We study a sample of $sim$50,000 dwarf starburst and late-type galaxies drawn from the COSMOS survey with the aim of investigating the presence of nuclear accreting black holes (BHs) as those seed BHs from which supermassive BHs could grow in the early Universe. We divide the sample into five complete redshift bins up to $z=1.5$ and perform an X-ray stacking analysis using the textit{Chandra} COSMOS-Legacy survey data. After removing the contribution from X-ray binaries and hot gas to the stacked X-ray emission, we still find an X-ray excess in the five redshift bins that can be explained by nuclear accreting BHs. This X-ray excess is more significant for $z<0.5$. At higher redshifts, these active galactic nuclei could suffer mild obscuration, as indicated by the analysis of their hardness ratios. The average nuclear X-ray luminosities in the soft band are in the range 10$^{39}-10^{40}$ erg s$^{-1}$. Assuming that the sources accrete at $geq$ 1% the Eddington rate, their BH masses would be $leq$ 10$^{5}$ M$_{odot}$, thus in the intermediate-mass BH regime, but their mass would be smaller than the one predicted by the BH-stellar mass relation. If instead the sources follow the correlation between BH mass and stellar mass, they would have sub-Eddington accreting rates of $sim$ 10$^{-3}$ and BH masses 1-9 $times$ 10$^{5}$ M$_{odot}$. We thus conclude that a population of intermediate-mass BHs exists in dwarf starburst galaxies, at least up to $z$=1.5, though their detection beyond the local Universe is challenging due to their low luminosity and mild obscuration unless deep surveys are employed.
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