Particle Horizon Research Articles

The generalized second law of thermodynamics in f(R) gravity for various choices of scale factor

The present study is aimed at investigating the validity of the generalized second law (GSL) of thermodynamics in $f(\cal R)$ gravity. Choosing $f(\cal R)=R+\xi R^{\mu}+\zeta R^{-\nu}$ [following Phys Rev D, 68, 123512 (2003)] we have computed the time derivatives of total entropy for various choices of scale factor pertaining to emergent, intermediate and logamediate scenarios of the universe. We have taken into account the radii of hubble, apparent, particle and event horizons while computing the time derivatives of entropy under various situations being considered. After analyzing through the plots of time derivative of total entropy against cosmic time it is observed that the derivative always stays at positive level that indicate the validity of GSL of thermodynamics in the $f(\cal R)$ gravity irrespective of the choices of scale factor and enveloping horizon.

Monitoring and prediction of soil moisture spatial–temporal variations from a hydropedological perspective: a review

Accurate prediction of soil moisture spatial–temporal variations remains critical in agronomic, hydrological, pedological, and environmental studies. Traditional approaches of soil moisture monitoring and prediction have limitations of being time-consuming, labour-intensive, and costly for direct field observation; and having low spatial resolution for remote sensing, and inconsistent accuracy and reliability for landscape feature (e.g. topography, land use, vegetation) modelling. Innovative and effective approaches for accurate soil moisture simulation are needed. Pedological properties, including soil structure, particle size distribution, porosity, horizon, redox feature, and organic matter content, have been accepted as important factors controlling soil moisture and can be potentially used in soil moisture prediction. However, pedological properties mostly lack quantification (e.g. redox feature, horizon, soil structure), and soil sampling and analysis are time-consuming and costly, especially at large spatial scale. These limitations have restricted the utilisation of pedological information to predict soil moisture spatial–temporal variations at different spatial scales. To overcome these difficulties, new tools including geophysical tools and computed tomography, and new methods including mining soil survey information and integrating pedological information with landscape features and modelling, are proposed in this paper.

Bianchi type I magnetized cosmological model for barotropoic fluid distribution in Lyra geometry

Bianchi type I cosmological model for barotropic fluid distribution with magnetic field in Lyra geometry is investigated. To get the deterministic solution in terms of comic time t, we have assumed that (eigenvalue of shear tensor ) is proportional to expansion (q). This leads to A = (BC)n, where A, B and C are metric potentials and n is a constant. We also assume that current is flowing along x-axis, therefore, the magnetic field is in yz-plane. The behaviour of the model in the presence and absence of the magnetic field is discussed. We find that the model starts with a big-bang and the expansion in the model decreases as time increases. The displacement vector decreases slowly with time. The model possesses point type and cigar type singularities under different conditions. It has been shown that particle horizon exists in the model. The present investigation is new and is different from other author’s solution. The physical and geometrical aspects of the model in the presence and absence of magnetic field are also discussed. Key words: Bianchi I, magnetized, cosmological, barotropic, Lyra geometry.

Acoustic oscillations in the early universe

Acoustic oscillations in the baryonic-photon plasma leave an imprint on both the cosmic microwave background radiation (CMBR) and the power spectrum of the mass distribution in the universe. This effect is well known and is currently applied to determine the value for quantities such as the percentage of dark matter and dark energy in the universe. This study examines the contributions of higher order terms in the equations for the radiation-baryonic acoustic oscillations prior to radiation decoupling from matter. The energy and momentum conservation equations are combined with the Einstein field equations for a Robertson Walker metric containing the perturbations. An attempt is made to consider the effect of the higher order perturbations on the observed power spectrum and on the anisotropy of the CMBR. The sensitivity of these higher order terms to adiabatic, instead of non-adiabatic, boundary conditions on the fluctuations outside the particle horizon is considered. [Work supported by KSA.]

Fractional Action Cosmology: Emergent, Logamediate, Intermediate, Power Law Scenarios of the Universe and Generalized Second Law of Thermodynamics

In the framework of Fractional Action Cosmology (FAC), we study the generalized second law of thermodynamics for the Friedmann Universe enclosed by a boundary. We use the four well-known cosmic horizons as boundaries namely, apparent horizon, future event horizon, Hubble horizon and particle horizon. We construct the generalized second law (GSL) using and without using the first law of thermodynamics. To check the validity of GSL, we express the law in the form of four different scale factors namely emergent, logamediate, intermediate and power law. For Hubble, apparent and particle horizons, the GSL holds for emergent and logamediate expansions of the universe when we apply with and without using first law. For intermediate scenario, the GSL is valid for Hubble, apparent, particle horizons when we apply with and without first law. Also for intermediate scenario, the GSL is valid for event horizon when we apply first law but it breaks down without using first law. But for power law expansion, the GSL may be valid for some cases and breaks down otherwise.

Validity of the Generalized Second Law of Thermodynamics in the Logamediate and Intermediate Scenarios of the Universe

In this work, we have investigated the validity of the generalized second law of thermodynamics in logamediate and intermediate scenarios of the universe bounded by the Hubble, apparent, particle and event horizons using and without using first law of thermodynamics. We have observed that the GSL is valid for Hubble, apparent, particle and event horizons of the universe in the logamediate scenario of the universe using first law and without using first law. Similarly the GSL is valid for all horizons in the intermediate scenario of the universe using first law. Also in the intermediate scenario of the universe, the GSL is valid for Hubble, apparent and particle horizons but it breaks down whenever we consider the universe enveloped by the event horizon.

Study of Thermodynamics in Generalized Holographic and Ricci Dark Energy Models

We have considered the flat FRW model of the universe which is filled with the combination of dark matter and dark energy. Here we have considered two types of dark energy models: (i) Generalized holographic and (ii) generalized Ricci dark energies. The general descriptions of first law and generalized second law (GSL) of thermodynamics have studied on the apparent horizon, particle horizon and event horizon of the universe. We have shown that the first law and GSL are always valid on apparent horizon and first law can not be satisfied on the particle and event horizons in Einstein's gravity. These results are always true for any types of dark energy models i.e., these results do not depend on the dark energy models in Einstein's gravity. But the GSL completely depends on the choices of dark energy models in Einstein's gravity. Here we have discussed the validity of GSL in Generalized holographic and generalized Ricci dark energy models. On the particle horizon GSL may be satisfied but on the event horizon the GSL can not be satisfied for both the dark energy models. Also we have considered the Generalized holographic dark energy and generalized Ricci dark energy as the original holographic dark energy, so in this situation we have calculated the expression of the radius of the horizon $L$. On this horizon, we have shown that the first law can not be satisfied. Finally, on the horizon of radius $L$, we have found that the GSL can not be satisfied for both the dark energy models.

A study of generalized second law of thermodynamics in magnetic universe in the light of non-linear electrodynamics

In this work, we have considered the magnetic universe in non-linear electrodynamics. The Einstein field equations for non-flat FRW model have been considered when the universe is filled with the matter and magnetic field only. We have discussed the validity of the generalized second law of thermodynamics of the magnetic universe bounded by Hubble, apparent, particle and event horizons using Gibbsʼ law and the first law of thermodynamics for interacting and non-interacting scenarios. It has been shown that the GSL is always satisfied for Hubble, apparent and particle horizons but for event horizon, the GSL is violated initially and satisfied at late stage of the universe.

Cosmological apparent and trapping horizons

The dynamics of particle, event, and apparent horizons in FLRW space are discussed. The apparent horizon is trapping when the Ricci curvature is positive. This simple criterion coincides with the condition for the Kodama-Hayward apparent horizon temperature to be positive, and also discriminates between timelike and spacelike character of the apparent horizon. We discuss also the entropy of apparent cosmological horizons in extended theories of gravity and we use the generalized 2nd law to discard an exact solution of Brans-Dicke gravity as unphysical.

Formula omitted]CDM model as a unified origin of holographic and agegraphic dark energy models

Motivated by the fact that any nonzero Λ can introduce a length scale or a time scale into Einsteinʼs theory, rΛ=ctΛ=3/|Λ|. Conversely, any cosmological length scale or time scale can introduce a Λ(t), Λ(t)=3/rΛ2(t)=3/(c2tΛ2(t)). In this Letter, we investigate the time varying Λ(t) corresponding to the length scales, including the Hubble horizon, the particle horizon and the future event horizon, and the time scales, including the age of the universe and the conformal time. It is found out that, in this scenario, the Λ(t)CDM model can be taken as the unified origin of the holographic and agegraphic dark energy models with interaction between the matter and the dark energy, where the interacting term is determined by Q=−ρ˙Λ. We place observational constraints on the Λ(t)CDM models originating from different cosmological length scales and time scales with the recently compiled “Union2 compilation” which consists of 557 Type Ia supernovae (SNIa) covering a redshift range 0.015⩽z⩽1.4. In conclusion, an accelerating expansion universe can be derived in the cases taking the Hubble horizon, the future event horizon, the age of the universe and the conformal time as the length scale or the time scale.

Origin of high oxide to nitride polishing selectivity of ceria-based slurry in the presence of picolinic acid**Project supported by the Center for Advanced Materials Processing (CAMP) at Clarkson University, the National Integrate Circuit Research Program of China (Grant No. 2009ZX02023-3), the National Basic Research Program of China (GrantNos. 2007CB935400, 2010CB934300 and 2006CB302700), the National High Technology Development Program of China

We report on the investigation of the origin of high oxide to nitride polishing selectivity of ceria-based slurry in the presence of picolinic acid. The oxide to nitride removal selectivity of the ceria slurry with picolinic acid is as high as 76.6 in the chemical mechanical polishing. By using zeta potential analyzer, particle size analyzer, horizon profilometer, thermogravimetric analysis and Fourier transform infrared spectroscopy, the pre- and the post-polished wafer surfaces as well as the pre- and the post-used ceria-based slurries are compared. Possible mechanism of high oxide to nitride selectivity with using ceria-based slurry with picolinic acid is discussed.

FRW universe models in conformally flat-spacetime coordinates III: Universe models with positive spatial curvature

We deduce general expressions for the line element of universe models with positive spatial curvature described by conformally flat-spacetime coordinates. Models with dust, radiation and vacuum energy are exhibited. Discussing the existence of particle horizons we show that there is continual annihilation of space, matter and energy in a dust- and radiation-dominated universe, and continual creation in a Lorentz Invariant Vacuum Energy (LIVE)-dominated universe when conformal time is used in Friedmann-Robertson-Walker (FRW) models with positive spatial curvature. A general procedure is given for finding coordinates to be used in Penrose diagrams. We also calculate the age and the redshift of some universe models using conformal time.

FRW universe models in conformally flat-spacetime coordinates II: Universe models with negative and vanishing spatial curvature

We deduce general expressions for the line element of universe models with negative and vanishing spatial curvature described by conformally flat spacetime coordinates. The empty Milne universe model and models with dust, radiation and vacuum energy are exhibited. Discussing the existence of particle horizons we show that there is continual creation of space, matter and energy when conformal time is used in Friedmann-Robertson-Walker models with negative spatial curvature.

Emergent flux from particle collisions near a Kerr black hole

The escape fraction at infinity is evaluated for massless particles produced in collisions of weakly interacting particles accreted into a density spike near the particle horizon of an extremal Kerr black hole, for the case of equatorial orbits. We compare with the Schwarzschild case, and argue that in the case of extremal black holes, redshifted signatures can be produced that could potentially explore the physics of particle collisions at centre of mass energies that extend beyond those of any feasible terrestrial accelerator.

A holographic energy model

We suggest a holographic energy model in which the energy coming from spatial curvature, matter and radiation can be obtained by using the particle horizon for the infrared cut-off. We show the consistency between the holographic dark-energy model and the holographic energy model proposed in this paper. Then, we give a holographic description of the universe.

The evolution of our local cosmic domain: effective causal limits

The causal limit usually considered in cosmology is the particle horizon, delimiting the possibilities of causal connection in the expanding universe. However it is not a realistic indicator of the effective local limits of important interactions in spacetime. We consider here the matter horizon for the Solar System, that is,the comoving region which has contributed matter to our local physical environment. This lies inside the effective domain of dependence, which (assuming the universe is dominated by dark matter along with baryonic matter and vacuum-energy-like dark energy) consists of those regions that have had a significant active physical influence on this environment through effects such as matter accretion and acoustic waves. It is not determined by the velocity of light c, but by the flow of matter perturbations along their world lines and associated gravitational effects. We emphasize how small a region the perturbations which became our Galaxy occupied, relative to the observable universe -- even relative to the smallest-scale perturbations detectable in the cosmic microwave background radiation. Finally, looking to the future of our cosmic domain, we suggest simple dynamical criteria for determining the present domain of influence and the future matter horizon. The former is the radial distance at which our local region is just now separating from the cosmic expansion. The latter represents the limits of growth of the matter horizon in the far future.

Future asymptotics of vacuum Bianchi type VI0 solutions

In this paper, we present a thorough analysis of the future asymptotic dynamics of spatially homogeneous cosmological models of Bianchi type VI0. Each of these models converges to a flat Kasner solution (Taub solution) for late times; we give detailed asymptotic expansions describing this convergence. In particular, we prove that the future asymptotics of Bianchi type VI0 solutions cannot be approximated in any way by Bianchi type II solutions, which is in contrast to Bianchi type VIII and IX models (in the direction toward the singularity). The paper contains an extensive introduction where we put the results into a broader context. The core of these considerations consists in the fact that there exist regions in the phase space of Bianchi type VIII models where solutions can be approximated, to a high degree of accuracy, by type VI0 solutions. The behavior of solutions in these regions is essential for the question of ‘locality’, i.e., whether particle horizons form or not. Since Bianchi type VIII models are conjectured to be important role models for generic cosmological singularities, our understanding of Bianchi type VI0 dynamics might thus be crucial to help to shed some light on the important question of whether to expect generic singularities to be local or not.

Causality and primordial tensor modes

We introduce the real space correlation function of B-mode polarization of the cosmic microwave background (CMB) as a probe of superhorizon tensor perturbations created by inflation.By causality, any non-inflationary mechanism for gravitational wave production after reheating, like global phase transitions or cosmic strings,must have vanishing correlations for angular separations greater than the angle subtended by the particle horizon at recombination, i.e. θ ≳ 2°.Since ordinary B-modes are defined non-locally in terms of the Stokes parameters Q and U and therefore don't have to respect causality, special care is taken to define `causal B̃-modes' for the analysis.We compute the real space B̃-mode correlation function for inflation and discuss its detectability on superhorizon scales where it provides an unambiguous test of inflationary gravitational waves.The correct identification of inflationary tensor modes is crucial since it relates directly to the energy scale of inflation. Wrongly associating tensor modes from causal seeds with inflation would imply an incorrect inference of the energy scale of inflation.We find that the superhorizon B̃-mode signal is above cosmic variance for the angular range 2° < θ < 4° and is therefore in principle detectable. In practice, the signal will be challenging to measure since it requires accurately resolving the recombination peak of the B-mode power spectrum.However, a future CMB satellite (CMBPol), with noise level ΔP ≃ 1μK-arcmin and sufficient resolution to efficiently correct for lensing-induced B-modes, should be able to detect the signal at more than 3σ if the tensor-to-scalar ratio isn't smaller than r ≃ 0.01.

DENSITY PERTURBATIONS IN DECAYING HOLOGRAPHIC DARK ENERGY MODELS

We study cosmological perturbations in the context of an interacting dark energy model, where the holographic dark energy with IR cutoff decays into the cold dark matter (CDM). For this purpose, we introduce three IR cutoffs of Hubble horizon, particle horizon, and future event horizon. Here we present small perturbations under the case that effective equation of state (EOS: ωeff) for the holographic energy density is determined to be the same negative constant as that for the CDM. Such new matter productions tend to dilute the density perturbations of CDM (matter contrast). For a decelerating universe of ωeff&gt; -1/3, the matter contrast is growing as the universe evolves, while for an accelerating universe of ωeff&lt; -1/3, the matter contrast is decaying, irrespective of the choice of IR cutoff. This shows clearly that the acceleration suppresses the growing of the density perturbations at the early universe.

The residual gravity acceleration effect in the Poincaré dodecahedral space

In a flat space, the global topology of comoving space can induce a weak acceleration effect similar to dark energy. Does a similar effect occur in the case of the Poincare dodecahedral space S^3/I^*? Does the effect distinguish the Poincare space from other well-proportioned spaces? The residual acceleration effect in the Poincare space is studied here using a massive particle and a nearby test particle of negligible mass, in S^3 embedded in R^4. The weak limit gravitational attraction on a test particle at distance r is set \propto [r_C \sin(r/r_C)]^{-2}, where r_C = curvature radius, in order to satisfy Stokes' theorem. A finite particle horizon large enough to include the adjacent topological images of the massive particle is assumed. The regular, flat, 3-torus T^3 is re-examined, and two other well-proportioned spaces, S^3/T^* and S^3/O^*, are also studied. The residual gravity effect occurs in all four cases. In a perfectly regular 3-torus of side length L_a, and in S^3/T^* and S^3/O^*, the highest order term in the residual acceleration is the third order term in the Taylor expansion of r/L_a (3-torus), or r/r_C, respectively. However, the Poincare dodecahedral space is unique among the four spaces. The third order cancels, leaving the fifth order term \sim \pm 300 (r/r_C)^5 as the most significant. Not only are three of the four perfectly regular well-proportioned spaces better balanced than most other multiply connected spaces in terms of the residual acceleration effect by a factor of about a million (setting r/L_a = r/r_C \sim 10^{-3}), but the fourth of these spaces is about 10^4 times better balanced than the other three. This is the Poincare dodecahedral space. Is this unique dynamical property of the Poincare space a clue towards a theory of cosmic topology?