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

TL;DR

The paper addresses whether modifications to gravity on cosmological scales can be detected via the ISW imprint in the CMB and growth of structure. It adopts a general parametrisation using $\mu(a,k)$ and $\gamma(a,k)$ to describe deviations from GR, specializing to $f(R)$ gravity and Yukawa-type dark matter interactions, and conducts a full MCMC analysis against CMB, ISW, and SN data with a $\Lambda$CDM background. The main findings are that for $f(R)$ models, the present-day Compton wavelength $\lambda_1$ (or $B_0$) is tightly constrained, e.g., $B_0<0.4$ ($\lambda_1<1900\,\mathrm{Mpc}/h$) at 95% c.l., with priors affecting the bound such that $\lambda_1<1400\,\mathrm{Mpc}/h$ ($B_0<0.2$) can be inferred under a less conservative prior; for Yukawa-type DM interactions, the coupling is constrained to $0.75<\beta_1<1.25$ (95% c.l.) while the lengthscale bounds weaken due to degeneracies. These results demonstrate the power of ISW and growth measurements to test gravity beyond GR and highlight the sensitivity of MG constraints to prior choices. Future work combining ISW with weak lensing, galaxy clusters, and peculiar velocities could further tighten these limits.

Abstract

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.

Figures (3)

• Figure 1: Top: theoretical predictions for a family of $f(R)$ theories compared with our ISW data Giannantonio:2008zi measuring the angular CCF between the CMB and six galaxy catalogues. The model with $B_0 = 0$ is equivalent to $\Lambda$CDM , while increasing departures from GR produce negative cross-correlations. Bottom: the same for a family of Yukawa--like theories with fixed $B_0=2$. In this case non-unitary coupling generate a redshift evolution of the signal.
• Figure 2: Left: posterior likelihood distributions for the model parameters for the $f(R)$ case, using the combined CMB and ISW data (red, dashed lines) and adding also the SNe data (black, solid). We can see that the usual $\Lambda$CDM parameters peak around the concordance values, while the extra parameter $B_0$ has an upper limit. The SNe tighten the constraints by reducing the degeneracy between $\Omega_m$ and $B_0$. Right: the same for the Yukawa--type case. Here we only show the full CMB+ISW+SN result. The upper limit on $B_0$ disappears in this case due to the removal of the corrective factor from Eq. (\ref{['par_mu']}) and the additional degeneracies, and we can not constrain $s$ either, but a value of the coupling $\beta_1$ close to unity is required to fit the data.
• Figure 3: 2D posterior likelihood distributions; the 68% and 95% probability contours are shown. In the top panel we can see the parameters $\Omega_m, B_0$ for the $f(R)$ case, using the combined CMB and ISW data (red, dashed lines) and adding also the SNe data (black, solid). The SNe tighten the constraint by reducing the degeneracy between $\Omega_m$ and $B_0$. In the bottom panels, we show the Yukawa--type case for the parameters $\Omega_m, B_0$ (left), $\Omega_m, \beta_1$ (centre), and $\beta_1, B_0$ (right).