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.

Figure 1

Two-dimensional 68% and 95% C.L. contours for the inflationary parameters $n_s$, $r$, and ${\alpha }_s$, using the full data set and parameter set B, and marginalized over the other ($10-2$) parameters.

Figure 2

Degeneracies between $r$ and $f_{\nu }$, $w$ for the full data set and parameter set B, marginalized over ($10-2$) parameters.

Figure 3

Two-dimensional 68% and 95% C.L. contours for $n_s$ and $r$, using parameter set C (consistent with predictions of chaotic inflation), and marginalized over ($9-2$) parameters. The upper panel uses $\mathrm{WMAP}+\mathrm{SDSS}$ data and the lower the full data set. The two short black/solid lines with boxes at the ends correspond to predictions of $\lambda {\varphi }^4$ (top left) and $m^2{\varphi }^2$ models of inflation, with 46 to 60 $e$-foldings (left to right).

Figure 4

Degeneracies between $r$ and $f_{\nu }$, $w$ for the full data set and parameter set C, marginalized over ($9-2$) parameters.

Figure 5

Two-dimensional marginalized constraints on $n_s$ and $r$ for the parameter set C, but with the restriction $w=-1$.

Figure 6

Two-dimensional marginalized contours for the $\mathrm{\text{vanilla}}+r$ parameter space, for both $\mathrm{WMAP}+\mathrm{SDSS}$ only (upper panel) and the full data set (lower panel).

Figure 7

Two-dimensional marginalized constraints on $n_s$ and $r$ for parameter set C. Only the linear part of the SDSS power spectrum has been used.

Figure 8

Two-dimensional marginalized 68% and 95% C.L. contours for ${\Omega }_c{h}^2$ and $w$, using various parameter and data sets. Top: Parameter set B, $\mathrm{WMAP}+\mathrm{SDSS}$. Middle: Parameter set B, the full data set. Bottom: Parameter set B with ${\alpha }_s=0$ (i.e., parameter set C), the full data set.

Figure 9

Two-dimensional marginalized 68% and 95% C.L. contours for ${\Omega }_c{h}^2$, ${\Omega }_k$, and $w$, using parameter set A and the full data set.