Narrow Results

We discuss the late-time property of universe and phantom field in the SO(1, 1) dark energy model for the potential V = V₀e^-βΦα with α and β two positive constants. We assume in advance some conditions satisfied by the late-time field to simplify equations, which are confirmed to be correct from the eventual results. For α < 2, the field falls exponentially off and the phantom equation of state rapidly approaches -1. When α = 2, the kinetic energy ρ_k and the coupling energy ρ_c become comparable but there is always ρ_k < -ρ_c so that the phantom property of field proceeds to hold. The analysis on the perturbation to the late-time field Φ illustrates the square effective mass of the perturbation field is always positive and thus the phantom is stable. The universe considered currently may evade the future sudden singularity and will evolve to de Sitter expansion phase.

The inflationary scenario in spatially homogeneous and anisotropic Bianchi Type I spacetime with exponential potential $V=e^{-\lambda \varphi }$, $\lambda >0$ and average scale factor (R) is considered as $R^3=ABC=e^{\lambda \varphi (t)}$ is discussed. The model isotropizes in special case and asymptotically. The spatial volume increases with time representing inflationary scenario and the expansion continues for long enough, thus solving the horizon problem. The model represents decelerating and accelerating phases of universe in special case. Also, the model is singularity free at t = 0. In special case, i.e. when constants b = 0, k = 0, then the model leads to FLRW model for which we have the average scale factor $R\propto t^{2/3}$, $𝜃\propto 1/t$ and deceleration parameter $(q)=\frac{1}{2}$. This paper gives the answer why anisotropic and homogeneous Bianchi Type I spacetime is considered than FRW model to discuss inflationary scenario.

In this paper, we consider an exponential potential $V_{(\varphi )}=V_0{e}^{-\alpha \varphi }$ in the framework of Barrow entropy under the constant-roll inflation and check their viability in the light of observable Planck 2020 data. By applying the first law of thermodynamics to the apparent horizon of the Universe, a modification of the Friedmann–Robertson–Walker (FRW) metric is derived in the context of Barrow entropy. We consider the early inflationary period of the universe to consist phenomenologically of a single inflationary state, that is, a state of the costant-roll inflation in which inflation is driven by an exponential potential field function. By fitting the constant-roll inflationary models to the observations, we examined the effect of the Barrow parameter $\mathrm{\Delta }$ on the inflation mechanism with the constant-roll parameter $\gamma$. As a result, we concluded that for a viable inflation, the observation limits of the inflation parameters determine that the constant-roll parameter is in the range $0.011\le \gamma \le 0.016$.

We study the half-lives of some nuclei via the alpha-decay process in ground-state to ground-state (g.s.→g.s.) transitions. To go through the problem, we consider the parabola and WKB approximations to fin the penetration probability. This new formula is used to evaluate alpha-decay half-lives and a good agreement with the experiment is obtained.

In this paper, we investigate the energy spectra, wave functions and the $B(E2)$ transition rates for ${}^{98–112}$Ru atomic nuclei, using the conformable fractional Bohr Hamiltonian model. For the $\beta$-part of the potential, the newly proposed Yukawa plus modified exponential potential is considered and the harmonic oscillator potential in $\gamma$-part, with $\gamma$ fixed around $\frac{\pi }{6}$. By using the conformable fractional Nikiforov–Uvarov method, energy spectra and wave functions are obtained analytically. The sensitivity of the potential parameters and the spectra with respect to the fractional order parameter is investigated. The normalized fractional energies and fractional electric quadrupole transition rates are compared with the available experimental predictions and those from existing theoretical studies. Comparisons are made at different values of the fractional derivative order. The results are presented across a broader range of values of $\alpha$, providing a systematic analysis of how variations in this parameter influence the energy spectra, wave functions, and $B(E2)$ transition rates in Ru nuclei. Overall, the comparison of our results with experimental data shows the good accuracy of our model, especially when the fractional parameter goes to lower values. It can be concluded that the order of fractional derivative plays a crucial role in refining theoretical predictions of electric quadrupole transition rates, especially for transitions involving higher multipolarities.