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Combining cosmic microwave background (CMB) data from Planck satellite data, Baryon Acoustic Oscillations (BAO) measurements and Type Ia supernovae (SNe Ia) data, we obtain the bounds on total neutrino masses $M_ u$ with the approximation of degenerate neutrino masses and for three dark energy models: the cosmological constant ($Lambda$CDM) model, a phenomenological emergent dark energy (PEDE) model and a model-independent quintessential parameterization (HBK). The bounds on the sum of neutrino masses $M_ u$ depend on the dark energy (DE) models. In the HBK model, we confirm the conclusion from some previous work that the quintessence prior of dark energy tends to tighten the cosmological constraint on $M_ u$. On the other hand, the PEDE model leads to larger $M_ u$ and a nonzero lower bound. Besides, we also explore the correlation between three different neutrino hierarchies and dark energy models.
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In this work we update the bounds on $sum m_{ u}$ from latest publicly available cosmological data and likelihoods using Bayesian analysis, while explicitly considering particular neutrino mass hierarchies. In the minimal $Lambdatextrm{CDM}+sum m_{ u}$ model with most recent CMB data from Planck 2018 TT,TE,EE, lowE, and lensing; and BAO data from BOSS DR12, MGS, and 6dFGS, we find that at 95% C.L. the bounds are: $sum m_{ u}<0.12$ eV (degenerate), $sum m_{ u}<0.15$ eV (normal), $sum m_{ u}<0.17$ eV (inverted). The bounds vary across the different mass orderings due to different priors on $sum m_{ u}$. Also, we find that the normal hierarchy is very mildly preferred relative to the inverted, using both minimum $chi^2$ values and Bayesian Evidence ratios. In this paper we also provide bounds on $sum m_{ u}$ considering different hierarchies in various extended cosmological models: $Lambdatextrm{CDM}+sum m_{ u}+r$, $wtextrm{CDM}+sum m_{ u}$, $w_0 w_a textrm{CDM}+sum m_{ u}$, $w_0 w_a textrm{CDM}+sum m_{ u}$ with $w(z)geq -1$, $Lambda textrm{CDM} + sum m_{ u} + Omega_k$, and $Lambda textrm{CDM} + sum m_{ u} + A_{textrm{Lens}}$. We do not find any strong evidence of normal hierarchy over inverted hierarchy in the extended models either.
In this paper, we make a comparison for the impacts of smooth dynamical dark energy, modified gravity, and interacting dark energy on the cosmological constraints on the total mass of active neutrinos. For definiteness, we consider the $Lambda$CDM model, the $w$CDM model, the $f(R)$ model, and two typical interacting vacuum energy models, i.e., the I$Lambda$CDM1 model with $Q=beta Hrho_{rm c}$ and the I$Lambda$CDM2 model with $Q=beta Hrho_{Lambda}$. In the cosmological fits, we use the Planck 2015 temperature and polarization data, in combination with other low-redshift observations including the baryon acoustic oscillations, the type Ia supernovae, the Hubble constant measurement, and the large-scale structure observations, such as the weak lensing as well as the redshift-space distortion. Besides, the Planck lensing measurement is also employed in this work. We find that, the $w$CDM model favors a higher upper limit on the neutrino mass compared to the $Lambda$CDM model, while the upper limit in the $f(R)$ model is similar with that of $Lambda$CDM model. For the interacting vacuum energy models, the I$Lambda$CDM1 model favors a higher upper limit on neutrino mass, while the I$Lambda$CDM2 model favors an identical neutrino mass with the case of $Lambda$CDM.
The combination of current large scale structure and cosmic microwave background (CMB) anisotropies data can place strong constraints on the sum of the neutrino masses. Here we show that future cosmic shear experiments, in combination with CMB constraints, can provide the statistical accuracy required to answer questions about differences in the mass of individual neutrino species. Allowing for the possibility that masses are non-degenerate we combine Fisher matrix forecasts for a weak lensing survey like Euclid with those for the forthcoming Planck experiment. Under the assumption that neutrino mass splitting is described by a normal hierarchy we find that the combination Planck and Euclid will possibly reach enough sensitivity to put a constraint on the mass of a single species. Using a Bayesian evidence calculation we find that such future experiments could provide strong evidence for either a normal or an inverted neutrino hierachy. Finally we show that if a particular neutrino hierachy is assumed then this could bias cosmological parameter constraints, for example the dark energy equation of state parameter, by > 1sigma, and the sum of masses by 2.3sigma.
As weak lensing surveys become deeper, they reveal more non-Gaussian aspects of the convergence field which can only be extracted using statistics beyond the power spectrum. In Cheng et al. (2020) we showed that the scattering transform, a novel statistic borrowing mathematical concepts from convolutional neural networks, is a powerful tool for cosmological parameter estimation in the non-Gaussian regime. Here, we extend that analysis to explore its sensitivity to dark energy and neutrino mass parameters with weak lensing surveys. We first use image synthesis to show visually that, compared to the power spectrum and bispectrum, the scattering transform provides a better statistical vocabulary to characterize the perceptual properties of lensing mass maps. We then show that it is also better suited for parameter inference: (i) it provides higher sensitivity in the noiseless regime, and (ii) at the noise level of Rubin-like surveys, though the constraints are not significantly tighter than those of the bispectrum, the scattering coefficients have a more Gaussian sampling distribution, which is an important property for likelihood parametrization and accurate cosmological inference. We argue that the scattering coefficients are preferred statistics considering both constraining power and likelihood properties.
We investigate cosmological models in which dynamical dark energy consists of a scalar field whose present-day value is controlled by a coupling to the neutrino sector. The behaviour of the scalar field depends on three functions: a kinetic function, the scalar field potential, and the scalar field-neutrino coupling function. We present an analytic treatment of the background evolution during radiation- and matter-domination for exponential and inverse power law potentials, and find a relaxation of constraints compared to previous work on the amount of early dark energy in the exponential case. We then carry out a numerical analysis of the background cosmology for both types of potential and various illustrative choices of the kinetic and coupling functions. By applying bounds from Planck on the amount of early dark energy, we are able to constrain the magnitude of the kinetic function at early times.
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