My understanding of Inflation Theory: Before 10^-35s the universe began to cool and the Inflaton Field approached a false vacuum. When it reached this false vacuum, there was a constant energy density in the universe which cause the universe to expand (for some reason? I don't really understand why a constant energy density would cause repulsive gravity. If you could briefly explain this too that would be appreciated). As it expanded the field became supercooled until it quantum tunneled to its true vacuum around 10^-34s, ending inflation in our pocket of space.

My main question: Is Dark Energy caused by or related to the Inflaton Field. Could today's expansion be a result of the Inflaton Field but just a much slower, weaker version than inflation because the Inflaton Field is in a much lower energy state now than it was during inflation.

My understanding of Inflation Theory: 

Before $10^{-35}$ seconds the universe began to cool and the Inflaton Field approached a false vacuum. When it reached this false vacuum, there was a constant energy density in the universe which cause the universe to expand (for some reason? I don't really understand why a constant energy density would cause repulsive gravity. If you could briefly explain this too that would be appreciated). As it expanded the field became supercooled until it quantum tunneled to its true vacuum around $10^{-34}$ seconds , ending inflation in our pocket of space.

My main question: 

Is Dark Energy caused by or related to the Inflaton Field. Could today's expansion be a result of the Inflaton Field but just a much slower, weaker version than inflation because the Inflaton Field is in a much lower energy state now than it was during inflation.