Hiding neutrino mass in modified gravity cosmologies

TL;DR

The paper analyzes how neutrino mass signals can be mimicked by Horndeski modified gravity in the linear regime using an EFT parameterization that includes the braiding scale $k_B$ and time-dependent functions $\alpha_K,\alpha_B,\alpha_M,\alpha_T$. It shows that a single parameter, primarily the braiding term $\alpha_B$, dominates the degeneracy with the total neutrino mass $\sum m_\nu$, and that a tuned $\alpha_B$ can nearly cancel the neutrino-induced power suppression at a given redshift; this cancellation depends on redshift and dataset, with Euclid-like forecasts able to partly lift the degeneracy. The study highlights the roles of $\alpha_K$ and the braiding scale in shaping the power spectrum and demonstrates that incorporating expansion-history information via Full $P(k)$ is crucial to constrain neutrino masses in MG contexts. Overall, the work provides a principled framework to quantify and potentially break the neutrino–gravity degeneracy in near-future cosmological surveys.

Abstract

Cosmological observables show a dependence with the neutrino mass, which is partially degenerate with parameters of extended models of gravity. We study and explore this degeneracy in Horndeski generalized scalar-tensor theories of gravity. Using forecasted cosmic microwave background and galaxy power spectrum datasets, we find that a single parameter in the linear regime of the effective theory dominates the correlation with the total neutrino mass. For any given mass, a particular value of this parameter approximately cancels the power suppression due to the neutrino mass at a given redshift. The extent of the cancellation of this degeneracy depends on the cosmological large-scale structure data used at different redshifts. We constrain the parameters and functions of the effective gravity theory and determine the influence of gravity on the determination of the neutrino mass from present and future surveys.

Figures (3)

• Figure 1: Relative difference in the matter power spectrum of three models with respect to the fiducial model GR$_\mathrm{fid}$ at redshift $z=1.4$. The blue line shows the suppression due to massive neutrinos M500 model vs M0. The green line corresponds to the MCMC best fit cosmological and MG parameters with the M0 neutrino model, showing the MG enhancement in the matter power spectrum at small scales. The red line represents the MCMC best fit of the MG model with massive neutrinos, which mimics the GR model with massless neutrinos.
• Figure 2: Neutrino mass posterior (relative to its maximum) of modified gravity models for several datasets. The fiducial is given by the M0 model. The posterior wide tail of the CMB dataset is considerably damped when power spectrum data is added. Significantly, heavy neutrinos, considered in the previous section, are highly disfavoured once we include information coming from the expansion history.
• Figure 3: Correlation between $c_B$ and $\Sigma m_\nu$ assuming a fiducial model GR+M0 (upper panels) or GR+M150 (lower panels). Fiducials are represented as black dots. Contours are shown for the $68\%$ and $95\%$ CL when considering CMB (left panels), CMB+P(k) and CMB+Full P(k) (right panels) datasets. In the latter case we have plotted the case with only observational errors, which is the most constraining case. Cuts in the correlations appear as a result of our assumptions: in our model $c_B$ cannot be negative without triggering instabilities and $\Sigma m_\nu$ cannot be less than $\simeq 0.06$ eV since we imposed that neutrinos obey the normal ordering mass scheme.