Imprints of Gravitational Millilensing on the Light Curve of GRBs
  In this work, we search for signatures of gravitational millilensing in
Gamma-ray bursts (GRB) in which the source-lens-observer geometry produces two
images that manifest in the GRB light curve as superimposed peaks with
identical temporal variability (or echoes), separated by the time delay between
the two images. According to the sensitivity of our detection method, we
consider millilensing events due to point mass lenses in the range of $10^5 -
10^7 M_{\odot}$ at lens redshift about half that of the GRB, with a time delay
in the order of $10$ seconds. Current GRB observatories are capable of
resolving and constraining this lensing scenario if the above conditions are
met. We investigated the Fermi/GBM GRB archive from the year 2008 to 2020 using
the autocorrelation technique and we found one millilensed GRB candidate out of
2137 GRBs searched, which we use to estimate the optical depth of millilensed
GRBs by performing a Monte-Carlo simulation to find the efficiency of our
detection method. Considering a point-mass model for the gravitational lens,
where the lens is a supermassive black hole, we show that the density parameter
of black holes ($\Omega_{BH}$) with mass $\approx10^6 M_\odot$ is about $0.007
\pm 0.004$. Our result is one order of magnitude larger compared to consist
with previous work in a lower mass range ($10^2 - 10^3 M_{\odot}$), which gave
a density parameter $\Omega_{BH} \approx 5\times 10^{-4}$, and recent work in
the mass range of $10^2 - 10^7 M_{\odot}$ that reported $\Omega_{BH} \approx
4.6\times 10^{-4}$. The mass fraction of black holes in this mass range to the
total mass of the universe would be $f\approx \Omega_{BH}/\Omega_M=0.027 \pm
0.016$.
