International Journal of Modern Physics D

We review various aspects of de Sitter spacetime in string theory: its status as an Effective Field Theory spacetime solution, its relation to the vacuum energy problem in string theory, its (global) holographic definition in terms of two entangled and noncanonical conformal field theories as well as a realization of a realistic de Sitter universe endowed with the observed visible matter and the necessary dark sector in order to reproduce the realistic cosmological structure. In particular, based on the new insight regarding the cosmological constant problem in string theory, we argue that in a doubled, $T$-duality-symmetric, phase-space-like and noncommutative generalized-geometric formulation, string theory can naturally lead to a small and positive cosmological constant that is radiatively stable and technically natural. Such a formulation is fundamentally based on a quantum spacetime, but in an effective spacetime description of this general formulation of string theory, the curvature of the dual spacetime is the cosmological constant of the observed spacetime, while the size of the dual spacetime is the gravitational constant of the same observed spacetime. Also, the three scales associated with intrinsic noncommutativity of string theory, the cosmological constant scale, the Planck scale as well as the Higgs scale, can be arranged to satisfy various seesaw-like formulae. Along the way, we show that these new features of string theory can be implemented in a particular deformation of cosmic-string-like models.

The consideration of a $1+3$ covariant approach to cold dark matter universe with no shear cosmological dust model with irrotational flows is developed in the context of $f(G)$ gravity theory in this study. This approach reveals the existence of integrability conditions which do not appear in noncovariant treatments. We constructed the integrability conditions in modified Gauss–Bonnet $f(G)$ gravity basing on the constraints and propagation equations. These integrability conditions reveal the linearized silent nature of quasi-Newtonian models in $f(G)$ gravity. Finally, the linear equations for the overdensity and velocity perturbations of the quasi-Newtonian spacetime were constructed in the context of modified $f(G)$ gravity. The application of harmonic decomposition and redshift transformation techniques to explore the behavior of the overdensity and velocity perturbations using $f(G)$ model was made. On the other hand, we applied the quasi-static approximation to study the approximated solutions on small scales which helps to get both analytical and numerical results of the perturbation equations. The analysis of the energy overdensity and velocity perturbations for both short- and long-wavelength modes in a dust-Gauss–Bonnet fluids was done and we see that both energy overdensity and velocity perturbations decay with redshift for both modes. In the limits to $\mathrm{\Lambda }$CDM, it means $f(G)=G$ the considered $f(G)$ model results coincide with $\mathrm{\Lambda }$CDM.

This paper explores the possibility of scalar quantum particles traversing generalized Ellis–Bronnikov wormholes, taking into account quantum effects like tunneling. We investigate the generalized Ellis–Bronnikov wormhole metric and discover that when the exponent parameter is $n=2$, there is a single barrier-shaped effective potential at the throat of the wormhole for any orbital angular momentum value. Conversely, for $n\ne 2$, the potential can be symmetric and double barrier-shaped, depending on the orbital angular momentum value. We only find analytical solutions for the Schrödinger-like equation in the generalized Ellis–Bronnikov spacetime for $n=2$, which are expressed using confluent Heun functions. By making certain approximations, we derive the transmission and reflection coefficients for scalar particles to tunnel through the generalized Ellis–Bronnikov wormhole.

The purpose of this paper is to explore the anisotropic exact Bianchi type II solutions in $f(T)$ gravity, where $T$ denotes the torsion scalar. We utilize the solutions to discuss conformal vector fields (CVFs) and energy conditions. In the first slot of this study, we find the CVFs. The CVFs being a generalization of the Killing vector fields (KVFs) are affiliated with the conservation laws of physics. Corresponding to the obtained solutions, we observe law of conservation of (linear or generalized) momentum. In the second slot, we derive the constraints under which the solution classes can admit certain energy conditions.

The model of generalized Tsallis holographic dark energy (which is known to be particular representative of Nojiri–Odintsov HDE) with event horizon as cut-off is investigated using methods of dynamical analysis. We take into consideration possible interaction with dark energy and matter in various forms. Critical points are determined. Cosmological evolution of the universe depends from interaction parameters. If we use event horizon scale as cut-off quasi-de Sitter expansion is possible only for interaction of type $\sim H(\alpha {\rho }_{\mathrm{\text{de}}}+\beta {\rho }_m)$ (where $H$ is the Hubble parameter). For interactions $\sim {\rho }_m{\rho }_{\mathrm{\text{de}}}/H$ and $\sim H{\rho }_m^{\alpha }{\rho }_{\mathrm{\text{de}}}^{1-\alpha }$ universe eventually stops ($H\to 0$) or ends its existence in final singularity ($H\to \infty$). In the first case, fraction of dark energy tends to $1$ or constant value lesser than 1 because dynamical equilibrium between matter and dark energy is established on late times.

We study the possibility to describe dark matter in a model of the universe with two-scale factors and a nonstandard Poisson bracket structure characterized by the deformation parameter $\kappa$. The dark matter evolution is analyzed in the early stages of the universe, and its relic density is obtained via the Freeze-In and Freeze-Out mechanism. We show that by fixing $\kappa$ and the initial ratio of energy densities present in the different sectors of the universe, the space of thermal average annihilation cross-sections and dark matter masses compatible with the standard cosmology prior to Big Bang Nucleosynthesis (BBN), is enlarged. This feature of the model is compatible with nonstandard cosmology.

The main findings of the generalized uncertainty principle (GUP), the phenomenological approach, for instance, the emergence of a minimal measurable length uncertainty, are obtained in various versions from theories of quantum gravity, such as string theory, loop quantum gravity, doubly special relativity and black hole physics. GUP counts for impacts of relativistic energies and finite gravitational fields on the fundamental theories of quantum mechanics (QM), the noncommutation and measurement uncertainty. Utilizing GUP in reconciling principles of general relativity (GR) and QM, thereby enables to draw convincing conclusions about quantum gravity. To resolve the shortcuts reported with the nonrelativistic three-dimensional GUP, namely, violation of Lorentz covariance, dependence on frame of reference, and violation of the linear additional law of momenta, we introduce relativistic four-dimensional generalized uncertainty principle (RGUP) to curved spacetime. To unify GR and QM, we apply the Born reciprocity principle (BRP), distance-momentum duality symmetry and RGUP to estimate the fundamental tensor in discretized curved spacetime. To this end, we generalize Riemann geometry. The Finsler geometry, which is characterized by manifold and Finsler structure, allows to directly apply RGUP to the Finsler structure of a free particle so that $F({\widehat{x}}_0,{ẋ}_0)$ can be expressed as $F({\widehat{x}}_0,\widehat{\varphi }{\widehat{p}}_0)$, from which the metric tensor in discretized Riemann spacetime could be deduced. We conclude that $F({\widehat{x}}_0,\widehat{\varphi }{\widehat{p}}_0)$ is homogeneous with degree $1$ in ${\widehat{p}}_0$, while $\widehat{\varphi }=1+{\beta }_1{\widehat{p}}_0^{\rho }{\widehat{p}}_{0\rho }$ is $0$-homogeneous resulting in ${\tilde{g}}_{\mu \nu }\simeq (\mathcal{𝒯}+2{\beta }_1{F}^2)[1+\mathcal{𝒯}{\bar{m}}^2|\widehat{ẍ}{|}^2]g_{\mu \nu }$. Despite, the astonishing similarity with the conformal transformation, know as Weyl tensor, this study suggests that principles of QMs could be unambiguously imposed on the resulting fundamental tensor. Also, we conclude that the features of Finsler geometry assumed in this study are likely the ones of the duel Hamilton geometry.

We investigated the stability condition of $f(Q)$ gravity theory with interacting and noninteracting models by using dynamical system. We assume the $f(Q)$ function as $f(Q)=\left(\right.\sqrt{Q}+\frac{M}{2}{\left)\right.}^2$, where $M$ is the free parameter. We evaluated the critical points for this model and examined the stability behavior. We found two stable critical points for interacting model. The phase plots for this system are examined and the physical interpretation is discussed. We illustrate all the cosmological parameters such as ${\mathrm{\Omega }}_m$, ${\mathrm{\Omega }}_{\varphi }$, $q$ and ${\omega }_{\mathrm{\text{Tot}}}$ at each fixed point and compare the parameters with observational values. Further, we assume hybrid scale factor and the equation of redshift and time is $t(z)=\frac{\mu }{\nu }W[\frac{\nu {(1+z)}^{-\frac{m}{\mu }}}{\mu }]$. We transform all the parameters in terms of redshift by using this equation and examine the behavior of these parameters. Our model represents the accelerated expansion of the universe. The energy conditions are examined in terms of redshift and strong energy conditions are not satisfied for the model. We also find the statefinder parameters $\{r,s\}$ in terms of z and discuss the nature of r–s and r–q plane. For both pairs $\{r,s\}$ and $\{r,q\}$ our model represents the $\mathrm{\Lambda }$CDM model. Hence, we determine that our $f(Q)$ model is stable and it satisfies all the observational values.