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

We present cosmological parameter constraints based on the final nine-year WMAP data, in conjunction with additional cosmological data sets. The WMAP data alone, and in combination, continue to be remarkably well fit by a six-parameter LCDM model. When WMAP data are combined with measurements of the high-l CMB anisotropy, the BAO scale, and the Hubble constant, the densities, Omegabh2, Omegach2, and Omega_L, are each determined to a precision of ~1.5%. The amplitude of the primordial spectrum is measured to within 3%, and there is now evidence for a tilt in the primordial spectrum at the 5sigma level, confirming the first detection of tilt based on the five-year WMAP data. At the end of the WMAP mission, the nine-year data decrease the allowable volume of the six-dimensional LCDM parameter space by a factor of 68,000 relative to pre-WMAP measurements. We investigate a number of data combinations and show that their LCDM parameter fits are consistent. New limits on deviations from the six-parameter model are presented, for example: the fractional contribution of tensor modes is limited to r<0.13 (95% CL); the spatial curvature parameter is limited to -0.0027 (+0.0039/-0.0038); the summed mass of neutrinos is <0.44 eV (95% CL); and the number of relativistic species is found to be 3.84+/-0.40 when the full data are analyzed. The joint constraint on Neff and the primordial helium abundance agrees with the prediction of standard Big Bang nucleosynthesis. We compare recent PLANCK measurements of the Sunyaev-Zel'dovich effect with our seven-year measurements, and show their mutual agreement. Our analysis of the polarization pattern around temperature extrema is updated. This confirms a fundamental prediction of the standard cosmological model and provides a striking illustration of acoustic oscillations and adiabatic initial conditions in the early universe.

We construct four-dimensional covariant non-linear theories of massive gravity which are ghost-free in the decoupling limit to all orders. These theories resum explicitly all the nonlinear terms of an effective field theory of massive gravity. We show that away from the decoupling limit the Hamiltonian constraint is maintained at least up to and including quartic order in non-linearities, hence, excluding the possibility of the Boulware-Deser ghost up to this order. We also show that the same remains true to all orders in a similar toy-model.

We consider the Lagrangian of gravity covariantly amended by the mass and polynomial interaction terms with arbitrary coefficients, and reinvestigate the consistency of such a theory in the decoupling limit, up to the fifth order in the nonlinearities. We calculate explicitly the self-interactions of the helicity-0 mode, as well as the nonlinear mixing between the helicity-0 and -2 modes. We show that ghost-like pathologies in these interactions disappear for special choices of the polynomial interactions, and argue that this result remains true to all orders in the decoupling limit. Moreover, we show that the linear, and some of the nonlinear mixing terms between the helicity-0 and -2 modes can be absorbed by a local change of variables, which then naturally generates the cubic, quartic, and quintic Galileon interactions, introduced in a different context. We also point out that the mixing between the helicity-0 and 2 modes can be at most quartic in the decoupling limit. Finally, we discuss the implications of our findings for the consistency of the effective field theory away from the decoupling limit, and for the Boulware-Deser problem.