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The minimal theory of massive gravity (MTMG) has two branches of stablecosmological solutions: a self-accelerating branch, which, except for the massof tensor modes has exactly the same behavior of linear perturbations as$\Lambda$CDM in general relativity (GR), and a normal branch with nontrivialbehavior. We explore the influence of the integrated Sachs-Wolfe-galaxycorrelation constraints on the normal branch of MTMG, which, in its simplestimplementation, has one free parameter more than $\Lambda$CDM in GR (or theself-accelerating branch of MTMG): $\theta$. This parameter is related to thegraviton mass and only affects the behavior of the cosmological linearperturbation dynamics. Using 2d-mass and SDSS data, we check which values of$\theta$ lead to a positive or negative cross-correlation. We find thatpositive cross-correlation is achieved for a large parameter-space interval.Within this allowed region of parameter space, we perform a $\chi^2$ analysisin terms of the parameter $\theta$, while keeping the other backgroundparameters fixed to the best-fit values of Planck. We then infer that thenormal branch of MTMG fits the data well in a nontrivial portion of theparameter space, and future experiments should be able to distinguish such amodel from $\Lambda$CDM in GR (or the self-accelerating branch of MTMG).

Integrated Sachs-Wolfe-galaxy cross-correlation bounds on the two branches of the minimal theory of massive gravity