Particle Horizon Research Articles

Large-scale microwave anisotropy from gravitating seeds

Topological defects could have seeded primordial inhomogeneities in cosmological matter. We examine the horizon-scale matter and geometry perturbations generated by such seeds in an expanding homogeneous and isotropic universe. Evolving particle horizons generally lead to perturbations around motionless seeds, even when there are compensating initial underdensities in the matter. We describe the pattern of the resulting large angular scale microwave anisotropy.

Cosmological constraints on cosmic-string gravitational radiation.

The primordial nucleosynthesis and pulsar timing noise constraints on cosmic-string gravitational radiation are computed. The computation consists of a numerical integration of the Friedmann-Robertson-Walker Einstein equations which describe a universe containing radiation, dust, and a "one-scale"-model cosmic-string component. The procedure takes into account the effects of the annihilations of massive particle species on the equation of state of the cosmological fluid. An expression for the power emitted per mode of oscillation by a cosmic-string loop, suggested by both analytic calculations and recent numerical simulations, is used. The results of the computation are spectra of the cosmicstring gravitational radiation at nucleosynthesis and at present. Comparison of these spectra with the observed bounds on pulsar timing noise, and the observed bound on the effective number of light neutrino species permitted by the model of nucleosynthesis, allows one to exclude a range of values of $\ensuremath{\mu}$, the cosmic-string linear mass density, for certain values of $\ensuremath{\alpha}$, the size of a newly formed loop as a fraction of the particle horizon radius. We find constraints to $\ensuremath{\mu}$ which are more restrictive than any previous limit.

Can galaxies exist within our particle horizon with Hubble recessional velocities greater than c?

A simple, global picture of photon exchange in the flat, matter-dominated universe is presented using relativistic cosmology. Equations for the photon’s recessional velocity and position relative to the receiver are derived. The results are discussed in the context of the ‘‘raisin bread universe.’’ Contrary to intuition, it is shown that the Hubble recessional velocity of the emitter can exceed the speed of light for sources within the particle horizon of the receiver. The model used to obtain these results can be used by introductory astronomy students to obtain the proper distance and the time-of-flight distance to sources with large redshifts.

Statistical properties of two-dimensional periodic Lorentz gas with infinite horizon

We study the asymptotic statistical behavior of the 2-dimensional periodic Lorentz gas with an infinite horizon. We consider a particle moving freely in the plane with elastic reflections from a periodic set of fixed convex scatterers. We assume that the initial position of the particle in the phase space is random with uniform distribution with respect to the Liouville measure of the periodic problem. We are interested in the asymptotic statistical behavior of the particle displacement in the plane as the timet goes to infinity. We assume that the particle horizon is infinite, which means that the length of free motion of the particle is unbounded. Then we show that under some natural assumptions on the free motion vector autocorrelation function, the limit distribution of the particle displacement in the plane is Gaussian, but the normalization factor is (t logt)1/2 and nott1/2 as in the classical case. We find the covariance matrix of the limit distribution.

Hubble spheres and particle horizons

Isotropy of the cosmic microwave background radiation highlights the horizon problem. Analysis of the horizon problem and its inflationary solution requires that we study the properties of the Hubble sphere and distinguish between the Hubble surface and the particle horizon. All regions in the visible universe become causally connected when inflation increases the distance of the particle horizon by a factor of 3. If exponential inflation occurs because of a phase transition at temperature ∼ 10 15 GeV, the number of e-foldings to effect this threefold increase in the particle horizon distance is N ∼ 60

Cosmological perturbations in a system of matter and radiation

A system of radiation and nonrelativistic particles is studied from a thermodynamical point of view. The transfer of perturbed energy density from the radiation to the matter component is described explicitly for adiabatic perturbations inside the particle horizon. For thermal perturbations the fluctuations of the radiation energy density vanish, but the corresponding temperature fluctuations are different from zero.

Gauge-invariant cosmological perturbations from a thermodynamical point of view

A thermodynamically oriented gauge-invariant description of scalar cosmological perturbations around a flat Friedman universe is given. All basic variables have their physical meaning on comoving hypersurfaces, i.e. on hypersurfaces orthogonal to the matter worldlines. Several well known growth and decay rates of cosmological perturbation modes are rediscovered in a transparent way. The formalism is extended to multicomponent systems and applied to a mixture of radiation and non-relativistic particles for perturbations both smaller and larger than the particle horizon. Thermodynamical perturbation relations in the Minkowski spacetime turn out to be valid in the expanding universe, provided all perturbed quantities are replaced by their gauge-invariant counterparts.

Is a horizon-free cosmology possible?

In a space of FRLW models, filled with a single fluid such that its energy-momentum tensor satisfies standard energy conditions and the dynamics of the universe is described by a second order differential equation,the existence of particle horizons is a generic property. To remove particle horizons one must invest nearly as much as to remove them together with the initial singularity.

On horizons in homogeneous isotropic universes

In homogeneous isotropic universes the particle horizon defines causally connected regions. For inflationary universes it is known that microphysics can interact coherently only on a much smaller scale. An interaction horizon is introduced that allows this scale to be determined for Robertson-Walker models. During inflation its upper bound is the event horizon.

The gravitational field of plane symmetric thick domain walls

Exact solutions of Einstein’s equations for a scalar field with a potential V(Φ) =V0 cos2(1−n) (Φ/f(n)) (0<n<1) are presented describing the gravitational field of thick, plane symmetric domain walls. The scalar field has a time-independent kinklike distribution, whereas the metric depends on a time coordinate. The metric is conformally flat and the hypersurfaces parallel to the wall (z=const) are three-dimensional de-Sitter spaces. A particle horizon exists on which the metric becomes Minkowski space. It is shown that the gravitational field experienced by a test particle is repulsive.

Self-similar perturbations of a Friedmann universe

The present analysis of spherically symmetric self-similar solutions to the Einstein equations gives attention to those solutions that are asymptotically k = 0 Friedmann at large z values, and possess finite but perturbed density at the origin. Such solutions represent nonlinear density fluctuations which grow at the same rate as the universe's particle horizon. The overdense solutions span only a narrow range of parameters, and resemble static isothermal gas spheres just within the sonic point; the underdense solutions may have arbitrarily low density at the origin while exhibiting a unique relationship between amplitude and scale. Their relevance to large-scale void formation is considered.

Cosmological solutions of the semiclassical Einstein-Dirac equations

Exact solutions to the semiclassical backreaction equations with an unquantised Dirac field are found when the ratio of the renormalisation parameters beta and alpha is 9/4. For alpha (0 there is a one-parameter family of solutions which do not have particle horizons and a two-parameter family of solutions which oscillate at about the Planck frequency and, on average, behave asymptotically as a matter-dominated Friedmann solution. There is a two-parameter family with an asymptotically de Sitter stage, which is stable for any alpha )0 and beta )0.

Exact Bianchi type-(I,V) solutions of the Einstein equations with scalar and spinor fields.

Exact solutions to the Einstein--Dirac--Klein-Gordon equations are found in Bianchi type-I and type-V spacetimes. When the spinor field is massive, the Bianchi type-I universe has singularities of the Zel'dovich type, and it may begin anisotropically at a singularity, leading to a dust-filled Friedmann stage at late times. For ``ghost neutrinos'' we get an axisymmetric Zel'dovich universe. These solutions have particle horizons. For the Bianchi type-V model there exist solutions which begin at a singularity, tending to flat spacetime at late times. In this case the neutrinos are not ``ghost'' ones.

Exact solutions of the Einstein equations including quantum effects and cosmological constant

The solutions to the semiclassical backreaction equations are found for conformally invariant free quantum fields in partially flat homogeneous and isotropic spacetimes with cosmological constant and with no classical source, for certain relations between the regularisation parameters alpha , beta and the cosmological constant Lambda . These solutions satisfy the classical Einstein equations for an effective perfect fluid of uniform density and isotropic pressure and, its effective stress-energy tensor can violate the energy conditions. For 3 alpha >or= beta there is always a one-parameter family of solutions which undergoes a time-symmetric bounce and which contains no singularities. For 3 alpha >or= beta >0 there is a one-parameter family of solutions with an initial singularity but no particle horizons. The stability of the de Sitter solutions are investigated and one of them is stable even when Lambda <0 or alpha <0.

Large- and small-angle anisotropies of the microwave background in cosmological models with nonzero Lambda term.

The influence of a small cosmological constant on the angle at which we observe today the particle horizon corresponding to the last scattering epoch and the size of fluctuations related to the typical mass of a galaxy in the Universe is investigated. In the former case numerical calculations are performed for the recombination epoch ${z}_{R}=1300$ as well as for the model in which the last scattering of photons took place most recently ($5&lt;{z}_{S}&lt;15$) because of reheating. It is shown that even a small admissible $\ensuremath{\Lambda}$ term may change this angle remarkably (up to 50% depending on the density of matter). Moreover a positive cosmological constant lowers the angle while a negative one enlarges it. In models with reheating the values of the redshifts for which the horizon problem may be solved are found. The surface of last scattering in these models is also calculated. In the latter case calculations are performed only for the recombination epoch. In contradistinction to the former case a large, but admissible by observations, cosmological constant immensely increases (up to an order of magnitude) the angle while a negative one slightly lowers it. Numerical values of all integrals appearing in the paper are found using elliptic functions.

Pedon Distribution of Minerals in Coastal Plain Paleudults

AbstractMineral distributions in three Florida Paleudults were investigated with respect to particle size, horizon, depth, and location within the soil matrix. Mineralogy of sand, silt, and clay was determined using optical microscopy, x‐ray diffraction, and thermal analysis. Also, mineralogy of sand‐grain coatings was compared with intergrain matrix material. Elemental‐oxide composition of siltsized phyllosilicate grains was determined by electron microprobe analysis. Sand fractions consisted mainly of quartz, with lesser amounts of feldspar and mica, which were more prevalent in lower horizons. Coarse‐ and medium‐silt fractions were also dominated by quartz, but contained appreciable feldspar and mica in B horizons. Kaolinite and hydroxy‐interlayered vermiculite (HIV) were most prevalent in fine‐silt and clay fractions. Abrupt changes in silt and clay mineralogy across the E‐ and B‐horizon boundary (E‐B) included a decrease in quartz and HIV and an increase in kaolinite. Relative amounts of HIV did not markedly change with depth in arenic epipedons, but decreased steadily below the E‐B boundary for all pedons. Sand‐grain coatings from Bt horizons contained more mica than did the intergrain matrix, whereas coatings in A and E horizons contained appreciably more HIV. Distribution of phyllosilicates in these pedons could be explained by a hypothetical sequence of processes which includes (i) illuviation of kaolinite formed from weathering or dispersed from clay lenses in the sediments, (ii) comminution of sand‐ and silt‐sized mica, (iii) incorporation of finegrained mica in sand‐grain coatings, and (iv) transformation of finegrained mica to HIV in highly permeable eluvial horizons.

Is the cosmological singularity thermodynamically possible?

The four broad approaches that have been suggested heretofore to eliminate the initial singularity from cosmology are briefly reviewed. None is satisfactory, basically because one does not know enough about the microphysics involved in the process. Thermodynamics has often been used in such dilemmas, and it is proposed to answer the question of whether there was a Friedmann-like singularity in the universe by exploiting the bound on specific entropy that has been established for finite system. It is made applicable to the universe by considering only a causally connected spacelike region within the particle horizon of a given observer. It is found that the specific entropy of radiation in such a region can exceed the bound if the observer is too early in the universe. Faith in the bound leads to the conclusion that the Friedmann models cannot be extrapolated back to nearer than a few Planck-Wheeler times from the singularity. The Friedmann initial singularity thus appears to be thermodynamically unacceptable.

Surfaces of constant redshift in an inflationary universe

During the period of exponential expansion in an inflationary cosmology, comoving particles that appear within view of a reference observer first move to smaller redshift and then to larger redshift, effectively disappearing after a finite time. It is shown that this passage into and out of communication is not described by either the particle or event horizon, but is well represented by surfaces of constant redshift. Formulas for these surfaces are derived. 5 references.

Particle creation in inhomogeneous spacetimes.

We study the creation of particles by inhomogeneous perturbations of spatially flat Friedmann-Robertson-Walker cosmologies. For massless scalar fields, the pair-creation probability can be expressed in terms of geometric quantities (curvature invariants). The results suggest that inhomogeneities on scales up to the particle horizon will be damped out near the Planck time. Perturbations on scales larger than the horizon are explicitly shown to yield no created pairs. The results generalize to inhomogeneous spacetimes several earlier studies of pair creation in homogeneous anisotropic cosmologies.

The problem of the maximum volumes and particle horizon in the Friedmann universe model

The maximum volume of the closed Friedmann universe is further investigated and is shown to be 2π2R3(t), instead of π2R3(t) as found previously. This discrepancy comes from the incomplete use of the volume formula of 3-dimensional spherical space in the astronomical literature. Mathematically, there exists the maximum volume at any cosmic timet in a 3-dimensional spherical case. However, the Friedmann closed universe in expansion reaches its maximum volume only at the timet m of the maximum scale factorR(t m ). The particle horizon has no limitation for the farthest objects in the closed Friedmann universe if the proper distance of objects is compared with the particle horizon as it should be. It will lead to absurdity if the luminosity distance of objects is compared with the proper distance of the particle horizon.