Physics NotePublished
General and Unified Solution for Perfect-Fluid Homogeneous and Isotropic Cosmological Models
M. J. D. Assad; J. A. S. Lima
1986
Publication details
- Authors
- M. J. D. Assad; J. A. S. Lima
- Type
- Physics Note
- Status
- Published
- Publication date
- 1986
- Description
- All perfect fluid spatially homogeneous and isotropic cosmological models (without cosmological constant) are solved in general and unified form when an equation of state <math> p = (\gamma - 1)\,\!</math> <math>\rho\,\!</math> is assumed. The explicit dependence of cosmological time on the metrical scale factor is determined for any values of <math>\gamma\,\!</math> and spatial curvature parameter <math>\varepsilon\,\!</math>. A set of four infinite numerable sequences for values of <math>\gamma\,\!</math>, all of them consistent with the energy conditions and each starting from one of the values 0,1/3, 1, 4/3, includes all cases having solutions described by elementary functions. A generation technique yields the construction of all solutions in each sequence. By the use of the conformal time coordinate, the differential equation for the scale factor may be set in the form of that describing the classical motion of a particle subject to a linear force. Closed models are analogous to harmonic oscillators and their "half periods" are determined as an explicit function of <math>\gamma\,\!</math>, both for the conformal and cosmological times.
- Year
- 1986
- Number
- CBPF-NF-050/86
- Linked to a thesis
- No
- Linked to a grant
- No