Equivalence classes of perturbations in cosmologies of Bianchi types I and V: Interpretation

Details Equivalence classes of perturbations in cosmologies of Bianchi types I and V: Interpretation Equivalence classes of perturbations in cosmologies of Bianchi types I and V: Interpretation

Aug 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999jmp....40.3995b&link_type=abstract

Journal of Mathematical Physics, Volume 40, Issue 8, pp. 3995-4010 (1999).

Mathematics

Mathematical Physics

2

Big Bang Nucleosynthesis, Field Theory

Scientific paper

In the preceding paper, 26 gauge-invariant variables were defined that characterize an almost-Bianchi type I or almost-Bianchi type V universe filled with a nonbarotropic perfect fluid. One can think of these basic variables, denoted collectively by D, as having at least two aspects. First, D gives an explicit (i.e., analytical) representation of the equivalence class of perturbations. In fact, this equivalence class is uniquely determined from D and vice versa. Second, any gauge-invariant quantity with respect to a Bianchi type I or Bianchi type V background model is obtainable linearly from D through purely algebraic and differential operations. Among many other things, the above properties of D facilitate new insights into the question of why a standard and well-known formulation based on the Stewart-Walker lemma does not enable one to describe the equivalence classes of perturbations and to find gauge-invariant variables independent of D. If we pose an analogous question in regard to almost-Robertson-Walker universe models, a different but none-the-less instructive answer is obtained. In this case, the Stewart-Walker lemma provides a complete framework both for constructing all gauge-invariant variables and for determining the equivalence classes of perturbations. Because of the sometimes confusing statements in the literature, nontrivial comparisons with other work on linear perturbations in anisotropic background models are made. We also present what we believe are some interesting applications of our ideas to the subject of quantum field theory in curved space-time.

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