Simple inflationary quintessential model II: Power law potentials

The present work is a sequel of our previous work Phys.Rev.D { 93}, 084018 (2016) [arXiv:1601.08175 [gr-qc]] cite{hap} which depicted a simple version of an inflationary quintessential model whose inflationary stage was described by a Higgs type potential and the quintessential phase was responsible due to an exponential potential. Additionally, the model predicted a nonsingular universe in past which was geodesically past incomplete. Further, it was also found that the model is in agreement with the Planck 2013 data when running is allowed. But, this model was found to be unsuccessful with Planck 2015 data with or without running. However, in this sequel we propose a family of models runs by a single parameter $alpha in [0, 1]$ which proposes another "inflationary quintessential model" where the inflation and the quintessence regimes are respectively described by a power law potential and a cosmological constant. The model is also nonsingular although geodesically past incomplete as in the cited model. However, the present one is found to be more simple in compared to the previous model and it is in excellent agreement with the observational data. We note that unlike the previous model which matched only with Planck 2013 data in presence of running, a large number of the models of this family with $alpha in [0,1/2)$ matches with both Planck 2013 and Planck 2015 data whether the running is allowed or not. Thus, the properties in the current family of models in compared to its past companion justify its need for a better cosmological model with the successive improvement of the observational data.1