https://doi.org/10.1140/epjc/s10052-018-6139-8
Regular Article - Theoretical Physics
Cosmological singularities and analytical solutions in varying vacuum cosmologies
1
Academy of Athens, Research Center for Astronomy and Applied Mathematics, Soranou Efesiou 4, 11527, Athens, Greece
2
Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia, Chile
3
Department of Mathematics and Natural Sciences,Core Curriculum Program, Prince Mohammad Bin Fahd University, AlKhobar, 31952, Kingdom of Saudi Arabia
4
Institute of Systems Science, Durban University of Technology, PO Box 1334, Durban, 4000, Republic of South Africa
5
DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Rd., Cambridge, CB3 0WA, UK
6
Faculty of Physics, Department of Astronomy-Astrophysics-Mechanics, University of Athens, Panepistemiopolis, 157 83, Athens, Greece
* e-mail: yiannis.papayiannopoulos@gmail.com
Received:
20
May
2018
Accepted:
4
August
2018
Published online:
27
August
2018
We investigate the dynamical features of a large family of running vacuum cosmologies for which 
evolves as a polynomial in the Hubble parameter. Specifically, using the critical point analysis we study the existence and the stability of singular solutions which describe de-Sitter, radiation and matter dominated eras. We find several classes of 
cosmologies for which new analytical solutions are given in terms of Laurent expansions. Finally, we show that the Milne universe and the 
model can be seen as perturbations around a specific model, but this model is unstable.
© The Author(s), 2018
