Unravelling the dark matter--dark energy paradigm.(1 Introducation-8 Generalised Schorodinger Equation: Emergent Gravity and Equivalence Principle)(Report)

1 Introduction

The current [LAMBDA]CDM standard model of cosmology is based upon General Relativity (GR) as applied to the spatially-flat Friedmann-Lemaitre-Robertson-Walker (FLRW-GR) spacetime metric together with the Weyl postulate for the energy-momentum density tensor, leading to the Friedmann equations for the 3-space scale factor [1, 2, 3, 4] (1). Fitting this model to the magnitude-redshift data from supernovae and gamma-ray-burst (GRB) data requires the introduction of dark energy and dark matter, and a concomitant future exponential acceleration of the universe [5]. The dark energy has been most simply interpreted as a cosmological constant [LAMBDA]. Fitting the data gives [[OMEGA].sub.[LAMBDA]] = 0.73 and [[OMEGA].sub.m] = 0.27, with baryonic matter forming only some [[OMEGA].sub.b] = 0.05 of [[OMEGA].sub.m], so that the 'dark matter' component has [[OMEGA].sub.[LAMBDA]] = 0.22. Hence according to the FLRW-GR model the universe expansion is determined mainly by dark energy and cold dark matter, leading to the [LAMBDA]CDM label. A peculiar aspect of the [LAMBDA]CDM model is that the universe can only expand if the energy density is non-zero, i.e. space itself cannot expand without that energy density being present. This has been a feature of the FLRW-GR dynamics from the beginning of cosmology, and as shown herein is a direct consequence of extending Newtonian gravity to cosmology, and so well beyond its established regime. It is probably not well known that the [LAMBDA]CDM model is a simple and direct consequence of Newtonian gravity, as shown later. Here we derive a new cosmology which leads to, apart from other numerous tests, an expanding flat 3-space which does not require the presence of energy for that expansion. This expansion gives a parameter-free fit to the supernovae/GRB data, without invoking dark energy or dark matter. Nevertheless, if we best-fit the FLRW-GR [LAMBDA]CDM model to the new cosmology dynamics over the redshift range z [member of] {0, 14}, by varying [[OMEGA].sub.[LAMBDA]], we obtain [[OMEGA].sub.[LAMBDA]] = 0.73, [[OMEGA].sub.m] = 1 - [[OMEGA].sub.[LAMBDA]] = 0.27. In other words, if the new cosmological model is valid, then we can predict that fitting the [LAMBDA]CDM model to the data will give the parameter values exactly as reported. However the new cosmology does not predict an accelerating universe; that is merely a spurious consequence of the FLRW-GR model having the wrong functional form for its Hubble function. These results change completely our understanding of the evolution of the universe, and of its contents. Basically there is just a very small amount of conventional matter, as indeed deduced from CMB temperature fluctuation data, and a dominant expanding dynamical 3-space.

2 The [LAMBDA]CDM Model from Newtonian Gravity

The simplest and most direct derivation of a theoretical model is also usually the most instructive and most revealing, for abstract formalism is very effective at hiding fundamental issues. Here we derive the [LAMBDA]CDM model directly and simply from Newtonian gravity (2). Newtonian gravity was based on Kepler's observations of the motion of planets within the solar system, with the attractive force between two point-like masses being given by the famous inverse square law [12]

F = G [m.sub.1][m.sub.2]/[r.sup.2] (1)

Let us consider galaxies interacting only via this force law, and so pressure-less. To model the Hubble expansion we take this collection of galaxies to have large-scale mass-density homogeneity and expanding in the Hubble manner, i.e. with a radial speed v(r, t) proportional to the distance r from any particular observer. Only this Hubble law is consistent with a centre-less expansion. Then the well-known energy equation for any particular galaxy of mass m distance r from the observer is

1/2mv(r, t) 2 - GrnM(r, t) = E, (2)

where M(r, t) is the total mass enclosed in the sphere of radius r at time t. This simply express the galactic energy E …