Search Results (10)

We investigate interacting Barrow holographic dark energy (BHDE) with the Hubble horizon as the infrared cutoff in a fractal cosmological background. The fractal measure modifies the Friedmann sector and leads to the nonstandard closure relation ${\mathsf{\Omega }}_{\mathrm{dm}}+{\mathsf{\Omega }}_{\mathrm{de}}=1+\gamma$. Using Planck-inspired present-day normalization ${\mathsf{\Omega }}_{\mathrm{de}0}=0.6847$ and the benchmark parameters $(\Delta ,\omega ,\beta )=(0.8,0.263,0.123)$, we study four linear and nonlinear dark-sector interactions over $-0.99\le z\le 3$. The benchmark solutions remain within the physical background domain throughout this interval: the density fractions are non-negative, the relevant denominators remain positive, and the nonlinear $Q_3$ and $Q_4$ terms remain real. All four prescriptions exhibit a transition from decelerated to accelerated expansion. The non-interacting limit gives $z_t\simeq 0.86$, whereas for $\xi =0.12$ the transition redshifts are approximately $2.02$, $1.97$, $1.26$, and $1.87$ for $Q_1$, $Q_2$, $Q_3$, and $Q_4$, respectively; in particular, the $Q_4$ solution recovers a finite transition within the plotted redshift range. A stronger positive coupling generally shifts acceleration onset to a higher redshift, with the strongest response for $Q_1$ and the weakest for $Q_3$. The statefinder quantities $S_3^{\left(1\right)}$, $S_3^{\left(2\right)}$, and the s–r trajectories distinguish the interaction structures through their finite-redshift evolution and present-day values. A fixed-background SN Ia comparison using 1046 selected Pantheon supernovae, diagonal FITRES uncertainties, and an analytically profiled additive nuisance parameter gives the lowest information criteria for flat $\mathsf{\Lambda }$CDM. Among the BHDE benchmarks that interact, $Q_4$ is the closest case, with $\Delta \mathrm{AIC}=\Delta \mathrm{BIC}\simeq 1.21$. This comparison is not intended as a global posterior constraint on the model parameters. Full article

We present a new perspective on the symmetries that govern the formation of large-scale structures across the Universe, particularly focusing on the transition from the seeds of galaxy clusters to the seeds of galaxies themselves. We address two main features of cosmological fluid dynamics pertaining to both the linear and non-linear regimes. The linear dynamics of cosmological perturbations within the Hubble horizon is characterized by the Jeans length, which separates stable configurations from unstable fluctuations due to the gravitational effect on sufficiently large (and therefore, massive enough) overdensities. On the other hand, the non-linear dynamics of the cosmological fluid is associated with a turbulent behavior once the Reynolds numbers reach a sufficiently high level. This turbulent regime leads to energy dissipation across smaller and smaller scales, resulting in a fractal distribution of eddies throughout physical space. The proposed scenario suggests that the spatial scale of eddy formation is associated with the Jeans length of various levels of fragmentation from an original large-scale structure. By focusing on the fragmentation of galaxy cluster seeds versus galaxy seeds, we arrived at a phenomenological law that links the ratio of the two structure densities to the number of galaxies in each cluster and to the Hausdorff number of the Universe matter distribution. Finally, we introduced a primordial magnetic field and studied its influence on the Jeans length dynamics. The resulting anisotropic behavior of the density contrast led us to infer that the main features of the turbulence could be reduced to a 2D Euler equation. Numerical simulations showed that the two lowest wavenumbers contained the major energy contribution of the spectrum. Full article

The Wheeler–DeWitt equation for a flat and compact Friedmann–Lemaître–Robertson–Walker cosmology at the pre-inflation epoch is studied in the contexts of the standard and fractional quantum cosmology. Working within the semiclassical regime and applying the Wentzel-Kramers-Brillouin (WKB) approximation, we show that some fascinating consequences are obtained for our simple fractional scenario that are completely different from their corresponding standard counterparts: (i) The conventional de Sitter behavior of the inflationary universe for constant potential is replaced by a power-law inflation. (ii) The non-locality of the Riesz’s fractional derivative produces a power-law inflation that depends on the fractal dimension of the compact spatial section of space-time, independent of the energy scale of the inflaton. Full article

Barrow proposed that the area law of the entropy associated with a horizon might receive a “fractal correction” due to quantum gravitational effects—in place of $S\propto A$, we have instead $S\propto A^{1+\delta /2}$, where $0⩽\delta ⩽1$ measures the deviation from the standard area law ($\delta =0$). Based on black hole thermodynamics, we argue that the Barrow entropy should run (i.e., energy scale dependent), which is reasonable given that quantum gravitational corrections are expected to be important only in the high-energy regime. When applied to the Friedmann equation, we demonstrate the possibility that such a running Barrow entropy index could give rise to a dynamical effective dark energy, which is asymptotically positive and vanishing, but negative at the Big Bang. Such a sign switching dark energy could help to alleviate the Hubble tension. Other cosmological implications are discussed. Full article

A brane-world metric with an external magnetic field is a modified theory of gravity. It is suitable for the description of compact sources on the brane such as stars and black holes. We design a class of explicit symplectic integrators for this spacetime and use one of the integrators to investigate how variations of the parameters affect the motion of test particles. When the magnetic field does not vanish, the integrability of the system is destroyed. Thus, the onset of chaos can be allowed under some circumstances. Chaos easily occurs when the electromagnetic parameter becomes large enough. Dark matter acts as a gravitational force, so that chaotic motion can become more obvious as dark matter increases. The gravity of the black hole is weakened with an increasing positive cosmological parameter; therefore, the extent of chaos can be also strengthened. The proposed symplectic integrator is applied to a ray-tracing method and the study of such chaotic dynamics will be a possible reference for future studies of brane-world black hole shadows with chaotic patterns of self-similar fractal structures based on the Event Horizon Telescope data for M87* and Sagittarius A*. Full article

This article is dedicated to establishing a novel approach to the cosmological constant, in which it is treated as an eigenvalue of a certain Sturm–Liouville problem. The key to this approach lies in the proper formulation of physically relevant boundary conditions. Our suggestion in this regard is to utilize the “holographic boundary condition”, under which the cosmological horizon can only bear a natural (i.e., non-fractional) number of bits of information. Under this framework, we study the general d-dimensional problem and derive the general formula for the discrete spectrum of a positive energy density of vacuum. For the particular case of two dimensions, the resultant problem can be analytically solved in the degenerate hypergeometric functions, so it is possible to define explicitly a self-action potential, which determines the fields of matter in the model. We conclude the article by taking a look at the d-dimensional model of a fractal horizon, where the Bekenstein’s formula for the entropy gets replaced by the Barrow entropy. This gives us a chance to discuss a recently realized problem of possible existence of naked singularities in the $D\ne 3$ models. Full article

Scale symmetry is a fundamental symmetry of physics that seems however not to be fully realized in the universe. Here, we focus on the astronomical scales ruled by gravity, where scale symmetry holds and gives rise to a truly scale invariant distribution of matter, namely it gives rise to a fractal geometry. A suitable explanation of the features of the fractal cosmic mass distribution is provided by the nonlinear Poisson–Boltzmann–Emden equation. An alternative interpretation of this equation is connected with theories of quantum gravity. We study the fractal solutions of the equation and connect them with the statistical theory of random multiplicative cascades, which originated in the theory of fluid turbulence. The type of multifractal mass distributions so obtained agrees with results from the analysis of cosmological simulations and of observations of the galaxy distribution. Full article

In this paper, we consider the flat FRW spacetime filled with interacting dark energy and dark matter in fractal universe. We work with the three models of dark energy named as Tsallis, Renyi and Sharma–Mittal. We investigate different cosmological implications such as equation of state parameter, squared speed of sound, deceleration parameter, statefinder parameters, ${\omega }_{eff}-\stackrel{\prime }{{\omega }_{eff}}$ (where prime indicates the derivative with respect to $lna$ , and a is cosmic scale factor) plane and Om diagnostic. We explore these parameters graphically to study the evolving universe. We compare the consistency of dark energy models with the accelerating universe observational data. All three models are stable in fractal universe and support accelerated expansion of the universe. Full article

A finite non-classical framework for qubit physics is described that challenges the conclusion that the Bell Inequality has been shown to have been violated experimentally, even approximately. This framework postulates the primacy of a fractal-like ‘invariant set’ geometry $I_U$ in cosmological state space, on which the universe evolves deterministically and causally, and from which space-time and the laws of physics in space-time are emergent. Consistent with the assumed primacy of $I_U$ , a non-Euclidean (and hence non-classical) metric $g_p$ is defined in cosmological state space. Here, p is a large but finite integer (whose inverse may reflect the weakness of gravity). Points that do not lie on $I_U$ are necessarily $g_p$ -distant from points that do. $g_p$ is related to the p-adic metric of number theory. Using number-theoretic properties of spherical triangles, the Clauser-Horne-Shimony-Holt (CHSH) inequality, whose violation would rule out local realism, is shown to be undefined in this framework. Moreover, the CHSH-like inequalities violated experimentally are shown to be $g_p$ -distant from the CHSH inequality. This result fails in the singular limit $p=\infty$ , at which $g_p$ is Euclidean and the corresponding model classical. Although Invariant Set Theory is deterministic and locally causal, it is not conspiratorial and does not compromise experimenter free will. The relationship between Invariant Set Theory, Bohmian Theory, The Cellular Automaton Interpretation of Quantum Theory and p-adic Quantum Theory is discussed. Full article

One important ingredient in the study of cosmological evolution is the equation of state of the primordial matter formed in the first stages of the Universe. It is believed that the first matter produced was of hadronic nature, probably the quark–gluon plasma which has been studied in high-energy collisions. There are several experimental indications of self-similarity in hadronic systems—in particular in multiparticle production at high energies. Theoretically, this property was associated with the dynamics of particle production, but it is also possible to relate self-similarity to the hadron structure—in particular to a fractal structure of this system. In doing so, it is found that the thermodynamics of hadron systems at equilibrium must present specific properties that are indeed supported by data. In particular, the well-known self-consistence principle proposed by Hagedorn 50 years ago is shown to be valid, and can correctly describe experimental distributions, mass spectrum of observed particles, and other properties of the hadronic matter. In the present work, a review of the theoretical developments related to the thermodynamical properties of hadronic matter and its applications in other fields is presented. Full article