Exploring massive neutrinos in dark cosmologies with eftcamb/EFTCosmoMC

We revisit the degeneracy between massive neutrinos and generalized theories of gravity in the framework of the effective field theory of cosmic acceleration. In particular, we consider $f(R)$ theories and a class of nonminimally coupled models parametrized via a coupling to gravity which is linear in the scale factor. In the former case, we find a slightly lower degeneracy with that found in the literature, due to the fact that we implement exact designer $f(R)$ models and evolve the full linear dynamics of perturbations. As a consequence, our bounds are slightly tighter on the $f(R)$ parameter but looser on the summed neutrino mass. We also set a new upper bound on the Compton wavelength parameter ${\text{Log}}_{10}{B}_0<-4.1$ at 95% C.L. with a fixed summed neutrino mass ($\sum m_{\nu }=0.06\mathrm{eV}$) in $f(R)$ gravity with the combined data sets from cosmic microwave background temperature and lensing power spectra of the Planck Collaboration, as well as galaxy power spectrum from the WiggleZ dark energy survey. We do not observe a sizable degeneracy between massive neutrinos and modified gravity in the nonminimally coupled model considered, which corresponds to a peculiar case of coupling that depends linearly on the scale factor. The analysis is performed with an updated version of the eftcamb/EFTCosmoMC package, which is now publicly available and extends the first version of the code with the consistent inclusion of massive neutrinos, tensor modes, several alternative background histories, and designer quintessence models.

Figure 1

Left: The marginalized joint likelihood for the present day value of ${\text{Log}}_{10}{B}_0$ and the sum of the neutrino masses, $\sum m_{\nu }$. Center and Right: The marginalized likelihood of ${\text{Log}}_{10}{B}_0$ for, respectively, designer $f(R)$ models with variable (a) or fixed (b) neutrino masses. In all three panels different colors correspond to different combinations of cosmological observations, as shown in the legend. The darker and lighter shades correspond, respectively, to the 68% C.L. and 95% C.L.

Figure 2

The marginalized joint likelihood for the present-day value of ${\text{Log}}_{10}{B}_0$, the sum of the neutrino masses, $\sum m_{\nu }$, and the amplitude of the (linear) power spectrum on the scale of $8h^{-1}\mathrm{Mpc}$, ${\sigma }_8$. Different colors correspond to the different codes used and, hence, a different modeling of $f(R)$, as shown in the legend. The darker and lighter shades correspond, respectively, to the 68% C.L. and 95% C.L. The solid line indicates the best-constrained direction in parameter space, while the dashed line indicates the least-constrained one. As we can see, these directions differ noticeably for the two codes.

Figure 3

Left: The marginalized joint likelihood for the present-day value of ${\text{Log}}_{10}{B}_0$ and the sum of the neutrino masses, $\sum m_{\nu }$. Center and Right: The marginalized likelihood of ${\text{Log}}_{10}{B}_0$ for models with variable (a) or fixed (b) neutrino masses. In all three panels different colors correspond to different numerical codes, as shown in the legend and described in Sec. 3b. The darker and lighter shades correspond, respectively, to the 68% C.L. and 95% C.L.

Figure 4

The marginalized joint likelihood for the present-day value of ${\mathrm{\Omega }}_0^{\mathrm{EFT}}$, the sum of the neutrino masses, $\sum m_{\nu }$, and the amplitude of the (linear) power spectrum on the scale of $8h^{-1}\mathrm{Mpc}$, ${\sigma }_8$. Different colors correspond to different combinations of cosmological observations, as shown in the legend. The darker and lighter shades correspond, respectively, to the 68% C.L. and 95% C.L. No new significant degeneracies between these parameters are found.