Appendix E Application of Einstein’s Equation in Cosmology – Demonstration of Friedmann–Lemaitre Equations

2021 ◽  
pp. 233-278
Keyword(s):  
Einstein's Equation

scholarly journals A METHOD FOR THE DETERMINATION OF DIFFUSION CONSTANTS AND THE CALCULATION OF THE RADIUS AND WEIGHT OF THE HEMOGLOBIN MOLECULE

1929 ◽  
Vol 12 (4) ◽  
pp. 543-554 ◽  
Author(s):  
John H. Northrop ◽  
M. L. Anson
Keyword(s):  
Molecular Weight ◽  
Carbon Monoxide ◽  
Diffusion Coefficient ◽  
Porous Membrane ◽  
Diffusion Constants ◽  
Einstein's Equation ◽  
Hemoglobin Molecule

A method is described for determining the diffusion coefficient of solutes by determining the rate of passage of the solute through a thin porous membrane between two solutions of different concentration. The method has been used to determine the diffusion coefficient of carbon monoxide hemoglobin. This was found to be 0.0420 ± 0.0005 cm.2 per day at 5°C. The molecular weight of carbon monoxide hemoglobin calculated by means of Einstein's equation from this quantity is 68,600 ± 1,000.

LEE–YANG FORCE, GAUGE SYMMETRY AND "DARK ENERGY"

2005 ◽  
Vol 20 (37) ◽  
pp. 2855-2859 ◽  
Author(s):  
JONG-PING HSU
Keyword(s):  
Dark Energy ◽  
Gauge Symmetry ◽  
Baryon Number ◽  
Lepton Number ◽  
Repulsive Force ◽  
Baryonic Matter ◽  
Gauge Invariant ◽  
Einstein's Equation ◽  
Expansion Of The Universe ◽  
The Universe

In 1955, Lee and Yang discussed a new massless gauge field based on the established conservation of baryon number. They predicted the existence of a repulsive force between baryonic matter, just as the conservation of electron–lepton number was later shown to imply the existence of a repulsive force between electrons. Although Eötvös experiments showed the force to be undetectably small at that time, such a force may be related to the dark-energy-induced acceleration of the expansion of the universe. If the gauge invariant Lagrangian involves a spacetime derivative of the field strength, the resultant potential has properties similar to that of the "dark energy" implied by the cosmological constant in the Einstein's equation.

scholarly journals Well-posedness of Einstein’s equation with redshift data

2009 ◽  
Vol 50 (11) ◽  
pp. 113515 ◽  
Author(s):  
Christopher J. Winfield
Keyword(s):  
Well Posedness ◽  
Einstein's Equation

Entwicklung einer physikalischen Geometrie der Raum-Zeit zum Zwecke der Interpretation der allgemeinen Relativitätstheorie

1964 ◽  
Vol 19 (6) ◽  
pp. 665-675 ◽  
Author(s):  
Ernst Schmutzer
Keyword(s):  
General Relativity ◽  
Physical Meaning ◽  
Physical Space ◽  
Equation Of Motion ◽  
Gravitational Acceleration ◽  
3 Dimensional ◽  
Einstein's Equation ◽  
Physical Geometry ◽  
Fixed System ◽  
Physical Components

Up to date the interpretation of the theory of general relativity is discussed. One cause for this situation is the use of mathematical coordinates without physical meaning. In continuation of thoughts of MØLLER and CATTANEO here physical coordinates are used and on this basis a 4-dimensional physical geometry of space-time is developed by projection the mathematical tensor components into physical components. For studying the curvature of the 3-dimensional physical space and for other purposes new socalled projective partial and projective covariant derivations are introduced. On this foundation EINSTEIN’S equation of motion is investigated. Definitions for the CORIOLIS acceleration and the centrifugal-gravitational acceleration for a fixed system of reference are given. The problem of energy conservation is analysed.

scholarly journals WHAT IS THE SUSY MASS SCALE?

2005 ◽  
Vol 14 (11) ◽  
pp. 1907-1917 ◽  
Author(s):  
REUVEN OPHER ◽  
ANA PELINSON
Keyword(s):  
Natural Extension ◽  
Mass Scale ◽  
Density Fluctuations ◽  
Quantum Corrections ◽  
Microwave Background ◽  
Particle Content ◽  
Starobinsky Model ◽  
Cosmological Scenario ◽  
Einstein's Equation ◽  
Very High

The energy, or mass scale M SUSY , of the supersymmetry (SUSY) phase transition is, as yet, unknown. If it is very high (i.e. ≫103 GeV ), terrestrial accelerators will not be able to measure it. We determine M SUSY here by combining theory with the cosmic microwave background (CMB) data. Starobinsky suggested an inflationary cosmological scenario in which inflation is driven by quantum corrections to the vacuum Einstein's equation. The modified Starobinsky model (MSM) is a natural extension of this. In the MSM, the quantum corrections are the quantum fluctuations of the supersymmetric (SUSY) particles, whose particle content creates inflation and whose masses terminate it. Since the MSM is difficult to solve until the end of the inflation period, we assume here that an effective inflaton potential (EIP) that reproduces the time dependence of the cosmological scale factor of the MSM can be used to make predictions for the MSM. We predict the SUSY mass scale to be M SUSY ≃ 1015 GeV , thus satisfying the requirement that the predicted density fluctuations of the MSM is in agreement with the observed CMB data.

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