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We study excitations in a normal Fermi liquid with a local scalarinteraction. Spectrum of bosonic scalar-mode excitations is investigated forvarious values and momentum dependence of the scalar Landau parameter $f_0$ inthe particle-hole channel. For $f_0 >0$ the conditions are found when the phasevelocity on the spectrum of the zero sound acquires a minimum at a non-zeromomentum. For $-1<f_0 <0$ there are only damped excitations, and for $f_0<-1$the spectrum becomes unstable against a growth of scalar-mode excitations (aPomeranchuk instability). An effective Lagrangian for the scalar excitationmodes is derived after performing a bosonization procedure. We demonstrate thatthe Pomeranchuk instability may be tamed by the formation of a static Bosecondensate of the scalar modes. The condensation may occur in a homogeneous orinhomogeneous state relying on the momentum dependence of the scalar Landauparameter. Then we consider a possibility of the condensation of thezero-sound-like excitations in a state with a non-zero momentum in Fermiliquids moving with overcritical velocities, provided an appropriate momentumdependence of the Landau parameter $f_0(k)>0$.

Pomeranchuk instability and Bose condensation of scalar quanta in a Fermi liquid