Manuel Drees, Encieh Erfani
A broad range of single field models of inflation are analyzed in light of
all relevant recent cosmological data, checking whether they can lead to the
formation of long-lived Primordial Black Holes (PBHs). To that end we calculate
the spectral index of the power spectrum of primordial perturbations as well as
its first and second derivatives. PBH formation is possible only if the
spectral index increases significantly at small scales, i.e. large wave number
$k$. Since current data indicate that the first derivative $\alpha_S$ of the
spectral index $n_S(k_0)$ is negative at the pivot scale $k_0$, PBH formation
is only possible in the presence of a sizable and positive second derivative
("running of the running") $\beta_S$. Among the three small-field and five
large-field models we analyze, only one small-field model, the "running mass"
model, allows PBH formation, for a narrow range of parameters. We also note
that none of the models we analyze can accord for a large and negative value of
$\alpha_S$, which is weakly preferred by current data.
View original:
http://arxiv.org/abs/1110.6052
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