Constraints on warm power-law inflation in light of Planck results

Abstract

The constraints on a general form of the power-law potential and the dissipation coefficient in the framework of warm single field inflation imposed by Planck data will be investigated. By considering a quasi-static Universe, besides a slow-roll condition, the suitable regions in which a pair of theoretical free parameters are in good agreement with Planck results will be estimated. In this method, instead of a set of free parameters, we can visualize a region of free parameters that can satisfy the precision limits on theoretical results. On the other side, when we consider the preformed quantity for the amplitude of scalar perturbations, the conflict between obtained results for free parameters in different steps will be dramatically decreased. As done in prominent literature, based on the friction of the environment, we can divide the primordial Universe into two different epochs, namely weak and strong dissipative regimes. For the aforementioned eras, the free parameters of the model will be constrained and the best regions will be obtained. To do so, the main inflationary observables such as tensor-to-scalar ratio, power-spectra of density perturbations and gravitational waves, scalar and tensor spectral indices, running spectral index and the number of e-folds in both weak and strong regimes will be obtained. Ultimately, it can be visualized, this model can make concord between theoretical results and data originated from cosmic microwave background and Planck 2013, 2015 and 2018.

Constraints of anisotropy on warm power-law inflation in light of Planck results

“…If the value of λ=1, we will have the same FLRW space-time flat with signature−2. As we know, the energy density and pressure of the scalar field and the density of the radiation field are defined as follows: [29]…”

“…We know that quantum and thermal fluctuations play an important role in the formation of initial cosmic density fluctuations and large-scale structures [13]− [18], [27]. In 1983, the theory of chaotic inflation was introduced following Linde's studies in which the power-law potentials were introduced, and today we see that the power-law potentials due to simplicity and compliance with observations and solve the problem of graceful exit from the horizon are considered in new models [28] Two structures are commonly used in the calculation of slow-roll parameters in inflation models; One is the structure in which the parameters are expressed in terms of the potential of the scalar field, and this is the structure that we have discussed in this article and Ref [29].And the other is the structure in which the parameters are expressed in terms of the Hubble parameter and is called the Hamilton Jacobi form. So far, many models in the framework of gravity theories, [30] and observational results related to CMB and the formation of large-scale structures measured by advanced instruments have been able to provide us with useful information [31]− [18].Among them is the existence of statistical anisotropy in the CMB spectrum, which has raised doubts about the existence of anisotropies in the inflation period.…”

Warm inflation with non-comoving scalar field and radiation fluid

“…To determine α we can use the generalized de Sitter scale factor, the so-called intermediate scale factor [168][169][170][171][172], and a power-law expression of the scale factor. As the first example we can consider a i (t) = a 0i e γ t n , while for the power-law case we will introduce the scale factor asā i (t) =ā 0i t m (see [173] and the references therein). Here a 0i ,ā 0i , n and m are some constants that will be fixed by means of observations.…”

Warm inflation with non-comoving scalar field and radiation fluid

“…To determine α we can use the generalized de Sitter scale factor, the so called intermediate scale factor [169][170][171], as well as a power law expression of the scale factor. As the first example we can consider a i (t) = a 0i e γt n , while for the power law case we will introduce the scale factor as āi (t) = ā0i t m (see [172], and references therein). Here a 0i , ā0i , n and m are some constants that will be fixed by means of observations.…”