Power-law Inflationary Models Research Articles

Non-extensive entropy and power-law inflation: Implications for observations

This study explores the interaction between non-extensive entropic FLRW cosmology and the power-law inflationary model, with a focus on the overlap between the scalar spectral index “[Formula: see text]” and the tensor-to-scalar ratio “r”. Based on a conjecture that non-extensive entropy alters the energy–momentum content of the cosmic fluid, the analysis examines how these overlaps shift with different model parameters and compares the findings to those from Bekenstein–Hawking (BH) entropic cosmology. The study highlights the impact of Tsallis, Rényi, and Sharma–Mittal entropies, uncovering a significant correlation between “[Formula: see text]” and “r” that suggests a deeper connection in power-law inflationary dynamics. The results demonstrate that non-extensive entropies not only enable viable inflation with a graceful exit but also address limitations inherent in the standard BH entropic framework, emphasizing the importance of precise parameter estimation. Specifically, Tsallis entropy allows for power-law inflation with [Formula: see text] to [Formula: see text] in alignment with Planck 2018 data. Moreover, the [Formula: see text] parameter in Rényi and Sharma–Mittal entropy models must be extremely small ([Formula: see text] in Planck mass units) to achieve successful power-law inflation with an e-folding number around 55–65, suggesting a unified thermodynamic perspective in cosmological studies.

Reheating in inflation models with the inflaton decaying into radiation

The physics of reheating can provide additional predictions for inflationary models and thus has spurred an increasing deal of interest. In this paper, by considering a special function for the decay of the inflaton into radiation, which renders the effective equation of state (EoS) parameter to be time varying during reheating, we investigate the constraints on reheating from the cosmic microwave background observations and the effect of reheating on the predictions for inflationary models. Our work is different from previous ones where a constant EoS parameter is assumed. Taking the power-law inflationary models as concrete examples, we find that the time-varying EoS parameter during reheating entails a non-negligible effect on the reheating predictions.

Power-law inflation with minimal and nonminimal coupling

Power-law inflationary scenarios based on minimal and non-minimal coupling of a scalar field to gravity with exponential- and power-law potential, respectively, are studied using the symmetry-based approach. In particular, we obtained only one parameter Lie point symmetry for both the minimal and non-minimal coupling cases and it is interesting to note that the non-minimal coupled equation is invariant under a scale transformation. We find the exact analytical group invariant solutions from invariant curve condition for both the minimal and non-minimal cases of the power-law inflationary model. The solutions obtained are consistent with the Friedmann equations subject to constraints on the inflationary potential parameter $ \lambda$ for the minimal case and on the coupling parameter $ \zeta$ for the non-minimal case. In this scenario, we find transformation relations for various inflationary parameters e.g. amplitude of the scalar power spectrum, spectral index, slow-roll parameters (SRP), tensor-to-scalar perturbation ratio, equation of state parameters, non-Gaussianity parameter as well as the form of the potential in two different frames, namely the Jordan and Einstein frames by making use of the conformal transformation. The results for various inflationary parameters for the non-minimal case are presented in the background of Planck2015 and Planck2018 and are in good agreement with the cosmological observations if the non-minimal coupling parameter is chosen properly. We treat minimally and non-minimally coupled scalar field equations by the dynamical system theory and present critical point analysis. By checking the stability of the critical points in the phase space for both cases we have shown that the solutions obtained from the Lie symmetry approach are the stable attractor solutions.

Gravitational wave generation in power-law inflationary models

We investigate the generation of gravitational waves in power-law inflationary models. The energy spectrum of the gravitational waves is calculated using the method of continuous Bogoliubov coefficients. We show that, by looking at the interval of frequencies between 10−5 and 105 Hz and also at the GHz range, important information can be obtained, both about the inflationary period itself and about the thermalization regime between the end of inflation and the beginning of the radiation-dominated era. We thus deem the development of gravitational wave detectors, covering the MHz/GHz range of frequencies, to be an important task for the future.

Application of the phase integral method in some inflationary scenarios

We apply the phase-integral approximation devised by Fröman and Fröman in order to compute cosmological perturbations in the power-law inflationary model. The phase-integral formulas for the scalar and tensor power spectra are explicitly obtained up to ninth order of approximation. Our approximate expressions reproduce the shape of the power spectra as well as the spectral indices. We compare the accuracy of the power-integral approximation with the results for the power spectrum obtained with the slow-roll and uniform approximation methods.

Computation of inflationary cosmological perturbations in the power-law inflationary model using the phase-integral method

The phase-integral approximation devised by Froeman and Froeman, is used for computing cosmological perturbations in the power-law inflationary model. The phase-integral formulas for the scalar and tensor power spectra are explicitly obtained up to ninth-order of the phase-integral approximation. We show that, the phase-integral approximation exactly reproduces the shape of the power spectra for scalar and tensor perturbations as well as the spectral indices. We compare the accuracy of the phase-integral approximation with the results for the power spectrum obtained with the slow-roll and uniform-approximation methods.

Trans-Planckian footprints in inflationary cosmology

We consider a minimum uncertainty vacuum choice at a fixed energy scale Λ as an effective description of trans-Planckian physics, and discuss its implications for the linear perturbations of a massless scalar field in power-law inflationary models. We find possible effects with a magnitude of order H/Λ in the power spectrum, in analogy with previous results for de Sitter space–time.

Qualitative properties of magnetic fields in scalar field cosmology

We study the qualitative properties of the class of spatially homogeneous Bianchi VI_o cosmological models containing a perfect fluid with a linear equation of state, a scalar field with an exponential potential and a uniform cosmic magnetic field, using dynamical systems techniques. We find that all models evolve away from an expanding massless scalar field model in which the matter and the magnetic field are negligible dynamically. We also find that for a particular range of parameter values the models evolve towards the usual power-law inflationary model (with no magnetic field) and, furthermore, we conclude that inflation is not fundamentally affected by the presence of a uniform primordial magnetic field. We investigate the physical properties of the Bianchi I magnetic field models in some detail.

Density and graviton perturbations in the cosmic microwave background

We evaluate and compare the gravitational wave and density perturbation contributions to the cosmic microwave background radiation on the basis of the same power-law inflationary model. The inflation to radiation transition is treated in this paper as instantaneous, but a model is constructed to allow for a smooth transition from the radiation- to the matter-dominated eras. The equations are numerically investigated and integrated, without any basic approximations being made. Use is made of the synchronous gauge, with appropriate gauge-invariant variables, thus eliminating any confusion arising from unphysical gauge modes. We find a non-negligible gravitational wave contribution, which becomes dominant for a power-law expansion with exponent $q<13$. We also explore the dependence of our results with the main characteristic of the transition region, its length.