I will give you the keys of the kingdom of heaven, and whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven,
Matthew 16:19.
Whoever wishes to understand this commission that the Lord gave to Peter properly must not confuse the kingdom of heaven with heaven itself. The kingdom of heaven is on earth. It is the kingdom of God in its present form, so long as Christ, the King, is in heaven and continues so until He appears to establish His reign on earth.
When Jesus Christ lived on earth, the Jews were expecting the kingdom of God in visible power and glory. The prophets had announced it in this form. But the mass of the people were under the influence of the religious leaders and rejected Christ. They remained infidel and crucified their King. So the kingdom took on the character of a mystery known only to believers. After Jesus Christ’s return to heaven Peter was to begin announcing the gospel under these new conditions and thus open up the kingdom of heaven.
This he did, using the “keys” entrusted to him. Through his ministry Peter opened the way to the kingdom of heaven first to the Jews, then to the Samaritans, and finally to the nations (cf. Acts ch.2; ch. 8:4-17; ch.10). Everyone who acknowledges Jesus as the Saviour sent by God can now enter this kingdom.
In no way did Jesus Christ give Peter authority over entrance to heaven itself. That can be obtained solely through faith in Christ, the Lord and Redeemer.