Simple inflationary quintessential model

Abstract

In the framework of a flat Friedmann-Lemaître-Robertson-Walker (FLRW) geometry, we present a non-geodesically past complete model of our universe without the big bang singularity at finite cosmic time, describing its evolution starting from its early inflationary era up to the present accelerating phase. We found that a hydrodynamical fluid with nonlinear equation of state could result in such scenario, which after the end of this inflationary stage, suffers a sudden phase transition and enters into the stiff matter dominated era, and the universe becomes reheated due to a huge amount of particle production. Finally, it asymptotically enters into the de Sitter phase concluding the present accelerated expansion. Using the reconstruction technique, we also show that, this background provides an extremely simple inflationary quintessential potential whose inflationary part is given by the well-known 1-dimensional Higgs potential, i.e., a Double Well Inflationary potential, and the quintessential one by an exponential potential that leads to a deflationary regime after this inflation, and it can depict the current cosmic acceleration at late times. Moreover the Higgs potential leads to a power spectrum of the cosmological perturbations which fit well with the latest Planck estimations. Further, we compared our viable potential with some known inflationary quintessential potential, which shows that our quintessential model, that is, the Higgs potential combined with the exponential one, is an improved version of them because it contains an analytic solution that allows us to perform all analytic calculations. Finally, we have shown that the introduction of a non zero cosmological constant simplifies the potential considerably with an analytic behavior of the background which again permits us to evaluate all the quantities analytically. INTRODUCTIONThe complete evolution of our universe is still a mystery, and probably, one of the most interesting topics in the history of cosmology. Until now, we have some theories describing different phases of our universe, in agreement with the latest observations, which tell us that our universe underwent a rapid accelerating phase during its very early evolution, namely, the inflation [1, 2], and presently it is going through a phase of accelerated expansion [3,4]. The gap between these two successive accelerating expansions is described by three sequential decelerated phases, the first one is the stiff matter dominated era, then there was a radiation dominated phase, and finally, before its current accelerating phase, the universe was matter dominated. However, since the beginning of modern cosmology, the big bang still remains as one of the controversial issues for cosmologists. Hence, it has been questioned several times, and alternatively, an existence of some kind of "nonsingular" universe (a model of our universe without finite cosmic time singularity) [5] has been proposed just to replace this big bang singularity, but the evolution of the universe will remain same. As a ...

Initial directional singularity in inflationary models

“…We have shown that the model in [1] and similar inflationary models [15] with the property This does not happen in other cosmological models for which there is no such discrepancy between the finiteness of proper time and coordinate time lapses.…”

“…A phase transition stops the inflation until in the far future accelerated expansion is dominant. An interesting feature shown in [1] is that the new singularity is at infinite cosmic time, for comoving observers, but at finite proper time for noncomoving observers. This resembles the behavior of directional singularities in [16,17].…”

“…In [1] it is shown that this model has no big bang singularity and there is no initial singularity in cosmic time. However, a singularity appears at finite proper time in the past for noncomoving observers.…”

“…The model [1] proposes a simple equation of state which succeeds in removing the big bang singularity, replacing it by another one, dubbed little bang in analogy with the little rip, and producing an inflationary era. A phase transition stops the inflation until in the far future accelerated expansion is dominant.…”

Reconstructions of the dark-energy equation of state and the inflationary potential

“…Since they lead to different inflationary scenarios, particularly in respect of the density fluctuations produced, they have different observational consequences for the cosmic microwave background radiation, and this permits them to be finely constrained by observational data. Various inflaton potentials in general relativistic scalar field cosmology have been proposed in [5][6][7][8][9][10][11][12][13][14][15][16][17][18] , while for inflationary models in other gravity theories, where there are more possibilities, see [1,[19][20][21][22][23][24][25][26][27][28][29][30] and references therein.…”