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New constraints on parametrised modified gravity from correlations of the CMB with large scale structure

We study the effects of modified theories of gravity on the cosmic microwave background (CMB) anisotropies power spectrum, and in particular on its large scales, where the integrated Sachs-Wolfe (ISW) effect is important. Starting with a general parametrisation, we then specialise to f(R) theories and theories with Yukawa-type interactions between dark matter particles. In these models, the evolution of the metric potentials is altered, and the contribution to the ISW effect can differ significantly from that in the standard model of cosmology. We proceed to compare these predictions with observational data for the CMB and the ISW, performing a full Monte Carlo Markov chain (MCMC) analysis. In the case of f(R) theories, the result is an upper limit on the lengthscale associated to the extra scalar degree of freedom characterising these theories. With the addition of data from the Hubble diagram of Type Ia supernovae, we obtain an upper limit on the lengthscale of the theory of B_0 < 0.4, or correspondingly λ_1 < 1900 Mpc/h at 95% c.l. improving previous CMB constraints. For Yukawa-type models we get a bound on the coupling 0.75 < β_1 < 1.25 at the 95% c.l. We also discuss the implications of the assumed priors on the estimation of modified gravity parameters, showing that a marginally less conservative choice improves the f(R) constraints to λ_1 < 1400 Mpc/h, corresponding to B_0 < 0.2 at 95% c.l.