The cosmological principle, the variational principle, and group theory

Details The cosmological principle, the variational principle, and group theory The cosmological principle, the variational principle, and group theory

May 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980ap%26ss..69..377p&link_type=abstract

Astrophysics and Space Science, vol. 69, no. 2, May 1980, p. 377-392. In French.

Mathematics

Group Theory

1

Astronomical Models, Cosmology, Group Theory, Variational Principles, Astrophysics, Orbital Mechanics, Particle Mass, Riemann Manifold, Space-Time Functions, Universe

Scientific paper

The paper examines ways of constructing a metric conformal with the Robertson-Walker metric by means of a variational principle that takes into account the cosmological principle as stated by Weinberg (1972); the approach is based on the existence of orbits generated by a one-parameter group of diffeomorphisms of physical space. The application of the cosmological principle to variational methods allows the determination of first integrals that can characterize the physical properties of the universe. For this purpose it is shown that the Lagrangian of the universe, considered as a mechanical system, can be chosen from the germs of functions, and that the form variations dq to the i-th power are tangent vectors of the group orbits in a Riemann manifold. The results lead to new statements of the cosmological principle: (1) at any point of space-time it is possible to construct a metric ds(overbar)-squared from the trajectories generated by a one-parameter group of diffeomorphisms of V4, and (2) any two points of space-time can always be joined by means of group trajectories.

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