The observational status of Galileon gravity after Planck

TL;DR

This work tests the observational viability of Galileon gravity against Planck CMB and BAO data across the Cubic, Quartic, and Quintic branches. By solving the linear perturbation equations with tracker-based background evolution and performing MCMC constraints, the authors show that including massive neutrinos can substantially alleviate tensions between datasets and yield competitive fits to Planck measurements, especially for lensing. The analysis reveals that the Cubic branch tends to predict a negative ISW effect and stronger late-time lensing signals, while Quartic and Quintic can suppress ISW power but introduce residual time-varying local gravity effects, which are tightly constrained by solar-system tests. Overall, Planck data favor reduced late-time modifications to gravity, with neutrino masses playing a crucial role in reconciling Galileon models with observations; future nonlinear-growth modeling and precise local gravity tests will be decisive in further assessing these theories.

Abstract

We use the latest CMB data from Planck, together with BAO measurements, to constrain the full parameter space of Galileon gravity. We constrain separately the three main branches of the theory known as the Cubic, Quartic and Quintic models, and find that all yield a very good fit to these data. Unlike in $Λ{\rm CDM}$, the Galileon model constraints are compatible with local determinations of the Hubble parameter and predict nonzero neutrino masses at over $5σ$ significance. We also identify that the low-$l$ part of the CMB lensing spectrum may be able to distinguish between $Λ{\rm CDM}$ and Galileon models. In the Cubic model, the lensing potential deepens at late times on sub-horizon scales, which is at odds with the current observational suggestion of a positive ISW effect. Compared to $Λ$CDM, the Quartic and Quintic models predict less ISW power in the low-$l$ region of the CMB temperature spectrum, and as such are slightly preferred by the Planck data. We illustrate that residual local modifications to gravity in the Quartic and Quintic models may render the Cubic model as the only branch of Galileon gravity that passes Solar System tests.

Figures (13)

• Figure 1: Marginalized two-dimensional $95\%$ confidence level contours obtained using the PL (open dashed) and PLB (filled) datasets for the base Cubic Galileon (blue), ${\nu} \rm{Cubic}$ Galileon (red) and ${\nu} \Lambda\rm{CDM}$ (green) models. In the top right panel, the horizontal bands indicate the $68\%$ confidence limits of the direct measurements of $h$ presented in Ref. Riess:2011yx (open dashed) and Ref. Humphreys:2013eja (grey filled). In the lower right panel, the horizontal dashed bands indicate the $95\%$ confidence interval on $\sigma_8$ for the base Galileon model, for which $\Sigma m_\nu = 0$.
• Figure 2: Time evolution of the Hubble expansion rate (top left), CMB temperature power spectrum (top right), CMB lensing potential power spectrum (middle left), linear matter power spectrum (middle right) and time evolution of $f\sigma_8$ for $k = 0.5 h/\rm{Mpc}$ (bottom left) and $k = 0.005 h/\rm{Mpc}$ (bottom right) for the best-fitting base Cubic (blue), ${\nu} \rm{Cubic}$ (red) and ${\nu} \Lambda\rm{CDM}$ (green) models obtained using the PL (dashed) and PLB (solid) datasets. In the top left panel, the ${\nu} \Lambda\rm{CDM}$ model used in the denominator is the corresponding best-fitting model to the PLB dataset. In the top right and middle left panels, the data points show the power spectrum measured by the Planck satelliteAde:2013zuvAde:2013tyw. In the middle right panel, the data points show the SDSS-DR7 Luminous Red Galaxy host halo power spectrum from Ref. Reid:2009xm, but scaled down by a constant factor to match approximately the amplitude of the best-fitting ${\nu} \rm{Cubic}$ ( PLB) model. In the lower panels, the data points show the measurements extracted by using the data from the 2dF 1475-7516-2009-10-004 (square), 6dF Beutler:2012px (triangle), SDSS DR7 (LRG) Samushia01032012 (circle), BOSS Reid:2012sw (dot) and WiggleZ Blake:2011ep (side triangles) galaxy surveys.
• Figure 3: Time evolution of the lensing potential, $\phi$, for the best-fitting base Cubic (blue), ${\nu} \rm{Cubic}$ (red) and ${\nu} \Lambda\rm{CDM}$ (green) for the PL (dashed) and PLB (solid) datasets for $k = 0.05 h/{\rm Mpc}$, $k = 0.005 h/{\rm Mpc}$, $k = 0.0008 h/{\rm Mpc}$ and $k = 0.0005 h/{\rm Mpc}$, as labelled in each panel.
• Figure 4: Time evolution of the ratio of the total lensing potential, $\phi$, and the lensing potential caused by the matter fluid only, $\phi^{f}$, for the ${\nu} \rm{Cubic}$ ( PLB) model and for a range of $k$ scales, as labelled. This quantity gives a measure of fifth force induced by the Galileon field.
• Figure 5: Same as Fig. \ref{['fig:cubic-contours']} but for the base Quartic (red dashed), ${\nu} \rm{Quartic}$ (red filled), base Quintic (blue dashed) and ${\nu} \rm{Quintic}$ (blue filled) models, using the PLB dataset.