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 quant...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.展开更多
Cosmological expansion or inflation is mathematically described by the theoretical notion of inverse gravity whose variations are parameterized by a factor that is a function of the distance to which cosmological expa...Cosmological expansion or inflation is mathematically described by the theoretical notion of inverse gravity whose variations are parameterized by a factor that is a function of the distance to which cosmological expansion takes prominence over gravity. This assertion is referred to as the inverse gravity inflationary assertion. Thus, a correction to Newtonian gravitational force is introduced where a parameterized inverse gravity force term is incorporated into the classical Newtonian gravitational force equation where the inverse force term is negligible for distances less than the distance to which cosmological expansion takes prominence over gravity. Conversely, at distances greater than the distance to which cosmological expansion takes prominence over gravity. The inverse gravity term is shown to be dominant generating universal inflation. Gravitational potential energy is thence defined by the integral of the difference (or subtraction) between the conventional Newtonian gravitational force term and the inverse gravity term with respect to radius (r) which allows the formulation, incorporation, and mathematical description to and of gravitational redshift, the Walker-Robertson scale factor, the Robinson-Walker metric, the Klein-Gordon lagrangian, and dark energy and its relationship to the energy of the big bang in terms of the Inverse gravity inflationary assertion. Moreover, the dynamic pressure of the expansion of a cosmological fluid in a homogeneous isotropic universe is mathematically described in terms of the inverse gravity inflationary assertion using the stress-energy tensor for a perfect fluid. Lastly, Einstein’s field equations for the description of an isotropic and homogeneous universe are derived incorporating the mathematics of the inverse gravity inflationary assertion to fully show that the theoretical concept is potentially interwoven into the cosmological structure of the universe.展开更多
文摘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.
文摘Cosmological expansion or inflation is mathematically described by the theoretical notion of inverse gravity whose variations are parameterized by a factor that is a function of the distance to which cosmological expansion takes prominence over gravity. This assertion is referred to as the inverse gravity inflationary assertion. Thus, a correction to Newtonian gravitational force is introduced where a parameterized inverse gravity force term is incorporated into the classical Newtonian gravitational force equation where the inverse force term is negligible for distances less than the distance to which cosmological expansion takes prominence over gravity. Conversely, at distances greater than the distance to which cosmological expansion takes prominence over gravity. The inverse gravity term is shown to be dominant generating universal inflation. Gravitational potential energy is thence defined by the integral of the difference (or subtraction) between the conventional Newtonian gravitational force term and the inverse gravity term with respect to radius (r) which allows the formulation, incorporation, and mathematical description to and of gravitational redshift, the Walker-Robertson scale factor, the Robinson-Walker metric, the Klein-Gordon lagrangian, and dark energy and its relationship to the energy of the big bang in terms of the Inverse gravity inflationary assertion. Moreover, the dynamic pressure of the expansion of a cosmological fluid in a homogeneous isotropic universe is mathematically described in terms of the inverse gravity inflationary assertion using the stress-energy tensor for a perfect fluid. Lastly, Einstein’s field equations for the description of an isotropic and homogeneous universe are derived incorporating the mathematics of the inverse gravity inflationary assertion to fully show that the theoretical concept is potentially interwoven into the cosmological structure of the universe.
