compatible results, with tensions ranging between 2.8$\sigma$ (using Pantheon+) up to 4.2$\sigma$ (using DESY5). We also test the effect of using an alternative low-$\ell$ EE likelihood, replacing SRoll2 with SimAll in the ACT combination, and find that changing the low-$\ell$ polarization likelihood has little impact in the significance in favor of $w_{0}w_{a}$CDM. This highlights the robustness of the results presented in [16], after including newer CMB datasets based on ACT or combinations of it with Planck.

Finally, we summarize the results from the parameter constraints in Table 3 for $\Lambda$CDM and $w_{0}w_{a}$CDM⁴⁴4While this paper was under final review, [52] presented constraints on $w_{0}w_{a}$CDM from DESI+P-ACT and DESI+P-ACT+Pantheon+. We find consistent results with theirs., as well as models with varying neutrino mass as discussed in the following section.

Despite the fact that BAO data alone cannot constrain the total neutrino mass, $\sum m_{\nu}$, determining $\Omega_{\mathrm{m}}$ and $H_{0}r_{\mathrm{d}}$ from low redshifts significantly enhances the CMB sensitivity to $\sum m_{\nu}$ via the neutrino-induced shift in the angular diameter distance to last scattering. CMB photons are sensitive to the neutrino mass through lensing, since neutrinos suppress the growth of structures below their free-streaming scale. Low-$\ell$ E-mode polarization of the CMB also plays an important indirect role in constraining neutrino masses by breaking the degeneracy between the optical depth to reionization and the amplitude of primordial scalar fluctuations measured from high-$\ell$ multipoles. This in turn gives a more accurate estimation of the lensing potential, which is suppressed on small scales by massive neutrinos. Therefore, the upper limits on $\sum m_{\nu}$ obtained from the combination of DESI and CMB depend on both the BAO constraining power and the choice of the CMB likelihood, as different likelihoods slightly vary in the amount of lensing power they infer from the lensed TT, TE, and EE spectra at both low- and high-$\ell$.

The inferred constraints on $\sum m_{\nu}$ from BAO+CMB depend on the underlying cosmological model. In the following, we focus on the $\Lambda$CDM and $w_{0}w_{a}$CDM models with free total neutrino mass, assuming three degenerate mass eigenstates. We also adopt a minimal physical prior, $\sum m_{\nu}>0$ eV, noting that scenarios allowing for a negative effective neutrino mass have recently gained interest [53, 54, 55, 20].

Recently, the ACT collaboration set an upper bound on the total neutrino mass of $\sum m_{\nu}<0.082\,\text{eV}$ at 95% confidence level (c.l.) under $\Lambda$CDM [33], based on the combination of DESI DR1 BAO measurements and what we refer to as P-ACT. Using the updated DESI DR2 BAO data, this limit tightens to $\sum m_{\nu}<0.077\,\text{eV}$ at 95% c.l., representing about a 6% reduction in the upper bound due to the improved BAO measurements in DESI DR2 with respect to DR1. This constraint is, however, about 20% weaker than the baseline bound recently reported by the DESI collaboration, $\sum m_{\nu}<0.064$ eV at 95% c.l. [16], which combines DESI DR2 BAO with Planck PR4. The difference between the P-ACT and PR4 combinations primarily arises from the treatment of low-$\ell$ EE and high-$\ell$ TT likelihoods, including specific choices of cuts.

However, we stress that these results, along with those presented below, are influenced by the prior $\sum m_{\nu}>0$ eV. This dependence has been discussed in [16], and more thoroughly in [20], that employed a profile likelihood analysis to quantify the impact of the prior and further investigated the implications of effective neutrino negative masses [55]. A similar profile likelihood analysis is presented in Appendix B.

Figure 4 illustrates how the constraints on the neutrino mass are influenced by the main CMB combinations — ACT, P-ACT, and PR4+ACT — when combined with DESI DR2 BAO. For comparison, we include the baseline results from [16] in magenta. For the PR4+ACT combination, we observe that by cutting the PR4 likelihood at the multipoles $\ell=2000$ in TT and $\ell=1000$ in TEEE, and merging with ACT data starting from these multipole cuts, tightens the upper bound to $\sum m_{\nu}<0.061$ eV at 95% c.l. (solid purple line) for $\Lambda$CDM. This results in a reduction of approximately 5% compared to the baseline results from [16], providing the tightest constraints on the total neutrino mass to date, derived exclusively from BAO and CMB datasets.

The difference in constraining power between PR4+ACT and the baseline results from [16] stems not only from the inclusion of ACT data, but also from the specific choice of the $\ell$-range where Planck is cut and ACT is added. In the PR4+ACT combination, we select the region of the spectrum where the ACT signal roughly exhibits lower uncertainty compared to Planck across most frequency spectra (see Figure 12 of [31]), leading to tighter neutrino mass constraints.

Additionally, Figure 4 includes the constraints from the joint DESI+ACT analysis, which, despite covering a smaller portion of the CMB power spectrum, yields an upper bound of $\sum m_{\nu}<0.073$ eV (95% c.l.), similar to those obtained with other CMB likelihood combinations.

In the $w_{0}w_{a}$CDM scenario, the combination of DESI DR2 BAO and the main CMB datasets (without SNe) yields marginalized 1D posterior distributions that peak at positive values of $\sum m_{\nu}$, consistent with the findings of [16]. This behavior is found across all main CMB dataset combinations. To avoid overcrowding, Figure 5 shows only the posteriors for ${\rm PR4}_{(\texttt{SRoll2})}$+ACT (dashed black) and PR4+ACT (solid black), the latter being the only DESI+CMB combination whose posterior peaks at zero. This case also provides the most stringent constraint on the neutrino mass within $w_{0}w_{a}$CDM, with $\sum m_{\nu}<0.15$ eV (95% c.l.).

Although the DESI+CMB results are largely consistent with positive neutrino masses, they also exhibit a preference for higher values of $\Omega_{m}$ (see Table 3), which are “stabilized” when including information from SNe Ia datasets. In that case, all posteriors peak at $\sum m_{\nu}=0$, and they would reach a maximum at negative $\sum m_{\nu}$ values if extrapolated.⁵⁵5This feature has motivated interest in exploring the implications of negative effective neutrino masses [55, 54, 53, 20]. This behavior is illustrated in Figure 5 for DESY5 and also holds when considering either Pantheon+ or Union3. These findings are consistent with those reported in [16, 26], and we explore them in more detail using the profile likelihood analysis in Appendix B.

Finally, we highlight the impact of the $\ell<30$ multipoles polarization data. In particular, we find that across all analyses, replacing the baseline low-$\ell$ EE likelihood with SRoll2 shifts the posterior peak toward higher values, as illustrated in Figure 5. This shift apparently loosens the neutrino mass constraints by up to 7%, in both the $\Lambda$CDM and $w_{0}w_{a}$CDM models.

In this paper, we reanalyze the cosmological results on the evidence for evolving dark energy and neutrino mass constraints of the official DESI DR2 BAO analysis presented in [16] by incorporating the latest ACT DR6 CMB data. The ACT DR6 data predict higher values for the physical densities of both baryons $\Omega_{\mathrm{b}}h^{2}$ and cold dark matter $\Omega_{\mathrm{c}}h^{2}$, compared to Planck. Within the $\Lambda$CDM model, this results in a discrepancy with DESI at a level exceeding $3\sigma$, which is larger than the 2.0$\sigma$ discrepancy observed with Planck PR4 (without CMB lensing). Since the ACT DR6 data cover a wide range of multipoles, partially sharing angular scales with Planck (in the range $600\leq\ell\leq 2500$), we combine these two CMB datasets using multipole cuts to avoid overlap. Along with ACT, we focus on two other CMB data combinations, namely, P-ACT (based on PR3, matching the combination presented in [31]), and PR4+ACT (our baseline CMB dataset). The PR4+ACT combination, based on PR4, uses cuts in the common multipole range between PR4 and ACT that lead to tighter constraints, showing a precision improvement of 14% in $n_{\rm s}$ and 23% in $\Omega_{\mathrm{b}}h^{2}$ with respect to PR4, and a 5% precision improvement over other combinations with a different $\ell$-cut scheme such as PR4_(1000,600)+ACT.

We explore the evidence for evolving dark energy under these three CMB datasets using ACT DR6 and find that DESI+ACT shows a 2.9$\sigma$ evidence in favor of the $w_{0}w_{a}$CDM model. This evidence is reduced to 2.4$\sigma$ when using DESI+P-ACT. This is due to the pull from P-ACT towards lower values of $\Omega_{\mathrm{c}}h^{2}$, compared to those from ACT and Planck individually, in the $\Lambda$CDM model. The combination DESI+PR4+ACT, which provides tighter constraints on cosmological parameters, leads to a 3.0$\sigma$ significance in favor of $w_{0}w_{a}$CDM. We also test the inclusion of the three SNe Ia datasets, namely Pantheon+, Union3 and DESY5, and find that variations in the CMB dataset leads to at most 0.3$\sigma$ differences and that the evidence for evolving dark energy can go up to 4.0$\sigma$. Therefore, we conclude that the results presented in [16] are robust in light of the new ACT CMB data.

We also present updated constraints in the neutrino mass bounds from cosmology and find that, in $\Lambda$CDM and assuming a physical prior $\sum m_{\nu}>0$ eV, DESI+ACT yields a neutrino mass constraint of $\sum m_{\nu}<0.073$ eV (95% c.l.). Our baseline CMB dataset, PR4+ACT, imposes an upper bound of $\sum m_{\nu}<0.061$ eV (95% c.l.) when combined with DESI. This represents a 5% reduction in the error compared to the neutrino mass constraints in [16], for the DESI+CMB baseline combination. Extending the background to an evolving dark energy component parameterized by $w_{0}$ and $w_{a}$ gives an upper mass limit of $\sum m_{\nu}<0.17$ eV and $\sum m_{\nu}<0.15$ eV at 95% c.l., for DESI+ACT and DESI+PR4+ACT, respectively. Consistent with [16], we find that combining DESI BAO with CMB data yields a preference for positive neutrino masses. However, this preference vanishes when SNe data are included in the analysis. Finally, we find that the use of the low-$\ell$ EE SRoll2 likelihood can relax the constraints on neutrino mass compared to the low-$\ell$ EE SimAll likelihood by up to 7%, mostly due to a shift of the best-fit $\sum m_{\nu}$ towards larger values.

Overall, we find the results presented in [16] to be robust under the inclusion of the ACT data for the CMB combinations tested in this work. A joint treatment of Planck and ACT DR6 covariance could eventually coalesce to a consolidated CMB dataset.

The data used in this analysis will be made public with Data Release 2 (details in https://data.desi.lbl.gov/doc/releases/). The data corresponding to the figures in this paper will be available in a Zenodo repository.