Galileon Gravity in Light of ISW, CMB, BAO and $H_0$ data

TL;DR

This work tests covariant Galileon gravity as an alternative to ΛCDM by confronting the full Galileon parameter space with Planck CMB (including lensing) and BAO data, and then probing the ISW signature via CMB–WISE cross-correlations. Using hi_class/MontеCarlo constraints, the authors demonstrate that the Cubic Galileon is decisively ruled out by the ISW signal, while Quartic and Quintic Galileons can yield ISW-compatible regions though tensions with BAO persist; these models also prefer a nonzero neutrino mass sum $\sum m_ u$ and a locally plausible $H_0$. The study highlights that current data do not exclude Galileon cosmologies outright, but future lensing, BAO, and ISW measurements can decisively test them, particularly through the redshift-dependent sign of the ISW amplitude. The results underscore the distinct observational signatures of Galileon gravity, such as a potentially evolving lensing potential and a nontrivial relation between $H_0$, $\sum m_ u$, and large-scale structure growth, which could be probed by upcoming surveys.

Abstract

Cosmological models with Galileon gravity are an alternative to the standard $Λ{\rm CDM}$ paradigm with testable predictions at the level of its self-accelerating solutions for the expansion history, as well as large-scale structure formation. Here, we place constraints on the full parameter space of these models using data from the cosmic microwave background (CMB) (including lensing), baryonic acoustic oscillations (BAO) and the Integrated Sachs-Wolfe (ISW) effect. We pay special attention to the ISW effect for which we use the cross-spectra, $C_\ell^{\rm T g}$, of CMB temperature maps and foreground galaxies from the WISE survey. The sign of $C_\ell^{\rm T g}$ is set by the time evolution of the lensing potential in the redshift range of the galaxy sample: it is positive if the potential decays (like in $Λ{\rm CDM}$), negative if it deepens. We constrain three subsets of Galileon gravity separately known as the Cubic, Quartic and Quintic Galileons. The cubic Galileon model predicts a negative $C_\ell^{\rm T g}$ and exhibits a $7.8σ$ tension with the data, which effectively rules it out. For the quartic and quintic models the ISW data also rule out a significant region of the parameter space but permit regions where the goodness-of-fit is comparable to $Λ{\rm CDM}$. The data prefers a non zero sum of the neutrino masses ($\sum m_ν\approx 0.5$eV) with $ \sim \! 5σ$ significance in these models. The best-fitting models have values of $H_0$ consistent with local determinations, thereby avoiding the tension that exists in $Λ{\rm CDM}$. We also identify and discuss a $\sim \! 2σ$ tension that Galileon gravity exhibits with recent BAO measurements. Our analysis shows overall that Galileon cosmologies cannot be ruled out by current data but future lensing, BAO and ISW data hold strong potential to do so.

Figures (7)

• Figure 1: Lensing potential on scale $k = 0.01 /$Mpc as a function of redshift (left panel) in code units of CLASS and CMB temperature - WISE galaxy cross-correlation (right panel) for $\Lambda$CDM and the Galileon models. The shaded region in the left panel indicates the WISE redshift selection function $\mathrm{d}N/\mathrm{d}z \mathrm{d} \Omega$ given in Eq. (\ref{['eq:sel_fct']}) with adjusted offset and normalization for display. The black solid line shows the prediction of ${\Lambda{\rm CDM}}$ while the coloured dashed/solid lines indicate examples of Galileon models with growing/decaying potentials within the redshift range of the WISE selection function. Cubic models are shown in orange ($\nu Gal3$), quartic in purple ($\nu Gal4$) and quintic ($\nu Gal5$) in green. The temperature-galaxy data are the Q-band measurements from Ferraro:2014msa.
• Figure 2: Lensing convergence-galaxy cross-correlation for ${\Lambda{\rm CDM}}$ and for a representative cubic, quartic and quintic model with the best-fitting values of $b_0$ for the redshift dependent bias model $b(z)= b_0 (1+z)$ indicated in the legend; note that the Galileon curves are overlapping and indistinguishable. The data points are from Ferraro:2014msa.
• Figure 3: 1-3 $\sigma$ contours in the 2-D marginalized $H_0 - \Sigma m_\nu$ plane (left panel) and in the $\xi - c_3$ plane (right panel) from the MCMCs with CMB and BAO13 data for ${\Lambda{\rm CDM}}$, Cubic, Quartic and Quintic Galileons. The horizontal shaded regions in the left panel indicate the constrains on $H_0$ from local (distance ladder) measurements Riess:2016jrr. We have omitted the quartic model in the $H_0 - \Sigma m_\nu$ plane for the purpose of clearness since the constrains are almost indistinguishable from the quintic case. The red, dotted lines in the right panel point to the contours of Cubic Galileons.
• Figure 4: ISW amplitude $\mathcal{A}^{{\rm ISW}}$ across the $c_3-\xi$ plane of the Quartic Galileon parameter space. The solid contours denote the two-dimensional marginalized $1\sigma$ and $2\sigma$ confidence regions from the MCMCs with CMB+BAO13 data. The dots correspond to points accepted in the MCMCs and are colour coded by their corresponding $\chi^2_{\rm ISW}$ values. We use different colourbars for points with positive and negative $\mathcal{A}^{{\rm ISW}}$ to facilitate interpreting the figure. Note that all models leading to a $\chi^2_{\rm ISW} > 30$ are shown in dark red. The rhombus, triangle and star symbols in purple indicate the models that give the best fit to the CMB+BAO13 dataset, ISW data alone and the combined CMB+BAO13+ISW set, respectively.
• Figure 5: Same as \ref{['fig:ISW_Gnu4']} but for the quintic Galileon model. See the main text for comments about the sampling at the tips of the contours.