How robust are inflation model and dark matter constraints from cosmological data?

High-precision data from observation of the cosmic microwave background and the large scale structure of the universe provide very tight constraints on the effective parameters that describe cosmological inflation. Indeed, within a constrained class of $\Lambda \mathrm{CDM}$ models, the simple $\lambda {\varphi }^4$ chaotic inflation model already appears to be ruled out by cosmological data. In this paper, we compute constraints on inflationary parameters within a more general framework that includes other physically motivated parameters such as a nonzero neutrino mass. We find that a strong degeneracy between the tensor-to-scalar ratio $r$ and the neutrino mass prevents $\lambda {\varphi }^4$ from being excluded by present data. Reversing the argument, if $\lambda {\varphi }^4$ is the correct model of inflation, it predicts a sum of neutrino masses at $0.3\to 0.5\mathrm{eV}$, a range compatible with present experimental limits and within the reach of the next generation of neutrino mass measurements. We also discuss the associated constraints on the dark matter density, the dark energy equation of state, and spatial curvature, and show that the allowed regions are significantly altered. Importantly, we find an allowed range of $0.094<{\Omega }_c{h}^2<0.136$ for the dark matter density, a factor of 2 larger than that reported in previous studies. This expanded parameter space may have implications for constraints on SUSY dark matter models.