Fermi surface nesting is key to understanding the origin of the itinerant antiferromagnetic spin density wave in chromium. This magnetic order is accompanied by a charge density wave, and both density waves disappear above the critical pressure $P_c\approx 10$ GPa at low temperatures, defining a quantum critical point. Whether this pressure-induced quantum phase transition is accompanied by a phonon instability remains an open question. Here, we use inelastic x-ray scattering to track the room-temperature acoustic phonon dispersions at pressures up to $P=15.6$ GPa, well above $P_c$. We focus on the Kohn anomalies near the $H$ and $N$ points of the Brillouin zone, with the $H$ point anomaly lying close to the incommensurate spin density wave ordering vector. The phonon branches harden smoothly under pressure, while the positions and wave-vector extents of both anomalies remain essentially unchanged across $P_c$, with no additional critical softening. Ab initio calculations likewise show that Fermi surface nesting remains robust above $P_c$. These results indicate that the pressure-induced quantum phase transition is not driven by a phonon instability and support a primarily spin density wave driven mechanism in presence of a robust Kohn anomaly.

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• Charge density waves
• Electron-phonon coupling
• Phonons
• Pressure effects
• Spin density waves