We study the neutral Higgs boson pair production through $e^{+} e^{-}$ collision in the noncommutative(NC) extension of the standard model using the Seiberg-Witten maps of this to the first order of the noncommutative parameter $Theta_{mu u}$. This process is forbidden in the standard model at the tree level with background space-time being commutative. After including the effects of earths rotation we analyse the time-averaged cross section of the pair production of Higgs boson (in the light of LEP II and LHC data) at the future Linear Collider which can be quite significant for the NC scale $Lambda$ lying in the range $0.3 - 1.0$ TeV. For the 125 GeV Higgs mass(the most promising value of Higgs mass as reported by LHC), we find the NC scale as $330 rm{GeV}$ $le Lambda le 660 rm{GeV}$ and using $m_h = 129(127.5) rm{GeV}$ (the lower threshold value of the excluded region of $m_h$ reported by ATLAS(CMS) collaborations of LHC), we find the bound on $Lambda$ as: (i) $339 (336) rm{GeV} le Lambda le 677 (670) rm{GeV}$ corresponding to the Linear Collider energy $E_{com} = 500 rm{GeV}$.
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