Does Space Have a Gravitational Susceptibility? A Model for the ΛCDM Density Parameters in the Friedmann Equation

Abstract

We propose a model for gravity based on the gravitational polarization of space. With this model, we can relate the density parameters within the Friedmann model, and show that dark matter is bound mass formed from massive dipoles set up within the vacuum surrounding ordinary matter. Aggregate matter induces a gravitational field within the surrounding space, which reinforces the original field. Dark energy, on the other hand, is the energy density associated with gravitational fields both for ordinary matter, and bound, or induced dipole matter. At high CBR temperatures, the cosmic susceptibility, induced by ordinary matter vanishes, as it is a smeared or average value for the cosmos as a whole. Even though gravitational dipoles do exist, no large scale alignment or ordering is possible. Our model assumes that space, i.e., the vacuum, is filled with a vast assembly (sea) of positive and negative mass particles having Planck mass, called planckions, which is based on extensive work by Winterberg. These original particles form a very stiff two component superfluid, where positive and negative mass species neutralize one another already at the submicroscopic level, leading to zero net mass, zero net gravitational pressure, and zero net entropy, for the undisturbed medium. It is theorized that the gravitational dipoles form from such material positive and negative particles, and moreover, this causes an intrinsic polarization of the vacuum for the universe as a whole. We calculate that in the present epoch, the smeared or average susceptibility of the cosmos equals, (χ_0 ) =.842, and the overall resulting polarization equals, (P_0 ) =2.396 kg/m^2. Moreover, due to all the ordinary mass in the universe, made up of quarks and leptons, we calculate a net gravitational field having magnitude, (g^((0)) ) =3.771 E-10 m/s^2. This smeared or average value permeates all of space, and can be deduced by any observer, irrespective of location within the universe. This net gravitational field is forced upon us by Gauss’s law, and although technically a surface gravitational field, it is argued that this surface, smeared value holds point for point in the observable universe. A complete theory of gravitational polarization is presented. In contrast to electrostatics, gravistatics leads to anti-screening of the original source field, increasing the original value, (g^((0)) ) , to, g = (g^((0)) ) + (g^((1)) ) >(g^((0)) ) , where (g^((1)) ) is the induced or polarized field. In the present epoch, this leads to a bound mass, M_B=(χ_0 ) /(K_0 ) M_F=5.33〖 M〗_F , where 〖 M〗_F is the sum of all ordinary source matter in the universe, and (K_0 ) equals the relative permittivity. A new radius, and new mass, for the observable universe is dictated by the density parameters in Friedmann's equation, and Gauss’s law. These lead to the very precise values, R_0=3.215 E27 meters, and, M_F=5.834 E55 kg, respectively, somewhat larger than current less accurate estimates.