Why were those who accompanied Peter convinced that the Holy Spirit had been given to Cornelius and his household?

The conviction among those who accompanied Peter that the Holy Spirit had been given to Cornelius and his household was primarily because they heard them speak with tongues. This phenomenon is significant in the early Christian context as it served as a clear and undeniable sign of the Holy Spirit's presence and activity within the individuals. Speaking in tongues, which is described in the Book of Acts, is often viewed as an outward manifestation of the inward work of the Holy Spirit, serving to confirm the authenticity of the spiritual experience.

Furthermore, this event parallels the experiences of the apostles at Pentecost, reinforcing the idea that the gift of the Holy Spirit is not limited to certain groups but available to all who believe, regardless of their background. The moment Cornelius and his household began speaking in tongues was a pivotal moment that illustrated the breaking down of barriers between Jews and Gentiles, underscoring the universal nature of the Gospel. Thus, the ability to speak in tongues was a powerful indicator to Peter and his companions that God was granting salvation to the Gentiles as well.