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We suggest that the "Big Bang" may be a result of the first-order phasetransition driven by changing scalar curvature of the 4D space-time inexpanding cold Universe, filled with nonlinear scalar field $\phi $ and neutralmatter with equation of state $p=\nu \varepsilon $ (where $p$ and $\varepsilon$ are pressure and energy density of matter). We consider a Lagrangian forscalar field in curved space-time with nonlinearity $\phi ^{4} $, which alongwith the quadratic term $-\xi R\left|\phi \right|^{2} $ (where $\xi $ is theinteraction constant and $R$ is scalar curvature) contains a term $\sim \xiR\left(\phi +\phi ^{+} \right)$ linear in $\phi $. Due to this term thecondition for the extrema of the potential energy of scalar field is given by acubic equation. Provided $\nu > 1/3$ the scalar curvature $R=[\kappa (3\nu-1)\varepsilon -4\Lambda ]$ (where $\kappa $ and $\Lambda $ are Einstein'sgravitational and cosmological constants) decreases along with decreasing$\varepsilon $ in the process of the Universe's expansion, and at some criticalvalue $R_{c} < 0$ a first-order phase transition occurs, induced by an"external field" parameter proportional to $R$. Given certain conditions thecritical radius of the early Universe at the point of the first-order phasetransition may reach arbitrary large values, so this scenario of unrestricted"inflation" of the Universe may be called "hyperinflation". Beyond the point ofphase transition the system is rolling down into the potential minimum with therelease of the potential energy of scalar field, accompanied by oscillations ofits amplitude $\phi $. The powerful heating of the Universe in the course ofattenuation of these oscillations plays the role of "Big Bang".

"Big Bang'' as a result of first-order phase transition driven by changing scalar curvature in expanding early Universe: "hyperinflation'' scenario