https://arxiv.org/abs/1810.09934
Submitted on 10 Oct 2018 (v1), last revised 7 Feb 2020
Inflationary Cosmology: From Theory to Observations:
The main aim of this paper is to provide a qualitative introduction to the cosmic inflation and its relationship with current cosmological observations. The inflationary model solves many of the fundamental problems that challenge the Standard Big Bang cosmology i.e. Flatness, Horizon and Monopole problem, and additionally provides an explanation for the initial conditions observed throughout the Large-Scale Structure of the Universe, such as galaxies. In this review we describe the general solutions carry out by a single scalar field. Then with the use of current surveys, we show the constraints imposed on the inflationary parameters (ns,r) which allow us to make the connection between theoretical and observational cosmology. In this way, with the latest results, it is possible to choose or at least to constrain the right inflationary model, parameterised by a single scalar field potential V(ϕ).
https://arxiv.org/pdf/1810.09934.pdf
8 Conclusions
Considering the analysis presented here, it is complicated to prove that a given model is correct, since these models could be just particular cases of more general scenarios with several parameters involved. However, it is possible to eliminate models
or at least give some constraints on their behavior, leading to a narrower range of study. Although we have presented some simple examples of potentials, the classification in small-field, large-field, and hybrid models is enough to cover the entire region of the ns–r plane, as illustrated in Figure 8. Different versions of the three types of models predict qualitatively different scalar and tensor spectra, so it should be particularly easy to work on them apart. We have seen that the favored models are those with small r (assuming dns/d ln k ∼ 0) and slightly red spectrum, hence models with blue power spectrum ns > 1.0 are inconsistent with the recent data. These simple but important constraints allow us to rule out the simplest models corresponding to hybrid inflation of the form V (φ) = Λ4 (1 + (µ/φ) p ). There remain models with red spectra in the hybrid classification: inverted models and models with logarithmic potentials. Table 2 summarizes the constraints on the ns and r parameters and their improvements through the years. The scaleinvariant power spectrum ns = 1 is consistent within 95% CL with WMAP3 data, and therefore, not ruled out; however, with WMAP5 data the HZ spectrum lays outside the 95% CL region, which indicates exclusion considering the lowest order on the ns, r parameters. When WMAP7 data is considered, the scale-invariant spectrum is totally excluded by more than 3σ; however, the inclusion of extra parameters in a particular model may weaken the constraints on the spectral index. When chaotic models V (φ) ∝ φ p are analyzed with current data, it is found that quartic models (p = 4) are ruled out, whilst models with p ≥ 3 are disfavored at > 95% CL. Moreover, the quadratic potential V (φ) = 1/2m2φ 2 is in agreement with all data sets presented here and therefore remains as a good candidate. Future surveys will provide a more accurate description of the universe, and therefore, narrow down the number of candidates, which might better explain the inflationary period.
