Thermodynamics in Little Rip cosmology in the framework of a type of f(R, T) gravity

M. J. S. Houndjo; F. G. Alvarenga; Manuel E. Rodrigues; Deborah F. Jardim; R. Myrzakulov

doi:10.1140/epjp/i2014-14171-6

2022 Impact factor 3.4

EPJ PLUS - Condensed Matter and Complex Systems

Eur. Phys. J. Plus (2014) 129: 171
https://doi.org/10.1140/epjp/i2014-14171-6

Regular Article

Thermodynamics in Little Rip cosmology in the framework of a type of f(R, T) gravity

M. J. S. Houndjo¹^,2^*, F. G. Alvarenga¹, Manuel E. Rodrigues³^,4, Deborah F. Jardim⁵ and R. Myrzakulov⁶

¹ Departamento de Engenharia e Ciências Naturais - CEUNES - Universidade Federal do Espírito Santo, CEP 29933-415, São Mateus/ES, Brazil
² Institut de Mathématiques et de Sciences Physiques (IMSP), 01 BP 613, Porto-Novo, Benin
³ Universidade Federal do Espírito Santo - Centro de Ciências Exatas - Departamento de Física, Av. Fernando Ferrari s/n, CEP29075-910, Vitória/ES, Brazil
⁴ Faculdade de Ciências Exatas e Tecnologia, Universidade Federal do Pará, Campus Universitário de Abaetetuba, CEP 68440-000, Abaetetuba, Brazil
⁵ Universidade Federal dos Vales do Jequitinhonha e Mucuri, ICTM, Rua do Cruzeiro, 01, Jardim São Paulo, CEP39803-371, Teofilo Otoni, MG, Brazil
⁶ Eurasian International Center for Theoretical Physics, L.N. Gumilyov Eurasian National University, 010008, Astana, Kazakhstan

^* e-mail: sthoundjo@yahoo.fr

Received: 29 November 2013
Revised: 16 March 2014
Accepted: 20 June 2014
Published online: 15 August 2014

Abstract

The cosmological reconstruction of the Little Rip model in f (R, T) gravity is investigated, where R is the curvature scalar and T the trace of the energy momentum tensor. The model perfectly reproduces the present stage of the universe, characterized by the CDM model, without singularity at future finite-time (without the Big Rip). The input parameters are determined according to Supernovae cosmology data and perfectly fit with the WMAP around the Little Rip. Moreover, the thermodynamics is considered in this Little Rip cosmology and it is illustrated that the second law of thermodynamics is always satisfied around the Little Rip universe for the temperature inside the horizon being the same as that of the apparent horizon. Moreover, we show the existence of a stable fixed point in the Little Rip universe which confirms that this is actually a late-time attractor in the phantom-dominated universe. The linear perturbation analysis is performed around the critical points, showing that the Little Rip model obtained is stable.