Constraining neutrino mass and extra relativistic degrees of freedom in dynamical dark energy models using Planck 2015 data in combination with low-redshift cosmological probes: basic extensions to $Λ$CDM cosmology

TL;DR

This work addresses how dark energy properties influence cosmological constraints on the sum of neutrino masses $\sum m_\nu$ and the effective number of relativistic species $N_{\rm eff}$ within basic extensions to $\Lambda$CDM, namely $w$CDM and $w_0w_a$CDM. It performs global fits using Planck 2015 CMB data combined with low-redshift probes (BAO, SN, $H_0$) and large-scale structure measurements (WL, RSD, SZ, CMB lensing), exploring three data combinations: Planck+BAO, Planck+BSH, and Planck+BSH+LSS. The results show that dynamical dark energy can significantly loosen the neutrino-mass bounds compared with $\Lambda$CDM, with higher upper limits allowed when phantom or quintom behavior is favored, while the constraints on $N_{\rm eff}$ remain consistent with the standard value $3.046$ across all models. The findings imply that dark energy parameters can modulate the cosmological weighing of neutrinos but have negligible impact on the inferred amount of dark radiation, offering robust support for the standard $N_{\rm eff}$ interpretation even in dynamical DE scenarios.

Abstract

We investigate how the properties of dark energy affect the cosmological measurements of neutrino mass and extra relativistic degrees of freedom. We limit ourselves to the most basic extensions of $Λ$ cold dark matter (CDM) model, i.e. the $w$CDM model with one additional parameter $w$, and the $w_{0}w_{a}$CDM model with two additional parameters, $w_{0}$ and $w_{a}$. In the cosmological fits, we employ the 2015 cosmic microwave background temperature and polarization data from the Planck mission, in combination with low-redshift measurements such as the baryon acoustic oscillations, Type Ia supernovae and the Hubble constant ($H_{0}$). Given effects of massive neutrinos on large-scale structure, we further include weak lensing, redshift space distortion, Sunyaev--Zeldovich cluster counts and Planck lensing data. We show that, though the cosmological constant $Λ$ is still consistent with the current data, a phantom dark energy ($w<-1$) or an early phantom dark energy (i.e. quintom evolving from $w<-1$ to $w>-1$) is slightly more favoured by current observations, which leads to the fact that in both $w$CDM and $w_0w_a$CDM models we obtain a larger upper limit of $\sum m_ν$. We also show that in the three dark energy models, the constraints on $N_{\rm eff}$ are in good accordance with each other, all in favour of the standard value 3.046, which indicates that the dark energy parameters almost have no impact on constraining $N_{\rm eff}$. Therefore, we conclude that the dark energy parameters can exert a significant influence on the cosmological weighing of neutrinos, but almost cannot affect the constraint on dark radiation.

Figures (11)

• Figure 1: Left-hand panel: The CMB temperature spectra $C_{\ell}^{TT}$ with different EoS of dark energy $w$. Here, we choose $w$$=$$-0.8$, $-1.0$ and $-1.2$, and fix $\sum m_{\nu}$ to be 0.06 eV. At $2$$<$$\ell$$<$$50$, it is found that a smaller $w$ leads to a suppression of CMB temperature power, namely, a smaller $C_{\ell}^{TT}$, due to the late ISW effect. Right-hand panel: the CMB temperature spectra with different total neutrino mass $\sum m_{\nu}$. Here, we choose $\sum m_{\nu}$$=$$0$, $0.6$ eV and $1.2$ eV, and fix $w$$=$$-1$. At $2$$<$$\ell$$<$$50$, a larger $\sum m_{\nu}$ leads to a smaller $C_{\ell}^{TT}$, due to the late ISW effect.
• Figure 2: 68 per cent and 95 per cent CL contours in the $w$$-$$\sum m_{\nu}$ plane from the three data combinations of Planck+BAO, Planck+BSH and Planck+BSH+LSS, where 'BSH' denotes the joint of BAO, SN and $H_{0}$ data, 'LSS' denotes the combination of WL, RSD, SZ and CMB lensing data. Planck+BSH gives a tighter constraint on $\sum m_{\nu}$, but Planck+BSH+LSS allows a larger $\sum m_{\nu}$. The constraints on dark energy from the three data combinations are all compatible with $\Lambda$CDM.
• Figure 3: Samples from the Planck+BSH chains in the $w_{0}$$-$$w_{a}$ plane, colour-coded by $\sum m_{\nu}$. The green contours show the constraints from the Planck+BAO data set, and the red contours show the constraints from Planck+BSH+LSS. The $\Lambda$CDM case with $w_{0}$$=$$-1$ and $w_{a}$$=$$0$ is shown in the plane by the cross of horizontal and vertical dashed lines. The samples show the points corresponding to larger $\sum m_{\nu}$ distribute the regions of $w$ evolving from $w$$<$$-1$ to $w$$>$$-1$.
• Figure 4: Joint, marginalized constraints from Planck+BSH+LSS on the $\Lambda$CDM (red), $w$CDM (green) and $w_{0}w_{a}$CDM (blue) models. The 68 per cent and 95 per cent CL contours in the $\sigma_{8}$$-$$\sum m_{\nu}$ plane are shown. Note here that there is a peak in the posterior distribution of $\sum m_{\nu}$ for the $w_{0}w_{a}$CDM case around $\sum m_{\nu}$$=$$0.285$ eV, but the statistical significance is rather low.
• Figure 5: The 68 per cent and 95 per cent CL contours in the $\sum m_{\nu}$$-$$\Omega_{\rm b}h^{2}$, $\sum m_{\nu}$$-$$\Omega_{\rm m}$ and $\sum m_{\nu}$$-$$H_{0}$ planes. We show the Planck+BAO constraints in the top panel and the Planck+BSH constraints in the bottom panel.