We study the impact of assumptions made about the neutrino mass ordering on cosmological parameter estimation with the purpose of understanding whether in the future it will be possible to infer the specific neutrino mass distribution from cosmological data. We find that although the commonly used assumption of a degenerate neutrino hierarchy is manifestly wrong and leads to changes in cosmological observables such as the cosmic microwave background and large scale structure compared to the correct (normal or inverted) neutrino hierarchy, the induced changes are so small that even with extremely optimistic assumptions about future data they will remain undetectable. We are thus able to conclude that while cosmology can probe the neutrino contribution to the cosmic energy density extremely precisely (and hence provide a detection of a non-zero total neutrino mass at high significance), it will not be possible to directly measure the individual neutrino masses.
The interplay between cosmology and earth based experiments is crucial in order to pin down neutrino physics. Indeed cosmology can provide very tight, yet model dependent, constraints on some neutrino properties. Here we focus on the neutrino mass sum, reviewing the up to date current bounds and showing the results of our forecast of the sensitivity of future experiments. Finally, we discuss the case for sterile neutrinos, explaining how non standard sterile neutrino self-interactions can reconcile the oscillation anomalies with cosmology.
In growing neutrino models, the neutrino mass increases in time and stops the dynamical evolution of a dark energy scalar field, thus explaining the 'why now' problem. A new attractive force, mediated by the 'cosmon' scalar field, makes non relativistic neutrino form lumps on the scales of superclusters and beyond. Nonlinear neutrino lumps are predicted to form at redshift z ~ 1 and, if observed, could be an indication for a new attractive force stronger than gravity.
It has been suggested that recent cosmological and flavor-oscillation data favor the existence of additional neutrino species beyond the three predicted by the Standard Model of particle physics. We apply Bayesian model selection to determine whether there is indeed any evidence from current cosmological datasets for the standard cosmological model to be extended to include additional neutrino flavors. The datasets employed include cosmic microwave background temperature, polarization and lensing power spectra, and measurements of the baryon acoustic oscillation scale and the Hubble constant. …
Cosmology provides an excellent laboratory for testing various aspects of neutrino physics. Here, I review the current status of cosmological searches for neutrino mass, as well as other properties of neutrinos. Future cosmological probes of neutrino properties are also discussed in detail.
Neutrino masses and the number of light neutrino species can be tested in a variety of laboratory experiments and also can be constrained by particle astrophysics and precision cosmology. A conflict between these various results could be an indication of new physics in the neutrino sector. In this paper we explore the possibility for reconciliation of otherwise discrepant results in a simple model containing a light scalar field which produces Mass Varying Neutrinos (MaVaNs). We extend previous work on MaVaNs to consider issues of neutrino clumping, the effects of additional contributions to n…
Short baseline neutrino oscillation experiments have shown hints of the existence of additional sterile neutrinos in the eV mass range. However, such neutrinos seem incompatible with cosmology because they have too large an impact on cosmic structure formation. Here we show that new interactions in the sterile neutrino sector can prevent their production in the early Universe and reconcile short baseline oscillation experiments with cosmology.
I review the current status of structure formation bounds on neutrino properties such as mass and energy density. I also discuss future cosmological bounds as well as a variety of different scenarios for reconciling cosmology with the presence of light sterile neutrinos.
We briefly discuss the main effects of the presence of a Light Sterile Neutrino (LS$ν$) in Cosmology and how its properties can be constrained by Cosmic Microwave Background (CMB) and other cosmological measurements.
Boltzmann solvers are an important tool for the computation of cosmological observables in the linear regime. In the presence of massive neutrinos, they involve solving the Boltzmann equation followed by an integration in momentum space to arrive at the desired fluid properties, a procedure which is known to be computationally slow. In this work we introduce the so-called generalized Boltzmann hierarchy (GBH) for massive neutrinos in cosmology, an alternative to the usual Boltzmann hierarchy, where the momentum dependence is integrated out leaving us with a two-parameter infinite set of ordina…
There exist a range of exciting scientific opportunities for Big Bang Nucleosynthesis (BBN) in the coming decade. BBN, a key particle astrophysics "tool" for decades, is poised to take on new capabilities to probe beyond standard model (BSM) physics. This development is being driven by experimental determination of neutrino properties, new nuclear reaction experiments, advancing supercomputing/simulation capabilities, the prospect of high-precision next-generation cosmic microwave background (CMB) observations, and the advent of 30m class telescopes.
Cosmology provides a unique and very powerful laboratory for testing neutrino physics. Here, I review the current status of cosmological neutrino measurements. Future prospects are also discussed, with particular emphasis on the interplay with experimental neutrino physics. Finally I discuss the possibility of a direct detection of the cosmic neutrino background and its associated anisotropy.
The energy scale of Dark Energy, $\sim 2 \times 10^{-3}$ eV, is a long way off compared to all known fundamental scales - except for the neutrino masses. If Dark Energy is dynamical and couples to neutrinos, this is no longer a coincidence. The time at which Dark Energy starts to behave as an effective cosmological constant can be linked to the time at which the cosmic neutrinos become nonrelativistic. This naturally places the onset of the Universe's accelerated expansion in recent cosmic history, addressing the why-now problem of Dark Energy. We show that these mechanisms indeed work in the …
Galaxy clusters --- in combination with CMB and BAO data --- can provide precise constraints on the sum of neutrino masses. However, these constraints depend on the calibration of the mass--observable relation. For instance, the mass calibration employed in Planck Collaboration (2011a,b) rules out the minimal 6-parameter ΛCDM model at 3.7σ, and implies a sum of neutrino masses \sum m_ν= 0.39 \pm 0.10. By contrast, the mass calibration favored by Rozo et al. (2012b) from a self-consistent analysis of X-ray, SZ, and optical scaling relations is consistent with a minimal flat ΛCDM model with no m…
In recent years precision cosmology has become an increasingly powerful probe of particle physics. Perhaps the prime example of this is the very stringent cosmological upper bound on the neutrino mass. However, other aspects of neutrino physics, such as their decoupling history and possible non-standard interactions, can also be probed using observations of cosmic structure. Here, I review the current status of cosmological bounds on neutrino properties and discuss the potential of future observations, for example by the recently approved EUCLID mission, to precisely measure neutrino propertie…
Sterile neutrinos in the electronvolt mass range are hinted at by a number of terrestrial neutrino experiments. However, such neutrinos are highly incompatible with data from the Cosmic Microwave Background and large scale structure. This paper discusses how charging sterile neutrinos under a new pseudoscalar interaction can reconcile eV sterile neutrinos with terrestrial neutrino data. We show that this model can reconcile eV sterile neutrinos in cosmology, providing a fit to all available data which is way better than the standard $Λ$CDM model with one additional fully thermalized sterile ne…
A new analytical approach allowing to account for massive neutrinos in the non-linear description of the growth of the large-scale structure of the universe is proposed. Unlike the standard approach in which neutrinos are described as a unique hot fluid, it is shown that the overall neutrino fluid can be equivalently decomposed into a collection of independent flows. Starting either from elementary conservation equations or from the evolution equation of the phase-space distribution function, we derive the two non-linear motion equations that each of these flows satisfies. Those fluid equation…
In $\rmΛ$CDM cosmology, Dark Matter (DM) and neutrinos are assumed to be non-interacting. However, it is possible to have scenarios, where DM-neutrino interaction may be present, leading to scattering of DM with neutrinos and annihilation of DM into neutrinos. We investigate the viability of such scenarios in the light of cosmological data by making use of the Planck 2018 dataset (high-l TT+TE+EE, low-l TT, low-l EE) and constrain these processes in the light of the same. We also discuss a viable particle DM model where DM-neutrino interaction is present, and map the constraints obtained to th…
We explore the complementarity between terrestrial neutrino oscillation experiments and astrophysical/cosmological measurements in probing the existence of sterile neutrinos. We find that upcoming accelerator neutrino experiments will not improve on constraints by the time they are operational, but that reactor experiments can already probe parameter space beyond the reach of Planck. We emphasize the tension between cosmological experiments and reactor antineutrino experiments and enumerate several possibilities for resolving this tension.
The Short BaseLine (SBL) neutrino oscillations anomalies hint at the presence of a sterile neutrino with a mass of around 1 eV. However, such neutrino is highly incompatible with the cosmological data, in particular from the Cosmic Microwave Background (CMB), if no new physics is assumed. An interesting possibility for reconciling the 1 eV sterile neutrino presence in cosmology is related to the existence of a new pseudoscalar interaction. If the sterile neutrinos experience such a pseudoscalar interaction, the cosmological analyses of the full CMB data prefer a sterile neutrino mass that is f…
Providing accurate predictions for the spatial distribution of matter and luminous tracers in the presence of massive neutrinos is an important task, given the imminent arrival of highly accurate large-scale structure observations. In this work, we address this challenge by extending cosmology-rescaling algorithms to massive neutrino cosmologies. In this way, a $Λ$CDM simulation can be modified to provide nonlinear structure formation predictions in the presence a hot component of arbitrary mass, and, if desired, to include non-gravitational modifications to the clustering of matter on large s…
Recent results from short--baseline neutrino oscillation experiments and Cosmic Microwave Background anisotropy measurements suggest the presence of additional sterile neutrinos. In this paper we properly combine these data sets to derive bounds on the sterile neutrino masses in the 3+1 and 3+2 frameworks, finding a potentially good agreement between the two datasets. However, when galaxy clustering is included in the analysis a tension between the oscillation and cosmological data is clearly present.
I give an overview of the effects of neutrino masses in cosmology, focussing on the role they play in the evolution of cosmological perturbations. I discuss how recent observations of the cosmic microwave background anisotropies and the large-scale matter distribution can probe neutrino masses with greater precision than current laboratory experiments. I describe several new techniques that will be used to probe cosmology in the future, as well as recent advances in the computation of the nonlinear matter power spectrum and related observables.
Precision cosmology enables to test fundamental physics, including neutrino properties, with unprecedented accuracy. In this work, I review the basics of neutrino cosmology. I briefly describe how neutrinos affect cosmological observables, such as anisotropies in the cosmic microwave background and fluctuations in the matter field. I show current constraints and projected sensitivities on the sum of the neutrino masses $Σm_ν$ and on the number of relativistic species $N_\mathrm{eff}$ from a selection of cosmological data. I finally comment about the implications of those bounds for neutrino ph…
We explore the dark matter phenomenology of a weak-scale right-handed neutrino in the context of a Two Higgs Doublet Model. The expected signal at direct detection experiments is different from the usual spin-independent and spin-dependent classification since the scattering with quarks depends on the dark matter spin. The dark matter relic density is set by thermal freeze-out and in the presence of non-standard cosmology, where an Abelian gauge symmetry is key for the dark matter production mechanism. We show that such symmetry allows us to simultaneously address neutrino masses and the flavo…
Precision cosmology and big-bang nucleosynthesis mildly favor extra radiation in the universe beyond photons and ordinary neutrinos, lending support to the existence of low-mass sterile neutrinos. We use the WMAP 7-year data, small-scale CMB observations from ACBAR, BICEP and QuAD, the SDSS 7th data release, and measurement of the Hubble parameter from HST observations to derive credible regions for the assumed common mass scale m_s and effective number N_s of thermally excited sterile neutrino states. Our results are compatible with the existence of one or perhaps two sterile neutrinos, as su…
We use a large suite of N-body simulations to study departures from universality in halo abundances and clustering in cosmologies with non-vanishing neutrino masses. To this end, we study how the halo mass function and halo bias factors depend on the scaling variable $σ^2(M,z)$, the variance of the initial matter fluctuation field, rather than on halo mass $M$ and redshift $z$ themselves. We show that using the variance of the cold dark matter rather than the total mass field, i.e., $σ^2_{cdm}(M,z)$ rather than $σ^2_{m}(M,z)$, yields more universal results. Analysis of halo bias yields similar…
With low redshift probes reaching unprecedented precision, uncertainty of the CMB optical depth is expected to be the limiting factor for future cosmological neutrino mass constraints. In this paper, we discuss to what extent combinations of CMB lensing and galaxy surveys measurements at low redshifts $z\sim 0.5-5$ will be able to make competitive neutrino mass measurements without relying on any optical depth constraints. We find that the combination of LSST galaxies and CMB-S4 lensing should be able to achieve constraints on the neutrino mass sum of 25meV without optical depth information, a…
It has been suggested that both recent cosmological data and the results of flavor oscillation experiments (MiniBooNE and LSND) lend support to the existence of low-mass sterile neutrinos. The cosmological data appear to weakly favor additional forms of radiation in the Universe, beyond photons and three standard neutrino families. We reconsider the cosmological evidence by making the resulting confidence intervals on the additional effective neutrino species as prior-independent as possible. We find that, once the prior-dependence is removed, the latest cosmological data show no evidence for …
There are three distinct regimes in which radio observations of the redshifted 21 cm line of HI can contribute directly to cosmology in unique ways. The regimes are naturally divided by redshift, from high to low, into: inflationary physics, the Dark Ages and reionization, and galaxy evolution and Dark Energy. Each measurement presents its own set of technical, theoretical, and observational challenges, making "what we need to know" not so much an astrophysical question at this early stage as a comprehensive experimental question. A wave of new pathfinder projects are exploring the fundamental…
We comprehensively analyse the cosmology dependence of counts-in-cell statistics. We focus on the shape of the one-point probability distribution function (PDF) of the matter density field at mildly nonlinear scales. Based on large-deviation statistics, we parametrise the cosmology dependence of the matter PDF in terms of the linear power spectrum, the growth factor, the spherical collapse dynamics, and the nonlinear variance. We extend our formalism to include massive neutrinos, finding that the total matter PDF is highly sensitive to the total neutrino mass $M_ν$ and can disentangle it from …
There are hints, both from cosmology and from neutrino oscillation experiments, that one or two sterile neutrinos with eV masses are favored. We consider the implications of combining data from short baseline neutrino experiments with cosmological observations. In particular we consider cosmological models where the equation of state of dark energy and the curvature are allowed to vary. We find that the consistency of results from short baseline experiments and cosmology is dependent on the cosmological data sets that are used. When the two are consistent, we find that the inclusion of informa…
Cosmology is making impressive progress and it is producing stringent bounds on the sum of the neutrino masses Σ, a parameter of great importance for the current laboratory experiments. In this letter, we exploit the potential relevance of the analysis of Palanque-Delabrouille et al. [JCAP 1502, 045 (2015)] to the neutrinoless double beta decay (0νββ) search. This analysis indicates small values for the lightest neutrino mass, since the authors find Σ < 84 meV at 1σ C. L., and provides a 1σ preference for the normal hierarchy. The allowed values for the Majorana effective mass, probed by 0νββ,…
I introduce the consequences of neutrino mass and mixing in the dense environments of the early Universe and in astrophysical environments. Thermal and matter effects are reviewed in the context of a two-neutrino formalism, with methods of extension to multiple neutrinos. The observed large neutrino mixing angles place the strongest constraint on cosmological lepton (or neutrino) asymmetries, while new sterile neutrinos provide a wealth of possible new physics, including lepton asymmetry generation as well as candidates for dark matter. I also review cosmic microwave background and large-scale…
Recent advances in cosmic observations have brought us to the verge of discovery of the absolute scale of neutrino masses. Nonzero neutrino masses are known evidence of new physics beyond the Standard Model. Our understanding of the clustering of matter in the presence of massive neutrinos has significantly improved over the past decade, yielding cosmological constraints that are tighter than any laboratory experiment, and which will improve significantly over the next decade, resulting in a guaranteed detection of the absolute neutrino mass scale.
Short baseline neutrino oscillation experiments have shown hints of the existence of additional sterile neutrinos in the eV mass range. Such sterile neutrinos are incompatible with cosmology because they suppress structure formation unless they can be prevented from thermalising in the early Universe or removed by subsequent decay or annihilation. Here we present a novel scenario in which both sterile neutrinos and dark matter are coupled to a new, light pseudoscalar. This can prevent thermalisation of sterile neutrinos and make dark matter sufficiently self-interacting to have an impact on ga…
We show how 21 cm cosmology can test relic neutrino radiative decays into sterile neutrinos. Using recent EDGES results, we derive constraints on the lifetime of the decaying neutrinos. If the EDGES anomaly will be confirmed, then there are two solutions, one for much longer and one for much shorter lifetimes than the age of the universe, showing how relic neutrino radiative decays can explain the anomaly in a simple way. We also show how to combine EDGES results with those from radio background observations, showing that potentially the ARCADE 2 excess can be also reproduced together with the…
It is shown that the tension between recent neutrino oscillation experiments, favoring sterile neutrinos with masses of the order of 1 eV, and cosmological data which impose stringent constraints on neutrino masses from the free streaming suppression of density fluctuations, can be resolved in models of the present accelerated expansion of the Universe based on f(R) gravity.
We explore the cosmological signals of theories in which the neutrinos decay into invisible dark radiation after becoming non-relativistic. We show that in this scenario, near-future large scale structure measurements from the Euclid satellite, when combined with cosmic microwave background data from Planck, may allow an independent determination of both the lifetime of the neutrinos and the sum of their masses. These parameters can be independently determined because the Euclid data will cover a range of redshifts, allowing the growth of structure over time to be tracked. If neutrinos are sta…
Neutrinos can play an important role in the evolution of the Universe, modifying some of the cosmological observables. In this contribution we summarize the main aspects of cosmological relic neutrinos and we describe how the precision of present cosmological data can be used to learn about neutrino properties, in particular their mass, providing complementary information to beta decay and neutrinoless double-beta decay experiments. We show how the analysis of current cosmological observations, such as the anisotropies of the cosmic microwave background or the distribution of large-scale struc…
Light sterile neutrinos with a mass around 1 eV have been studied for many years as a possible explanation of the so called short-baseline neutrino oscillation anomalies. Recently, several neutrino oscillation experiments reported preferences for non-zero values of the mixing angles and squared mass differences for active-sterile mixing, which however are not always in agreement. I review our current knowledge of the light sterile neutrino in the 3+1 model, starting with a separate discussion on the status of the most relevant searches and then analyzing the problems that arise when combining …
Cosmology is well suited to study the effects of long range interactions due to the large densities in the early Universe. In this article, we explore how the energy density and equation of state of a fermion system diverge from the commonly assumed ideal gas form under the presence of scalar long range interactions with a range much smaller than cosmological scales. In this scenario, "small"-scale physics can impact our largest-scale observations. As a benchmark, we apply the formalism to self-interacting neutrinos, performing an analysis to present and future cosmological data. Our results s…
We consider generic models of quintessence and we investigate the influence of massive neutrino matter with field-dependent masses on the matter power spectrum. In case of minimally coupled neutrino matter, we examine the effect in tracker models with inverse power-law and double exponential potentials. We present detailed investigations for the scaling field with a steep exponential potential, non-minimally coupled to massive neutrino matter, and we derive constraints on field-dependent neutrino masses from the observational data.
Despite the impressive success of the standard cosmological model, several anomalies defy its triumph. Among them is the so-called lensing anomaly: the Planck satellite observes stronger CMB gravitational lensing than expected. The role of neutrinos in this anomaly has been mostly overlooked, despite their key role in CMB lensing, because in the standard scenario they tend to increase the tension. Here, we show that this strongly depends on the assumed neutrino equation of state. We demonstrate that if neutrinos have yet undiscovered long-range interactions, the lensing pattern is significantl…
We show that, if they exist, lepton number asymmetries ($L_α$) of neutrino flavors should be distinguished from the ones ($L_i$) of mass eigenstates, since Big Bang Nucleosynthesis (BBN) bounds on the flavor eigenstates cannot be directly applied to the mass eigenstates. Similarly, Cosmic Microwave Background (CMB) constraints on mass eigenstates do not directly constrain flavor asymmetries. Due to the difference of mass and flavor eigenstates, the cosmological constraint on the asymmetries of neutrino flavors can be much stronger than conventional expectation, but not uniquely determined unle…
In this paper we revisit the question of the information which cosmology provides on the scenarios with sterile neutrinos invoked to describe the SBL anomalies using Bayesian statistical tests. We perform an analysis of the cosmological data in $Λ$CDM$+r+ν_s$ cosmologies for different cosmological data combinations, and obtain the marginalized cosmological likelihood in terms of the two relevant parameters, the sterile neutrino mass $m_s$ and its contribution to the energy density of the early Universe $N_{\rm eff}$. We then present an analysis to quantify at which level a model with one steri…
In this essay we extend the standard discussion of neutrino oscillations to astrophysical neutrinos propagating through expanding space. This extension introduces a new cosmological parameter $I$ into the oscillation phase. The new parameter records cosmic history in much the same manner as the redshift z or the apparent luminosity D_L. Measuring $I$ through neutrino oscillations could help determine cosmological parameters and discriminate among different cosmologies.
We briefly review the recent developments in neutrino physics and astrophysics which have import for frontline research in nuclear physics. These developments, we argue, tie nuclear physics to exciting developments in observational cosmology and astrophysics in new ways. Moreover, the behavior of neutrinos in dense matter is itself a fundamental problem in many-body quantum mechanics, in some ways akin to well-known issues in nuclear matter and nuclei, and in some ways radically different, especially because of nonlinearity and quantum de-coherence. The self-interacting neutrino gas is the onl…
We explore the neutrinoless double beta ($0νββ$) decay induced by an ultralight dark matter field coupled to neutrinos. The effect on $0νββ$ decay is significant if the coupling violates the lepton number, for which the $ΔL=2$ transition is directly driven by the dark matter field without further suppression of small neutrino masses. As the ultralight dark matter can be well described by a classical field, the effect features a periodic modulation pattern in decay events. However, we find that in the early Universe such coupling will be very likely to alter the standard cosmological results. I…
Sterile neutrinos are natural extensions to the standard model of particle physics in neutrino mass generation mechanisms. If they are relatively light, less than approximately 10 keV, they can alter cosmology significantly, from the early Universe to the matter and radiation energy density today. Here, we review the cosmological role such light sterile neutrinos can play from the early Universe, including production of keV-scale sterile neutrinos as dark matter candidates, and dynamics of light eV-scale sterile neutrinos during the weakly-coupled active neutrino era. We review proposed signat…
We present a comprehensive overview of an extension of the Standard Model that contains three right-handed (sterile) neutrinos with masses below the electroweak scale [the Neutrino Minimal Standard Model, (nuMSM)]. We consider the history of the Universe from the inflationary era through today and demonstrate that most of the observed phenomena beyond the Standard Model can be explained within the framework of this model. We review the mechanism of baryon asymmetry of the Universe in the nuMSM and discuss a dark matter candidate that can be warm or cold and satisfies all existing constraints. …
We explore the potential of measurements of cosmological effects, such as neutrino spectral distortions from the neutrino decoupling and neutrino clustering in our Galaxy, via cosmic neutrino capture on tritium. We compute the precise capture rates of each neutrino species including such cosmological effects to probe them. These precise estimates of capture rates are also important in that the would-be deviation of the estimated capture rate could suggest new neutrino physics and/or a non-standard evolution of the universe. In addition, we discuss the precise differences between the capture ra…
Consistent treatment of flavour-specific neutrino self-interactions in cosmology
Instituto de Física Corpuscular, CSIC-Universitat de València（粒子物理研究所，西班牙瓦伦西亚大学）；Departament de Física Tèorica, Universitat de València（理论物理系，西班牙瓦伦西亚大学）；UCLouvain, Centre for Cosmology, Particle Physics and Phenomenology (CP3)（天主教鲁汶大学，宇宙学、粒子物理与现象学中心）；Technische Universität München（慕尼黑工业大学）；Bielefeld University（比勒费尔德大学）
Relic neutrinos play an important role in the evolution of the Universe, modifying some of the cosmological observables. We summarize the main aspects of cosmological neutrinos and describe how the precision of present cosmological data can be used to learn about neutrino properties. In particular, we discuss how cosmology provides information on the absolute scale of neutrino masses, complementary to beta decay and neutrinoless double-beta decay experiments. We explain why the combination of Planck temperature data with measurements of the baryon acoustic oscillation angular scale provides a …
In light of the improved sensitivities of cosmological observations, we examine the status of quasi-degenerate neutrino mass scenarios. Within the simplest extension of the standard cosmological model with massive neutrinos, we find that quasi-degenerate neutrinos are severely constrained by present cosmological data and neutrino oscillation experiments. % % We find that Planck 2018 observations of cosmic microwave background (CMB) anisotropies disfavour quasi-degenerate neutrino masses at $2.4$ Gaussian $σ$'s, while adding Baryon acoustic oscillations (BAO) data brings the rejection to 5.9$σ$…
We propose a simple method to quantify a possible exclusion of the inverted neutrino mass ordering from cosmological bounds on the sum of the neutrino masses. The method is based on Bayesian inference and allows for a calculation of the posterior odds of normal versus inverted ordering. We apply the method for a specific set of current data from Planck CMB data and large-scale structure surveys, providing an upper bound on the sum of neutrino masses of 0.14 eV at 95% CL. With this analysis we obtain posterior odds for normal versus inverted ordering of about 2:1. If cosmological data is combin…
