Machian General Relativity A possible solution to the Dark Energy problem and an alternative to Big Bang cosmology ? Robin Booth Theoretical Physics Imperial College

Contents Review of Big Bang problems Supernova results and Dark Energy Machian General Relativity Solving the Big Bang problems Consequences The ultimate fate of the Universe

Our place in space Ptolemaic System Copernican System

Rationale for change Inability to account for Big Bang problems Supernova cosmology project results General Relativity is not scale invariant, leading to: – Planck units – Initial spacetime singularity GR is not explicitly Machian

The Big Bang Problems Flatness problem – why is   1 today? Horizon problem – why is the temperature of the CMB so uniform between regions of space that have never been in causal contact? Cosmological constant problem – what mechanism provides the fine tuning necessary for  to be small but non-zero today?

Type Ia Supernova

The Supernovae Results Age (10 9 years) Distance t0t0 1015

SN1997ff z = 1.7  m-M=45.2  Preprint: astro-ph/ WWW:

Hubble Diagram  M =0,   =1  M =0,   =0  M =0.28   =0.72  M =0,   =0,  k =0  M =1,   =0 SCP+HZST data SN1997ff

Hubble Diagram

The Planck Scale The gravitational constant is fundamentally different from Planck’s constant and the speed of light. A constant G implies a preferred system of units:

Mach’s Principle (Extended) The rest mass energy of a particle is equal and opposite to the sum of the sum of the gravitational potential energy between the particle and all other matter in the universe, such that:

What if Einstein didn’t know about Newton ? The curvature of spacetime in a given region of space, relative to a surrounding region, is proportional to the ratio of the stress-energy density in that region relative to the stress- energy density of the surrounding region.

A problem of time cf. Brans-Dicke scalar-tensor theory: Solution: we need a new kind of time!

Cosmological dynamics

The Flatness Problem

The Horizon Problem AB time t0t0

Resolving the horizon problem In a universe expanding with constant velocity c All points have been in causal contact at some time AB

The Cosmological Constant Boomerang Supernova

Time Euclidian metric Lorentzian – de Sitter metric Quantum tunnelling Euclidian metric Time

Predictions Hubble constant = 63 km s -1 Mpc -1 Gravitational ‘constant’ proportional to time – No initial singularity – Planck scale depends on age of universe No preferred time frame  Redshifted photons do not loose energy

Gravitational Structure Constant

Planck Units

Verification Can not use experiments that measure e.g. planetary radar ranging, as Have to use Cavendish experiment, but this needs to detect variations of 1 part in Primordial nucleosynthesis results CMB photon counting experiment

Primordial nucleosynthesis Cold neutron cloud Beta decay raises temperature to  K One photon per baryon generated Formation of Duterium, Tritium, Helium, and light elements Insufficient photons to remove baryon entropy Universe remains ionised E Baryon   

CMB photon counting experiment Determine CMB photon number density experimentally by measuring variations in noise power spectrum using short time sampling window Prediction: – photon-baryon ratio  =1 – E   h  

Conclusions Solves the Big Bang problems Explains the supernovae results Eliminates the concept of the Planck scale Accounts for the Large Number Hypothesis Avoids the initial singularity Provides an alternative concept of time Predicts the ultimate fate of the Universe By making the field equations of GR explicitly Machian, the Omega paradigm:

Evolution of Universe Initial quantum fluctuation Chaotic frequency doubling Bose-Einstein condensate Boson-Fermion phase transition Cold, dense, neutron cloud  -decay Hot proton-neutron plasmaLight elements Nucleosynthesis Star and galaxies Neutrons Micro Black Holes ? Reverse  -decay Gravitational collapse

The End (for now) NB. The Universe will end in about years