Search Results (27)

In this work, we apply fractional calculus to study quantum cosmology. Specifically, our Wheeler-DeWitt (WDW) equation includes a Friedman-Robertson-Walker (FRW) geometry, a radiation fluid, a positive cosmological constant ($\mathsf{\Lambda }$), and an ad-hoc potential. We employ the Riesz fractional derivative, which introduces a parameter $\alpha$, where $1<\alpha \le 2$, in the WDW equation. We investigate numerically the tunneling probability for the Universe to emerge using a suitable WKB approximation. Our findings are as follows. When we decrease the value of $\alpha$, the tunneling probability also decreases, suggesting that if fractional features could be considered to ascertain among different early universe scenarios, then the value $\alpha =2$ (meaning strict locality and standard cosmology) would be the most likely. Finally, our results also allow for an interesting discussion between selecting values for $\mathsf{\Lambda }$ (in a non-fractional conventional set-up) versus balancing, e.g., both $\mathsf{\Lambda }$ and $\alpha$ in the fractional framework. Full article

We discuss an extended model of FRW cosmology with additional chiral tensor particles. We discuss the influence of these particles on the expansion rate of the Universe, their direct interactions with the constituents of the early Universe plasma, we determine their cosmological place and derive updated cosmological constraints on their interaction strength. Full article

Using monitored job cycles to design and model random maintenance strategies for ensuring life-cycle reliability has been extensively researched. The reliability heterogeneity over the life cycle has been ignored universally in this type of strategy. In this paper, using two different areas of regions that can screen reliability, two random maintenance strategies were customized for the life-cycle reliabilities of warrantied products with monitored job cycles to be ensured based on reliability heterogeneity. In the case of using minimal repair, the first one was flexibly customized depending on whether the first failure occurs in the region consisting of limited job cycles or a period of warranty service, whichever occurs first. Such a strategy is called flexible repair warranty first (FRWF) and can be used to ensure warranty-stage reliability during a product’s life cycle. The FRWF strategy is modeled from the perspectives of cost and time measures. Based on whether the first failure of the product through its FRWF occurs in another region, random periodic replacement (RPR) and classic periodic replacement (CPR) are triggered to customize the second one, which is named bivariate customized random maintenance (BCRM) because two decision variables are considered. The BCRM and its variants are modeled from the perspectives of the average cost rates. Finally, numerical analysis of some of the customized strategies was performed from the numerical perspective. Numerical analysis showed that the presented FRWF is superior to the classic free repair warranty (FRW) strategy because the servicing time of the presented FRWF strategy is longer than the servicing time of the classic FRW strategy at the same cost. Full article

Using an open thermodynamic systems theory, the effect of particle creation on the evolution and dynamics of the standard cosmological FLRW model in a higher-dimensional spacetime with functionally dependent cosmological and gravitational constants $\mathsf{\Lambda }$ and G is investigated. The gravitational field equations have been transformed into a dimensionless system of non-linear, first-order, coupled differential equations (DEs) as functions of the universe’s density parameters ${\Omega }_i$ and rate of particle creation $\mathsf{\Psi }$ in redshift space, which can be numerically casted. Two cosmological models are obtained, depending on the choice of particle creation rate—$\mathsf{\Psi }\sim H^2$ and $\mathsf{\Psi }\sim n^2$ for dust-, radiation- and dark-energy-dominated universes, respectively. The dynamic behaviour of each model is discussed. Full article

In this paper, we investigate a scalar field cosmological model of accelerating Universe with the simplest parametrization of the equation of state parameter of the scalar field. We use $H\left(z\right)$ data, pantheon compilation of SN Ia data and BAO data to constrain the model parameters using the ${\chi }^2$ minimization technique. We obtain the present values of Hubble constant $H_0$ as $66.2_{-1.34}^{+1.42}$, $70.7_{-0.31}^{+0.32}$ and $67.{74}_{-1.04}^{+1.24}$ for $H\left(z\right)$, $H\left(z\right)$ + Pantheon and $H\left(z\right)$ + BAO respectively. In addition, we estimate the present age of the Universe in a derived model $t_0=14.{38}_{-0.64}^{+0.63}$ for joint $H\left(z\right)$ and pantheon compilation of SN Ia data which has only $0.88\sigma$ tension with its empirical value obtained in Plank collaboration. Moreover, the present values of the deceleration parameter $q_0$ come out to be $-0.{55}_{-0.038}^{+0.031}$, $-0.{61}_{-0.021}^{+0.030}$ and $-0.{627}_{-0.025}^{+0.022}$ by bounding the Universe in the derived model with $H\left(z\right)$, $H\left(z\right)$ + Pantheon compilation of SN Ia and $H\left(z\right)$ + BAO data sets, respectively. We also have performed the state-finder diagnostics to discover the nature of dark energy. Full article

We uncover the general mechanism and the nature of today’s dark energy (DE). This is only based on well-known quantum physics and cosmology. We show that the observed DE today originates from the cosmological quantum vacuum of light particles, which provides a continuous energy distribution able to reproduce the data. Bosons give positive contributions to the DE, while fermions yield negative contributions. As usual in field theory, ultraviolet divergences are subtracted from the physical quantities. The subtractions respect the symmetries of the theory, and we normalize the physical quantities to be zero for the Minkowski vacuum. The resulting finite contributions to the energy density and the pressure from the quantum vacuum grow as $loga\left(t\right)$, where $a\left(t\right)$ is the scale factor, while the particle contributions dilute as $1/a^3\left(t\right)$, as it must be for massive particles. We find the explicit dark energy equation of state of today to be $P=w\left(z\right)\mathcal{H}$: it turns to be slightly $w\left(z\right)<-1$ with $w\left(z\right)$ asymptotically reaching the value $-1$ from below. A scalar particle can produce the observed dark energy through its quantum cosmological vacuum provided that (i) its mass is of the order of ${10}^{-3}$ eV = 1 meV, (ii) it is very weakly coupled, and (iii) it is stable on the time scale of the age of the universe. The axion vacuum thus appears as a natural candidate. The neutrino vacuum (especially the lightest mass eigenstate) can give negative contributions to the dark energy. We find that $w(z=0)$ is slightly below $-1$ by an amount ranging from $(-1.5\times {10}^{-3})$ to $(-8\times {10}^{-3})$ and we predict the axion mass to be in the range between 4 and 5 $\mathrm{meV}$. We find that the universe will expand in the future faster than the de Sitter universe as an exponential in the square of the cosmic time. Dark energy today arises from the quantum vacuum of light particles in FRW cosmological space-time in an analogous way to the Casimir vacuum effect of quantum fields in Minkowski space-time with non-trivial boundary conditions. Full article

In this manuscript, we investigate the cosmological and thermodynamic aspects of the Brans–Dicke theory of gravity for a spatially flat FRW universe. We consider a theoretical model for interacting Kaniadakis holographic dark energy with the Hubble horizon as the infrared cutoff. We deal with two interaction scenarios ($Q_1$ and $Q_2$) between Kaniadakis holographic dark energy and matter. In this context, we study different possible aspects of cosmic evolution through some well-known cosmological parameters such as Hubble $\left(H\right)$, deceleration $\left(q\right)$, jerk $\left(j\right)$, and equation of state $\left({\omega }_d\right)$. For both interaction terms, it is observed that the deceleration parameter exhibits early deceleration to the current accelerating universe and also lies within the suggested range of Planck data. The equation of state parameter shows quintessence behavior (for the first interaction term) and phantom-like behavior (for the second interaction term) of the universe. The jerk parameter represents consistency with the $\Lambda$CDM model for both interaction terms. In the end, we check the thermodynamic behavior of the underlying model. It is interesting to mention here that the generalized second law of thermodynamics holds for both cases of interaction terms. Full article

A particular form of the time-dependent deceleration parameter is used to examine the accelerated expansion of the universe and the phase transition in this expansion in the context of $f(R,T)$ gravity theory for the flat FRW model. The modified field equations are solved under the choice of $f(R,T)=R+2f\left(T\right)$. The best fit values of the model parameters that would be consistent with the recent observational datasets that are estimated. For this estimation, 57 points from Cosmic Chronometers (CC) datasets and 1048 points from Pantheon supernovae datasets are used. Bayesian analysis and likelihood function are applied together with Markov Chain Monte Carlo (MCMC) method at $1\sigma$ and $2\sigma$ confidence levels. Then, the physical behavior of parameters such as density, pressure and cosmographic parameters corresponding to these constrained values of the model parameters are analyzed. Looking at the deceleration parameter, it is seen that the universe has passed from a decelerating expansion phase to an accelerating phase. As a result, it has been shown that the cosmological model $f(R,T)$ that we discussed can explain the accelerating expansion of the late universe well without resorting to any dark energy component in the energy-momentum tensor. Full article

The main objective of this article is to examine the stability of Einstein static universe using inhomogeneous perturbations in the context of energy–momentum squared gravity. For this purpose, we used FRW spacetime with perfect matter distribution and formulated static as well as perturbed field equations. We took a minimal model of this theory to investigate the stable regions of the Einstein universe for conserved and non-conserved energy–momentum tensors. We found that stable modes of the Einstein universe appeared in both conserved and non-conserved cases for all values of the equation of state and model parameters corresponding to both open and closed cosmic models. We found that stable solutions in this modified theory were obtained for a broader $\omega$-region compared to other modified theories. Full article

We consider the late-time accelerated universe in the Friedmann–Robertson–Walker (FRW) spacetime with a nonzero curvature, and investigate cosmological models when the cosmic fluid is taken to be inhomogeneous and viscous (bulk viscous), coupled to dark matter. We consider the influence from thermal effects caused by Hawking radiation on the formation of singularities of various classified types, within a finite time. It is shown that under the influence of Hawking radiation, the time of formulation of a singularity and the nature of the singularity itself can change. It is also shown that by jointly taking into account radiation, viscosity, and space curvature, one can obtain a singularity-free universe. The symmetry properties of this kind of theory lie in the assumption about spatial isotropy. The spatial isotropy is also reflected in our use of a bulk instead of a shear viscosity. Full article

In this paper, we explore the gravitational collapse of matter (dust) under the effect of zero-point length $l_0$. During the gravitational collapse, we neglect the backreaction effect of pre-Hawking radiation (in the sense that it is a small effect and cannot prevent the formation of an apparent horizon), then we recast the internal metric of a collapsing star as a closed FRW universe for any spherically symmetric case and, finally, we obtain the minimal value for the scale factor, meaning that the particles never hit the singularity. We argue that the object emerging at the end of the gravitational collapse can be interpreted as Planck stars (black hole core) hidden inside the event horizon of the black hole, with a radius proportional to ${(GM{l}_0^2/c^2)}^{1/3}$. Quite interestingly, we found the same result for the radius of the Planck star using a free-falling observer point of view. In addition, we point out a correspondence between the modified Friedmann’s equations in loop quantum gravity and the modified Friedmann’s equation in string T-duality. In the end, we discuss two possibilities regarding the final stage of the black hole. The first possibility is that we end up with Planck-size black hole remnants. The second possibility is that the inner core can be unstable and, due to the quantum tunneling effect, the spacetime can undergo a black-hole-to-white-hole transition (a bouncing Planck star). Full article

A non-minimally coupled cosmological scenario is considered in the context of $f(R,T)=f_1\left(R\right)+f_2\left(R\right)f_3\left(T\right)$ gravity (with R being the Ricci scalar and T the trace of the energy-momentum tensor) in the background of the flat Friedmann–Robertson–Walker (FRW) model. The field equations of this modified theory are solved using a time-dependent deceleration parameter for a dust. The behavior of the model is analyzed taking into account constraints from recent observed values the deceleration parameter. It is shown that the analyzed models can explain the transition from the decelerating phase to the accelerating one in the expansion of the universe, by staying true to the results of the observable universe. It is shown that the models are dominated by a quintessence-like cosmological dark fluid at the late universe. Full article

In this work, the Friedmann–Robertson–Walker (FRW) Universe is considered a thermodynamic system, where the cosmological constant generates the thermodynamic pressure. Using a unified first law, we have determined the amount of energy $dE$ crossing the apparent horizon. Since heat is one of the forms of thermal energy, so the heat flows $\delta Q$ through the apparent horizon = amount of energy crossing the apparent horizon. Using the first law of thermodynamics, on the apparent horizon, we found $TdS=A(\rho +p)H{\tilde{r}}_{h}dt+A\rho d{\tilde{r}}_h$ where $T,S,A,H,{\tilde{r}}_h,\rho ,p$ are respectively the temperature, entropy, area, Hubble parameter, horizon radius, fluid density and pressure. Since the apparent horizon is dynamical, so we have assumed that $d{\tilde{r}}_h$ cannot be zero in general, i.e., the second term $A\rho d{\tilde{r}}_h$ is non-zero on the apparent horizon. Using Friedmann equations with the unified first law, we have obtained the modified entropy-area relation on the apparent horizon. In addition, from the modified entropy-area relation, we have obtained modified Friedmann equations. From the original Friedmann equations and also from modified Friedmann equations, we have obtained the same entropy. We have derived the equations for the main thermodynamical quantise, such as temperature, volume, mass, specific heat capacity, thermal expansion, isothermal compressibility, critical temperature, critical volume, critical pressure and critical entropy. To determine the cooling/heating nature of the FRW Universe, we have obtained the coefficient of Joule–Thomson expansion. Next, we have discussed the heat engine phenomena of the thermodynamical FRW Universe. We have considered the Carnot cycle and obtained its completed work. In addition, we studied the work completed and the thermal efficiency of the new heat engine. Finally, we have obtained the thermal efficiency of the Rankine cycle. Full article

We have considered the holographic dark energy and modified holographic Ricci dark energy models to analyze the time-dependent gravitational constant $G\left(t\right)$ and cosmological constant $\Lambda \left(t\right)$ in the context of Chern–Simons modified gravity theory. The FRW metric is used to examine the physical and kinematical properties of these models, which predicted the accelerated expansion phase of universe. Further, the $\Lambda \left(t\right)$ showed increasing trends while $G\left(t\right)$ showed decreasing trends for both cases. Finally, the range $-1.99\times {10}^{-10}{\mathrm{yr}}^{-1}\le \frac{\dot{G}}{G}\le 0$ was estimated mathematically, which is similar to the results obtained from observational data. Full article

Most quantum gravity theories quantize space-time on the order of Planck length (${\ell }_p^{}$). Some of these theories, such as loop quantum gravity (LQG), predict that this discreetness could be manifested through Lorentz invariance violations (LIV) over travelling particles at astronomical length distances. However, reports on LIV are controversial, and space discreetness could still be compatible with Lorentz invariance. Here, it is tested whether space quantization on the order of Planck length could still be compatible with Lorentz invariance through the application of a covariant geometric uncertainty principle (GeUP) as a constraint over geodesics in FRW geometries. Space-time line elements compatible with the uncertainty principle are calculated for a homogeneous, isotropic expanding Universe represented by the Friedmann–Lemaitre–Robertson–Walker solution to General Relativity (FLRW or FRW metric). A generic expression for the quadratic proper space-time line element is derived, proportional to Planck length-squared, and dependent on two contributions. The first is associated to the energy–time uncertainty, and the second depends on the Hubble function. The results are in agreement with space-time quantization on the expected length orders, according to quantum gravity theories, and within experimental constraints on putative LIV. Full article