Friedman vs Abel equations: A connection unraveled
arXiv:0809.1216 · doi:10.1063/1.3460856
Abstract
We present an interesting connection between Einstein-Friedmann equations for the models of universe filled with scalar field and the special form of Abel equation of the first kind. This connection works in both ways: first, we show how, knowing the general solution of the Abel equation (corresponding to the given scalar field potential) one can obtain the general solution of the Friedman Equation (and use the former for studying such problems as existence of inflation with exit for particular models). On the other hand, one can invert the procedure and construct the Bäcklund auto-transformations for the Abel equation.
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Cited by in corpus (8)
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- A geometric approach to integrability of Abel differential equations
- Application of the Abel Equation of the 1st kind to an inflation analysis of non-exactly solvable cosmological models
- Exact Solutions and Constraints on the Dark Energy Model in FRW Universe
- The KdV in Cosmology: a useful tool or a distraction?
- Exact solutions of Friedmann equation