A new method of solving the Einstein–Friedmann dynamical equations of a spatially homogeneous and isotropic universe is presented. The method is applicable when the equation of state of the material content assumes the form P=(γ−1)ρ, γ=constant. The solution for the expansion factor is commonly given only for γ=0, 1, and 4/3 when the curvature index is K=±1. The proposed procedure is valid for general γ and K and it allows for ease of derivation of the solutions. This alternative method is useful pedagogically to introduce basic cosmology.

1.
C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973), pp. 733–742.
2.
S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1972), pp. 475–491.
3.
L. D. Landau and E. M. Lifschitz, The Classical Theory of Fields (Pergamon, Oxford, 1989), pp. 363–367.
4.
R. M. Wald, General Relativity (Chicago U.P., Chicago, 1984), Chap. 5.
5.
E. W. Kolb and M. S. Turner, The Early Universe (Addison–Wesley, Reading, MA, 1990), pp. 58–60.
6.
T. Padmanabhan, Cosmology and Astrophysics Through Problems (Cambridge U.P., Cambridge, 1996), pp. 79–89.
7.
R. D’Inverno, Introducing Einstein’s Relativity (Clarendon, Oxford, 1992), pp. 334–344.
8.
E. Hille, Lectures on Ordinary Differential Equations (Addison–Wesley, Reading, MA, 1969), pp. 273–288.
9.
E. L. Ince, Ordinary Differential Equations (Dover, New York, 1944), pp. 23–25.
10.
A. R.
Liddle
and
D. H.
Lyth
, “
The Cold Dark Matter Density Perturbation
,”
Phys. Rep.
231
,
1
–
105
(
1993
).  
Google Scholar
Crossref
Search ADS
 
This content is only available via PDF.
© 1999 American Association of Physics Teachers.
1999
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.