On Formation of Primordial Naked Singularities

The density fluctuations in the nearly homogeneous background in the very early universe are argued to be the origin of the cosmic structures we observe in our present universe. Along with many other structures, these fluctuations would have also given rise to primordial black holes at the end of unhindered gravitational collapse of high-density matter blobs that developed due to these fluctuations. We study here such a collapse, which are seeded by a scalar field $\phi$ associated to a non-trivial potential function $V(\phi)$, minimally coupled to gravity. Such a continual collapse is presumed to form a black hole always and is named a primordial black hole (PBH). Examining the dynamics of such a collapse, we find the parameter range where the apparent horizon does not form, thus resulting in the visibility of the final singularity of collapse for faraway external observers. This treatment is within the classical limits dictated by Planck's constraints. The slow-roll parameters are analysed here to keep the relic abundance of the scalar field high enough so that the abundance of produced primordial naked singularities (PNaSs) falls within the range of resolution of possible observational probes.