https://doi.org/10.1140/epjc/s10052-018-5795-z
Regular Article - Theoretical Physics
The method of generating functions in exact scalar field inflationary cosmology
1
Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X54 001, Durban, 4000, South Africa
2
Bauman Moscow State Technical University, 2-nd Baumanskaya Street, 5, Moscow, 105005, Russia
3
Department of Mathematical Sciences, University of Zululand, Private Bag X1001, Kwa-Dlangezwa, 3886, South Africa
* e-mail: beeshama@unizulu.ac.za
Received:
8
February
2018
Accepted:
10
April
2018
Published online:
17
April
2018
The construction of exact solutions in scalar field inflationary cosmology is of growing interest. In this work, we review the results which have been obtained with the help of one of the most effective methods, viz., the method of generating functions for the construction of exact solutions in scalar field cosmology. We also include in the debate the superpotential method, which may be considered as the bridge to the slow roll approximation equations. Based on the review, we suggest a classification for the generating functions, and find a connection for all of them with the superpotential.
© The Author(s), 2018