I Developing Inflation Theory w/o Dark Energy: Alan Guth 1980

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The term "dark energy" was first coined by physicist Michael Turner in 1998. Alan Guth and his team proposed the inflation theory in 1980. The Einstein–Hamilton–Jacobi equation was used by researchers to calculate the rate of cosmic inflation by taking into account the effects of dark energy. Specifically, the equation was used to calculate the rate of inflation of the universe by using the density of dark energy, its pressure and the rate at which it is expanding.

The density and pressure of dark energy were calculated in 1998 by physicists Michael Turner and Martin White. They proposed that dark energy is a form of energy that is responsible for the acceleration of the universe's expansion.

NB: The dark energy theory was proposed by Albert Einstein in his paper "Cosmological Considerations of the General Theory of Relativity" in 1917.
 
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The dark energy that currently drives accelerated expansion of our universe is not the same thing as the inflaton field that drives inflation in models like the one Guth proposed.

Aromalsp said:
the equation was used to calculate the rate of inflation of the universe by using the density of dark energy,
Not in inflation models, no. You will not find the term "dark energy" in any of Guth's papers or other references on inflation models. Inflation models use the density and pressure of the inflaton field.
 
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