Particle Horizon Research Articles

Constraining the entropy corrected (m, n)-type pilgrim dark energy in fractal cosmology

This study explores the impact of introducing particle and future event horizon as infrared (IR) cutoff on (m, n)-type entropy corrected versions of pilgrim dark energy. We investigate (m, n)-type power-law entropy corrected pilgrim dark energy in a flat fractal platform by considering a non-interacting scenario with cold dark matter. Then, our focus shifts to (m, n)-type logarithmic entropy corrected pilgrim dark energy. We derive the evolution of some relevant cosmological parameters and cosmological planes. Finally, we constrain the model parameters using H(z)+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H(z)+$$\\end{document}BAO combined observational data from the DA and BAO methods. For statistical analysis, we apply the χ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi ^2$$\\end{document}-minimization technique (equivalent to the maximum likelihood method) to estimate the best-fit value of the model parameters. We incorporate public Cosmo Hammer (EMCEE) Python package code to perform the MCMC method. Finally, we display the plot of cosmological parameters and cosmological plane and analyze the triangular contour plot by using the optimal values of the model parameters.

Holographic bounce cosmological models induced by viscous dark fluid from a generalized non-singular entropy function

Bounce cosmological models containing a dark viscous fluid in a spatially flat Friedmann–Robertson–Walker (FRW) universe are considered. The universe’s evolution is described in terms of generalized equation of state (EoS) parameters, in the presence of the bulk viscosity. Entropic cosmology plays a key role in the discussion, and the matter bounce behavior is described based on a nonsingular, generalized entropy function, recently proposed by S. D. Odintsov and T. Paul. Three different forms of the scale factor are investigated: an exponential, a power-law and a double-exponential function, respectively. Appropriate bounce cosmological models are formulated, via the relevant parameters of the modified EoS, and analytical expressions for the corresponding infrared cut-off are obtained, via the particle horizon. Results are displayed in holographic form, making use of generalized holographic cut-offs first introduced by S. Nojiri and S. D. Odintsov. In addition, the viability of the corresponding bounce cosmological models is investigated, taking into account the actual thermodynamic properties of our universe, by means of a no-singular, generalized entropy function. In the asymptotic case, an expression for the generalized entropy is obtained, which remarkably has the additivity property.

Estimating the Minimum Possible Deceleration of Cosmic Expansion Post-inflation

The inflationary epoch, occurring shortly after the Big Bang, initiated an extraordinarily rapid exponential expansion of the universe. Following this period, the rate of cosmic expansion decelerated for approximately 9.8 billion years, until observations indicated a transition to an accelerated expansion of space-time. This paper aims to estimate the minimum possible deceleration of cosmic expansion during the post-inflationary epoch, addressing an unresolved aspect of cosmological studies. The observable universe is modeled as a spherical region defined by the particle horizon in the FLRW metric. The model operates on the principle that the speed of light cannot exceed the speed of space-time expansion, given that photons are bound by space-time constraints. This paper hypothesizes that at the end of the 9.8 billion years of deceleration, the expansion speed was at its lowest, nearly equating to the speed of light. Subsequently, this speed has increased, correlating with the current accelerated expansion. Through a graphical representation assuming a uniform rate of change in expansion speed (for minimum possible values), we apply concepts of onedimensional motion to derive our estimates. This novel approach provides a foundational calculation of the minimum deceleration, significantly contributing to the understanding of the dynamics of cosmic expansion and offering a basis for future research and observational refinement.

Degeneracy pressure in the presence of maximum length for non-interacting electrons

Combining quantum theory with the fundamental principles of gravity results in the modification of the uncertainty principle. In this study, we employ the extended uncertainty principle (EUP) with the maximum length derived from the cosmological particle horizon. The impact of this specific kind of modification is examined in a non-interacting electron gas system. We analytically derive the generalized relations for the degeneracy pressure and the bulk modulus. An intriguing finding is that the degeneracy pressure is reduced, as confirmed by the observed size of white dwarfs, which is smaller than what is predicted by the standard theory. Nevertheless, it is still capable of providing support against gravitational collapse.

Creation Field Cosmological Model with Variable Cosmological Term (Λ) in Bianchi Type III Space-Time

The paper is devoted to the study of cosmological models with time-varying cosmological term (Λ) in the presence of creation field in the framework of Bianchi type III space-time. To obtain deterministic model of the universe, we have assumed Λ∝1/R3, where R is the scale factor, for steady state cosmology and creation field, and shear (σ) is proportion to expansion (θ) which leads to B=Cn, where B and C are the metric potentials to explain small anisotropic behaviour of the universe and its isotropy. To obtain the results in terms of cosmic time t, we have assumed n=2. The model satisfies conservation equations, and creation field increases with time. The present model is free from singularity, has particle horizon, and provides a natural explanation for inflationary scenario and isotropization. Creation field and Einstein field equations are derived using principle of least action and Lagrangian formulation of variable cosmological term. For illustrative purposes, evolutionary behaviour of some cosmological parameters are shown graphically. The other physical aspects like accelerating behaviour of the model are also discussed. Thus, the model represents not only expanding universe but also accelerating which matches with the results of present-day observations.

Observation constraints on scalar field cosmological model in anisotropic universe

In this study, we have explored a scalar field cosmological model in the axially symmetric Bianchi type-I universe. In this study, our aim is to constrain the scalar field dark energy model in an anisotropic background. For this purpose, the explicit solution of the developed field equations for the model is determined and analyzed. Constraints on the cosmological model parameters are established utilizing Markov Chain Monte Carlo (MCMC) analysis and using the latest observational datasets of OHD, BAO, and Pantheon. For the combined dataset (OHD, BAO, and Pantheon), the best-fit values of Hubble and density parameters are estimated as [Formula: see text], [Formula: see text] [Formula: see text] and [Formula: see text]. The model shows a flipping nature and redshift transition occurs at [Formula: see text], and the present value of decelerated parameter is computed to be [Formula: see text] for the combined dataset. We have explored characteristics like the universe’s age, particle horizon, deceleration parameter, and jerk parameter. The dynamical properties, such as energy density [Formula: see text], scalar field pressure [Formula: see text], and equation of state parameter [Formula: see text], are analyzed and presented. We have also described the behavior of the scalar potential [Formula: see text] and scalar field. Furthermore, the authors also described the behavior of energy conditions in scalar-tensor cosmology. The scenario of the present accelerated expansion of the universe is described by the contribution of the scalar field.

Cosmological constraints on 4-dimensional Einstein-Gauss-Bonnet gravity

4-Dimensional Einstein-Gauss-Bonnet (4DEGB) gravity has garnered significant attention in the last few years as a phenomenological competitor to general relativity. We consider the theoretical and observational implications of this theory in both the early and late universe, (re-)deriving background and perturbation equations and constraining its characteristic parameters with data from cosmological probes. Our investigation surpasses the scope of previous studies by incorporating non-flat spatial sections. We explore consequences of 4DEGB on the sound and particle horizons in the very early universe, and demonstrate that 4DEGB can provide an independent solution to the horizon problem for some values of its characteristic parameter α. Finally, we constrain an unexplored regime of this theory in the limit of small coupling α (empirically supported in the post-Big Bang Nucleosynthesis era by prior constraints). This version of 4DEGB includes a geometric term that resembles dark radiation at the background level, but whose influence on the perturbed equations is qualitatively distinct from that of standard forms of dark radiation. In this limit, only one beyond-ΛCDM degree of freedom persists, which we denote as α̃ C . Our analysis yields the estimate α̃ C = (-9 ± 6) × 10-6 thereby providing a new constraint of a previously untested sector of 4DEGB.

Using entropy bounds to avoid the cosmological singularity and constrain cosmological particle production

In this work, we study the applications of entropy bounds in two toy cosmological models with particle production (annihilation), i.e., a radiation-dominated universe and a dust-dominated universe. We consider the co-moving volume and the volume covered by the particle horizon of a given observer as the thermodynamic systems satisfying entropy bounds. For the Bekenstein bound and the spherical entropy bound, it is found that the cosmological singularity can be avoided and cosmological particle production needs to be truncated in some special cases. Our study can be extended to other cosmological models with particle production.

Observational constraints on anisotropic cosmological model in Lyra’s manifold

In the present study, we have explored an axially symmetric Bianchi I universe with Lyra’s geometry. We assumed variable displacement vector as component of Lyra’s geometry in the Einstein’s field equations. We developed and presented exact solutions of the field equations of proposed model. The parameters of model have been extracted using latest observational finding of OHD, Pantheon and BAO data sets. The best fit values are estimated using MCMC method. Features like deceleration parameter, particle horizon, age of universe and jerk parameter are explored. Further Om and statefinder diagnosis of the assumed model are also discussed for geometrical comparison with the standard ΛCDM model.

Holographic description of the dissipative unified dark fluid model with axion field

In this paper, we extend an axion [Formula: see text] gravity model, and apply the holographic principle to describe in a unifying manner the early and the late-time universe when the general equation-of-state (EoS) contains a bulk viscosity. We assume a spatially flat Friedmann–Robertson–Walker (FRW) universe model. We use a description based on the generalized infrared-cutoff holographic dark energy proposed by Nojiri and Odintsov [Eur. Phys. J. C 77 (2017) 528; Gen. Relativ. Gravit. 38 (2006) 1285], and explore the evolution of the universe when the EoS describes the asymptotic behavior between the dust in the early universe and the late universe. We explore various forms of the bulk viscosity, and calculate analytical expressions for the infrared cutoffs in terms of the particle horizon. In this way, we obtain a unifying description of the early and the late-time universe in the presence of axion matter, via a viscous holographic fluid model.

Simulation of the expanding universe in hyperbolic metamaterials.

The particle horizon represents the boundary between observable and unobservable regions of the universe, which changes as the universe expands. Based on transformation optics, hyperbolic electromagnetic metamaterials can be utilized to simulate metrics with different signs due to their unique anisotropic properties. In this paper, we use hyperbolic metamaterials to visually depict the variation of the particle horizon under three models of an expanding universe (open, flat, and closed) by substituting one-dimensional time with one-dimensional space. The good agreement between theory and simulation confirms that hyperbolic metamaterials are excellent for simulating space-times, suggesting their potential as a new platform for cosmological analogies.

An examination of the logotropic equation of state for Chaplygin gas and a generalized holographic model, as well as thermodynamic analysis utilizing scalar fields

This study proposes a method to reconstruct a generalized form of holographic dark energy and to analyse its cosmology, based on a logotropic equation of state. By assuming that the dark energy density is caused by holographic Ricci dark energy, one can calculate a scale factor for the universe’s overall energy density, provided by baryons, dark matter, and dark energy density. For the situation where the internal energy is in logarithmic form, the equation of state parameter is similarly obtained. In the following stage, a generalized Chaplygin gas is investigated using a logotropic equation of state, considering the scenario of a logarithmic internal energy. Modified generalized Chaplygin gas is also examined in the situation of logarithmic internal energy with logotropic equation of state, and related reconstruction is carried out. The generalized second law of thermodynamics is subsequently validated for event, particle, and Hubble horizons after taking into account the phantom and quintessence models using a logotropic technique.

Holographic realization of constant roll inflation and dark energy: An unified scenario

In the formalism of generalized holographic dark energy, the infrared cut-off LIR is generalized to the form, LIR=LIR(Lp,L˙p,L¨p,⋯,Lf,L˙f,L¨f,⋯,a,H,H˙,H¨,⋯), where Lp and Lf are the particle horizon and the future horizon, respectively (moreover, a is the scale factor and H is the Hubble parameter of the universe). Based on such formalism, we establish a holographic realization of constant roll inflation during the early universe, where the corresponding cut-off depends on the Hubble parameter and its derivatives (up to the second order). The viability of this holographic constant roll inflation with respect to the Planck data in turn puts a certain bound on the infrared cut-off at the time of horizon crossing. Such holographic correspondence of constant roll inflation is extended to the scenario where the infrared cut-off is corrected by the ultraviolet one, which may originate due to quantum effects. Besides the mere inflation, we further propose the holographic realization of an unified cosmic scenario from constant roll inflation (at the early time) to the dark energy era (at the late time) with an intermediate radiation dominated era followed by a Kamionkowski like reheating stage. In such a unified holographic scenario, the inflationary quantities (like the scalar spectral index and the tensor-to-scalar ratio) and the dark energy quantities (like the dark energy EoS parameter and the present Hubble rate) prove to be simultaneously compatible with observable constraints for suitable ranges of the infrared cut-off and the other model parameters. Moreover the curvature perturbations at super-Hubble scale prove to be a constant (with time) during the entire cosmic era, which in turn ensures the stability of the model under consideration.

Imprint of galactic rotation curves and metric fluctuations on the recombination era anisotropy

In applications of the conformal gravity theory it has been shown that a scale of order 105 Mpc due to large scale inhomogeneities such as clusters of galaxies is imprinted on the rotation curves of galaxies. Here we show that this same scale is imprinted on recombination era anisotropies in the cosmic microwave background. We revisit an analysis due to Mannheim and Horne, to show that in the conformal gravity theory the particle horizon distance scale of metric signals that originate in the primordial nucleosynthesis era at 109∘ K can encompass the entire recombination era sky. Similarly, the particle horizon distance scale of acoustic signals that originate at 1013∘ K can also encompass the entire recombination era sky. We show that the amplitudes of metric fluctuations that originate in the nucleosynthesis era can grow by a factor of 1012 by recombination, and by a factor of 1018 by the current time. In addition we find that without any period of exponential expansion a fluctuation amplitude that begins at a temperature of order 1033∘ K can grow by a factor of 1060 by recombination and by a factor of 1066 by the current time.

A non-singular generalized entropy and its implications on bounce cosmology

We propose a new five-parameter entropy function that proves to be singular-free during the entire cosmic evolution of the universe, and at the same time, also generalizes the Tsallis, Barrow, Rényi, Sharma-Mittal, Kaniadakis and Loop Quantum Gravity entropies for suitable limits of the parameters. In particular, all the above mentioned known entropies become singular (or diverge) when the Hubble parameter vanishes in course of the universe’s evolution (for instance, in bounce cosmology at the instant of bounce), while the newly proposed entropy function seems to be singular-free even at H=0 (where H represents the Hubble parameter of the universe). Such non−singular behaviour of the entropy function becomes useful in describing bouncing scenario, in which case, the universe undergoes through H=0 at the instant of bounce. It turns out that the entropic cosmology corresponding to the singular-free generalized entropy naturally allows symmetric bounce scenarios, such as – exponential bounce and quasi-matter bounce scenario respectively. In the case of exponential bounce, the perturbation modes are in the super-Hubble domain at the distant past, while for the quasi-matter bounce, the perturbation modes generate in the deep sub-Hubble regime far before the bounce and hence resolves the “horizon issue”. Based on this fact, we perform a detailed perturbation analysis for the quasi-matter bounce in the present context of singular-free entropic cosmology. As a result, the primordial observable quantities like the spectral tilt for the curvature perturbation (ns) and the tensor-to-scalar ratio (r) are found to depend on the entropic parameters, as expected. The theoretical expectations of ns and r turn out to be simultaneously compatible with the recent Planck data for suitable ranges of the entropic parameters, which in turn ensures the viability of the entropic bounce scenario. Furthermore the entropic cosmology in the present context is shown to be equivalent with the generalized holographic cosmology where the holographic cut-offs are determined in terms of either future horizon and its derivative or the particle horizon and its derivative.

Generalized Barrow entropic holographic dark energy with Granda–Oliver cut-off

Holographic dark energy (HDE) models are significantly different from standard dark energy (DE) models since they are based on holographic principles rather than mentioning a term in Lagrangian. Nojiri et al. [Barrow entropic dark energy: A member of generalized holographic dark energy family, Phys. Lett. B 825 (2022) 136844] proposed a generalized Barrow HDE (BHDE) model depending on particle horizon and future horizon, where the infra-red cut-off is considered as a usual cut-off. In this paper, we have revisited the generalized BHDE adopting the Granda–Oliver cut-off as the standard cut-off for the model. We have generalized BHDE behaviors with two different cut-offs, future horizon [Formula: see text] and particle horizon [Formula: see text]. The holographic cut-off is extended to depend on [Formula: see text], where a is the scale factor. Using this formalism, we demonstrated that the Barrow entropic DE model is equivalent to the generalized HDE model, where two ways are used to compute the respective holographic cut-off: first, in terms of particle horizon and its derivative, and second, future horizon and its derivative. We use 57 observational data points to determine the current Hubble constant [Formula: see text]. We have studied the behavior of few quantities, such as DE density [Formula: see text], pressure [Formula: see text], equation of state (EoS) parameter under the observational data. Here, we have to find the EoS parameter for generalized HDE, equivalent to Barrow entropic DE model. Besides this, we have also discussed k-essence and tachyon DE models.

Holographic dark energy from acceleration of particle horizon

Following the holographic principle, which suggests that the energy density of dark energy may be inversely proportional to the area of the event horizon of the Universe, we propose a new energy density of dark energy through the acceleration of the particle horizon scaled by the length of this parameter. The proposed model depends only on one free parameter: . For values of near zero, the deviation between the proposed model and the CDM model is significant, while for , the suggested model has no conflict with the CDM theory. Regardless of the value of , the model considers dark energy to behave as matter with positive pressure in high redshifts, , while for present and near-future Universe, it is considered to behave similar to that in the cosmological constant model and phantom field. Comparing the model with the Ricci dark energy model, we show that our model reduces the errors of the Ricci dark energy model concerning the calculation of the age of old supernovae and evolution of different cosmic components in high redshifts. Moreover, we calculated matter structure formation parameters such as the CMB temperature and matter power spectrum of the model to consider the effects of matter-like dark energy during the matter-dominated era.

Creation field cosmological models for dust distribution and time-dependent cosmological term (Λ) in Bianchi type II space-time

In this paper, we present solution of Einstein field equations which admit dust distribution and negative energy massless scalar field as a source with cosmological term ([Formula: see text]) in the frame work of Bianchi type II space-time. The models satisfy conservation equation and creation field increases with time satisfying the result as investigated by Hoyle and Narlikar [A new theory of gravitation, Proc. Roy. Soc. A 282 (1964) 191]. The deceleration parameter ([Formula: see text]) for the model (22) shows a transition from decelerating to accelerating regime with creation. A comparison with other cosmological models shows a transition from decelerating to accelerating regime with and without creation is mentioned. The present model is free from singularity, particle horizon and provides a natural explanation for inflationary scenario and isotropization. These features make the creation field cosmological models theoretically superior to the Big Bang models. Creation field and Einstein field equation are derived using principle of least action and the Lagrangian formulation of variable cosmological term is derived as mentioned by Moffat [Lagrangian formulation of a solution to the cosmological constant problem (1996), arXiv:astro-ph/9608202v1]. The current creation rate with other physical consequences is also discussed. For illustrative purposes, evolutionary behaviors of some cosmological parameters are shown graphically. In the figures, the cosmic time [Formula: see text] is given in gravitational units assuming the velocity of light [Formula: see text]. This [Formula: see text] and [Formula: see text]. Therefore, by multiplying cosmic time [Formula: see text] by (light years)−1, we obtain the coordinate time in years.

On holonomy singularities in general relativity and the Cloc0,1-inextendibility of space-times

This paper investigates the structure of gravitational singularities at the level of the connection. We show in particular that for FLRW space-times with particle horizons a local holonomy, which is related to a gravitational energy, becomes unbounded near the big-bang singularity. This implies the Cloc0,1-inextendibility of such FLRW space-times. Again using an unbounded local holonomy, we also give a general theorem establishing the Cloc0,1-inextendibility of spherically symmetric weak null singularities which arise at the Cauchy horizon in the interior of black holes. Our theorem does not presuppose the mass-inflation scenario and in particular applies to the Reissner–Nordström-Vaidya space-times, as well as to space-times which arise from small and generic spherically symmetric perturbations of two-ended subextremal Reissner–Nordström initial data for the Einstein–Maxwell scalar field system. In previous work, Luk and Oh proved the C2-formulation of strong cosmic censorship for this latter class of space-times—and based on their work we improve this to a Cloc0,1-formulation of strong cosmic censorship.

A consistent approach to the path integral formalism of quantum mechanics based on the maximum length uncertainty

We have developed a proper path integral formalism consistent with the deformed version of the quantum mechanics that contains a maximum observable length scale at the order of the cosmological particle horizon, existing in cosmology. We have started by modifying the classical mechanics which shows non-minimal effects on the equation of motion of a particle. Next, we have provided representation of the deformed quantum mechanical algebra. With this algebra in hand, we have calculated the general form of the path integral propagator in this deformed background. Thereafter, as a most simple case, we have built up the explicit form of the free particle propagator. The modifications to the free particle propagator show some non-trivial effects in this case. Our formalism can be applied to analyze the quantum properties and observations emerging in the context of cosmology.