The parameter space in Galileon gravity models

TL;DR

This work constrains the full covariant Galileon gravity parameter space by marrying a 9D Galileon–cosmological parameter set to the complete CMB data along with SN Ia and BAO, using an MCMC approach implemented in CosmoMC/CAMB. It reveals a scaling degeneracy that makes one Galileon combination effectively unconstrained unless a reference parameter (here $c_3$) is fixed, and shows that the Integrated Sachs-Wolfe effect tightly bounds the Galileon sector. The results indicate that the Galileon model can fit the WMAP9 data slightly better than LCDM, but the addition of low-redshift distance measurements reduces its overall fit, with best-fit cosmological parameters differing by more than $2\sigma$ from LCDM. The analysis underscores the ISW signature as a key discriminator and discusses the potential of forthcoming weak-lensing and clustering data to further test Galileon gravity once nonlinear screening is adequately modeled.

Abstract

We present the first constraints on the full parameter space of the Galileon modified gravity model, considering both the cosmological parameters and the coefficients which specify the additional terms in the Lagrangian due to the Galileon field, which we call the Galileon parameters. We use the latest cosmic microwave background measurements, along with distance measurements from supernovae and baryonic acoustic oscillations, performing a Monte Carlo Markov Chain exploration of the 9-dimensional parameter space. The integrated Sachs-Wolfe signal can be very different in Galileon models compared to standard gravity, making it essential to use the full CMB data rather than the CMB distance priors. We demonstrate that meaningful constraints are only possible in the Galileon parameter space after taking advantage of a scaling degeneracy. We find that the Galileon model can fit the WMAP 9-year results better than the standard Λ-Cold Dark Matter model, but gives a slightly worse fit overall once lower redshift distance measurements are included. The best-fitting cosmological parameters (e.g. matter density, scalar spectral index, fluctuation amplitude) can differ by more than 2σ in the Galileon model compared with ΛCDM. We highlight other potential constraints of the Galileon model using galaxy clustering and weak lensing measurements.

Figures (7)

• Figure 1: (Color online) Points accepted by the Metropolis-Hastings algorithm, including those sampled during the burn-in period, using WMAP9+SNLS+BAO (blue dots). The points are projected onto different planes of the Galileon subset of the parameter space. All of the Galileon parameters were allowed to vary in order to manifest the scaling degeneracy. The remaining cosmological parameters were also sampled (not shown; see Fig. \ref{['cosmological-constraints']}). There are approximately $48000$ points (around $8000$ per chain) and the large red circles represent the fifty best-fitting points.
• Figure 2: (Color online) Marginalized two-dimensional posterior distributions and respective 68$\%$ and 95$\%$ contour limits obtained for the Galileon sector of the parameter space with WMAP9 data alone (top panels) and the combined WMAP9+SNLS+BAO datasets (bottom panels). The shading represents the distribution, where darker regions mean higher probability density. The posterior distribution and the respective contours were smoothed using a Gaussian filter that did not change the underlying results. In these chains the parameter $c_3$ was held fixed at $c_3 = 10$ and $\dot{\bar{\varphi}}_i$ was allowed to take only positive values.
• Figure 3: (Color online) Same as Fig. \ref{['galileon-constraints']} but for the cosmological sector of the parameter space. The corresponding contours obtained for the $\Lambda$CDM model are also shown for comparison (dashed contours). The scalar amplitude at recombination $A_s$ refers to a pivot scale $k = 0.02 \rm{Mpc}^{-1}$.
• Figure 4: (Color online) Marginalized one-dimensional distributions obtained for the combined WMAP9+SNLS+BAO dataset (solid blue). The distributions obtained for the $\Lambda$CDM model are also shown for comparison (dashed black curves). The scalar amplitude at recombination $A_s$ refers to a pivot scale $k = 0.02 \rm{Mpc}^{-1}$. In these chains the parameter $c_3$ was held fixed at $c_3 = 10$ and $\dot{\bar{\varphi}}_i$ was allowed to take only positive values.
• Figure 5: (Color online) Time evolution of the ratio of the Hubble expansion rates of the Galileon and $\Lambda$CDM models, $H/H_{\Lambda\rm{CDM}}$ (top panel) and of the Galileon field equation of state parameter $w$ (bottom panel) for the maximum likelihood points of the chains using the WMAP9 data alone (dashed green) and the combined dataset WMAP9+SNLS+BAO (solid blue). The $\Lambda$CDM model used in the ratio of the upper panel is the best-fitting model obtained using the WMAP9+SNLS+BAO combined dataset.