  Models of galaxy formation predict that gas accretion from the cosmic web is
a primary driver of star formation over cosmic history. Except in very dense
environments where galaxy mergers are also important, model galaxies feed from
cold streams of gas from the web that penetrate their dark matter haloes.
Although these predictions are unambiguous, the observational support has been
indirect so far. Here we report spectroscopic evidence for this process in
extremely metal-poor galaxies (XMPs) of the local Universe, taking the form of
localized starbursts associated with gas having low metallicity. Detailed
abundance analyses based on Gran Telescopio Canarias (GTC) optical spectra of
ten XMPs show that the galaxy hosts have metallicities around 60 % solar on
average, while the large star-forming regions that dominate their integrated
light have low metallicities of some 6 % solar. Because gas mixes azimuthally
in a rotation timescale (a few hundred Myr), the observed metallicity
inhomogeneities are only possible if the metal-poor gas fell onto the disk
recently. We analyze several possibilities for the origin of the metal-poor
gas, favoring the metal-poor gas infall predicted by numerical models. If this
interpretation is correct, XMPs trace the cosmic web gas in their surroundings,
making them probes to examine its properties.
