In the Lucan phrase, the word used is paradise – and it's used only three times in the NT:
One is by Paul is 2 Corinthians 12:2-4:
"I know a man in Christ above fourteen years ago (whether in the body, I know not, or out of the body, I know not; God knoweth), such a one caught up to the third heaven (
ouranos).
And I know such a man (whether in the body, or out of the body, I know not: God knoweth), That he was caught up into paradise (
paradeisos), and heard secret words, which it is not granted to man to utter."
Paul reflects contemporary eschatological speculation of his era.
Sheol was introduced as the place of the departed, where knowledge of and fellowship with God was not possible. As the thought of vindication for the righteous beyond the grave arose, culminating in the hope of personal resurrection, so also Sheol was divided, the righteous waiting for final salvation in a form of paradise. The word paradise (
paradeisos) was almost certainly a Persian word taken into both Hebrew and Greek, originally referring to a 'park' or 'garden'. It is used only three times in the Hebrew Scriptures (Song of Solomon 4:13; Nehemiah 2:8 and Ecclesiastes 2:5), but appears 47 times in the Septuagint, notably as a term for the garden of Eden.
In 2 Corinthians, Paul recounts an experience in which he was caught up to the third heaven, to paradise.
Paradise then in a 'garden' an intermediate state, a resting in God's presence. Revelation 2:7 says: "He, that hath an ear, let him hear what the Spirit saith to the churches: To him, that overcometh, I will give to eat of the tree of life, which is in the paradise of my God." Clearly a reference to the Garden of Eden.
So we have a hierarchy of eschatalogical states, and Paradise is one, a third heaven, where heaven as such is the totality.
The 'harrowing of hell' is where Jesus takes the souls of the righteous to paradise, and there the souls of the departed faithful dwell, until the Final Judgement.
+++
The fact that the robber will be there 'today' means Christ has forgiven him, 'here and now'.