Abstract
Using Hall and Reginatto’s condition for a Wheeler De Witt Equation for a Friedman-Walker metric coupled to a (Inflaton) scalar field Φ, we delineate the outer boundary of the value of a scale factor a (t) for quantum effects, in an expanding universe. The inflaton field is from Padmanabhan’s reference, “An Invitation to Astrophysics” which yields a nonstandard Potential U (a, Φ) which will lead to an algebraic expression for a (t) for the value of the outer boundary of quantum effects in the universe. Afterwards, using the scale factor a (t)=ainitial·tα, with alpha given different values, we give an estimation as to a time, t (time) which is roughly the boundary of the range of quantum effects. How this is unusual? We use the Wheeler De Witt Equation, as a coupling to a given inflaton field Φ and find a different way as to delineate a time regime for the range of quantum effects in an expanding universe.
Highlights
We work with the Wheeler De Witt Equation as given by [1], as part of the work by Hall and Reginatto, in 2016, where an ordering, called p, is used to link a Wheeler De Witt Equation, as given below, to an inflaton, and the Friedman Walker space-time metric, with the inflaton described by [2] and the Friedman Walker metric given in [2] [3].What we are doing is using [1] with its Wheeler De Witt equation to look at the following ∂2 ∂a + p a ∂ ∂a − 1 a2 ∂2 ∂φ 2 −U (a,φ ) Ψ
Using Hall and Reginatto’s condition for a Wheeler De Witt Equation for a Friedman-Walker metric coupled to a (Inflaton) scalar field φ, we delineate the outer boundary of the value of a scale factor a (t ) for quantum effects, in an expanding universe
The inflaton field is from Padmanabhan’s reference, “An Invitation to Astrophysics” which yields a nonstandard Potential U (a,φ ) which will lead to an algebraic expression for a (t ) for the value of the outer boundary of quantum effects in the universe
Summary
We work with the Wheeler De Witt Equation as given by [1], as part of the work by Hall and Reginatto, in 2016, where an ordering, called p, is used to link a Wheeler De Witt Equation, as given below, to an inflaton, and the Friedman Walker space-time metric, with the inflaton described by [2] and the Friedman Walker metric given in [2] [3]. What we are doing is using [1] with its Wheeler De Witt equation to look at the following. The wave function we use in Equation (1) we will use the ansatz of ( ) Ψ = Ψinitial exp β ⋅ a (t )φ (t ). These three sets of equations will be referenced, in our article, and will form the template of the subsequent analysis
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