A wide variety of astrophysical and cosmological sources are expected to contribute to a stochastic gravitational-wave background .
Following the observations of GW150914 and GW151226 , the rate and mass of coalescing binary black holes appear to be greater than many previous expectations .
As a result , the stochastic background from unresolved compact binary coalescences is expected to be particularly loud .
We perform a search for the isotropic stochastic gravitational - wave background using data from Advanced LIGO ’ s first observing run .
The data display no evidence of a stochastic gravitational - wave signal .
We constrain the dimensionless energy density of gravitational waves to be \Omega _ { 0 } < 1.7 \times 10 ^ { -7 } with 95 \% confidence , assuming a flat energy density spectrum in the most sensitive part of the LIGO band ( 20 - 86 { Hz } ) .
This is a factor of \sim 33 times more sensitive than previous measurements .
We also constrain arbitrary power-law spectra .
Finally , we investigate the implications of this search for the background of binary black holes using an astrophysical model for the background .