Search for pair production of Higgs bosons in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>b</mml:mi><mml:mover accent="true"><mml:mi>b</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mi>b</mml:mi><mml:mover accent="true"><mml:mi>b</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover></mml:math>final state using proton-proton collisions at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msqrt><mml:mi>s</mml:mi></mml:msqrt><mml:mo>=</mml:mo><mml:mn>13</mml:mn><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>TeV</mml:mi></mml:math>with the ATLAS detector

A search for Higgs-boson pair production in the $b\overline{b}b\overline{b}$ final state is carried out with $3.2\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of proton-proton collision data collected at $\sqrt{s}=13\text{ }\text{ }\mathrm{TeV}$ with the ATLAS detector. The data are consistent with the estimated background and are used to set upper limits on the production cross section of Higgs-boson pairs times branching ratio to $b\overline{b}b\overline{b}$ for both nonresonant and resonant production. In the case of resonant production of Kaluza-Klein gravitons within the Randall-Sundrum model, upper limits in the 24 to 91 fb range are obtained for masses between 600 and 3000 GeV, at the 95% confidence level. The production cross section times branching ratio for nonresonant Higgs-boson pairs is also constrained to be less than 1.22 pb, at the 95% confidence level.