The challenge for single field inflation with BICEP2 result

The detection of B-mode power spectrum by the BICEP2 collaboration constrains the tensor-to-scalar ratio $r=0.20^{+0.07}_{-0.05}$ for the lensed-$\Lambda$CDM model. The consistency of this big value with the {\em Planck} results requires a large running of the spectral index. The large values of the tensor-to-scalar ratio and the running of the spectral index put a challenge to single field inflation. For the chaotic inflation, the larger the value of the tensor-to-scalar ratio is, the smaller the value of the running of the spectral index is. For the natural inflation, the absolute value of the running of the spectral index has an upper limit.Comment: 4 figures, 3 pages, some references added, PLB in pres

On the effect of the degeneracy between w_0 and w_a

The dynamics of scalar fields as dark energy is well approximated by some general relations between the equation of state parameter $w(z)$ and the fraction energy density $\Omega_\phi$. Based on the approximation, for slowly-rolling scalar fields, we derived the analytical expressions of $w(z)$ which reduce to the popular Chevallier-Polarski-Linder parametrization with explicit degeneracy relation between $w_0$ and $w_a$. The models approximate the dynamics of scalar fields well and help eliminate the degeneracies among $w_a$, $w_0$ and $\Omega_{m0}$. With the explicit degeneracy relations, we test their effects on the constraints of cosmological parameters. We find that: (1) The analytical relations between $w_0$ and $w_a$ for the two models are consistent with observational data; (2) The degeneracies have little effect on $\Omega_{m0}$; (3) The $1\sigma$ error of $w_0$ was reduced about 30% with the degeneracy relations.Comment: add discussions on the reconstruction of thawing potentials, Eur. Phys. J. C in pres