A tetrad-based procedure is presented for solving Einstein's field equations for spherically-symmetric systems; this approach was first discussed by Lasenby et al. in the language of geometric algebra. The method is used to derive metrics describing a point mass in a spatially-flat, open and closed expanding universe respectively. In the spatially-flat case, a simple coordinate transformation relates the metric to the corresponding one derived by McVittie. Nonetheless, our use of non-comoving (`physical') coordinates greatly facilitates physical interpretation. For the open and closed universes, our metrics describe different spacetimes to the corresponding McVittie metrics and we believe the latter to be incorrect. In the closed case, our metric possesses an image mass at the antipodal point of the universe. We calculate the geodesic equations for the spatially-flat metric and interpret them. For radial motion in the Newtonian limit, the force acting on a test particle consists of the usual $1/r^2$ inwards component due to the central mass and a cosmological component proportional to $r$ that is directed outwards (inwards) when the expansion of the universe is accelerating (decelerating). For the standard $Λ$CDM concordance cosmology, the cosmological force reverses direction at about $z\approx 0.67$. We also derive an invariant fully general-relativistic expression, valid for arbitrary spherically-symmetric systems, for the force required to hold a test particle at rest relative to the central point mass.
We want to find the cosmological constant influence on cosmic microwave background (CMB) temperature due to moving linear cosmic strings. Considering the space-time metric of a linear cosmic string in an accelerated expanding universe, the Gott-Kaiser-Stebbins (GKS) effect, as an important mechanism in producing temperature discontinuity in the CMB, is considered and its modification due to the effect of the cosmological constant is calculated. The result shows that a positive cosmological constant (i.e. the presence of cosmic strings in an accelerated expanding universe) weakens the discontin…
We expose the scenarios of primordial baryon-photon plasma evolution within the framework of the Milne-like universe models. Recently, such models find a second wind and promise an inflation-free solution of a lot of cosmological puzzles including the cosmological constant one. Metric tensor perturbations are considered using the five-vectors theory of gravity admitting the Friedmann equation satisfied up to some constant. The Cosmic Microwave Background (CMB) spectrum is calculated qualitatively.
The complete relativistic kinetic model of violation of symmetry in isotopic expanding plasma and production of baryons in hot Universe. I. Exact model
An introduction to the physics and mathematics of the expanding universe, using no more than high-school level / undergraduate mathematics. Covered are the basics of scale factor expansion, the dynamics of the expanding universe, various distance concepts and the generalized redshift-luminosity relation, among other topics.
The complete relativistic kinetic model of violation of symmetry in isotopic expanding plasma and production of baryons in hot Universe. II. Numerical model: X-boson distribution function
It is pointed out that very recent results based on supernovae observations that the universe will accelerate and expand for ever with ever decreasing density have been predicted in a recent cosmological model which also deduces hitherto purely empirical features like the mysterious relation between the pion mass and the Hubble Constant.
We study the scalar curvature of spacelike hypersurfaces in the family of cosmological models known as generalized Robertson-Walker spacetimes, and give several rigidity results under appropriate mathematical and physical assumptions. On the other hand, we show that this family of spacetimes provides suitable models obeying the null convergence condition to explain accelerated expanding universes.
In this review we focus our attention on scalar-tensor gravity models and their empirical verification in terms of black hole and wormhole physics. We focus on a black hole, embedded in an expanding universe, describing both cosmological and astrophysical scales. We show that in scalar-tensor gravity it is quite common that the local geometry is isolated from the cosmological expansion, so that it does not backreact on the black hole metric. We try to extract common features of scalar-tensor black holes in an expanding universe and point out the gaps that must be filled.
The general plane wave solutions of the Proca field in conformal charts of the de Sitter expanding universe are derived for arbitrary polarizations showing how the frequencies can be separated in rest frames, defining thus the rest frame vacuum of this field.
We discuss the diffusion equation resulting from a strong dissipation limit of the random wave equation arising in the models of warm inflation. We show that the long wave power spectrum of scalar perturbations in the model of an exponential expansion coincides with the spectrum of quantum fluctuations on this space time.
We construct a model of a universe filled with a perfect fluid with isotropic particle pressure. The anisotropic plane symmetric Kasner spacetime is used as a seed metric and through a conformal mapping a perfect fluid is generated. The model is inhomogeneous, irrotational, shearing and accelerating. For negative time, the universe is expanding while for positive time it is collapsing. With the aid of graphical three dimensional plots it is established that the density and pressure hypersurfaces are smooth and singularity free. Additionally the sound-speed index is computed and the fluid obeys…
The primordial Universe might be highly inhomogeneous. We perform the 3+1D Numerical Relativity simulation for the evolution of scalar field in an initial inhomogeneous expanding Universe, and investigate how it populates the landscape with both de Sitter (dS) and AdS vacua. The simulation results show that eventually either the field in different region separates into different vacua, so that the expanding dS or AdS bubbles (the bubble wall is expanding but the spacetime inside AdS bubbles is contracting) come into being with clear bounderies, or overall region is dS expanding with a few smal…
In this article, we study the effect of the universe accelerating expansion on the structure of the general relativistic thick disks. Hence, by applying a conformal transformation on the metric of a static disk in isotropic coordinates, we transform the disk to the spacetime of a Friedman-Robertson-Walker (FRW) of an expanding universe. Also, by solving Einstein equations in the presence of the cosmological constant, $Λ$, which leads to the expansion of the universe, we investigate the structure of this disk in a dynamical state, and the changes in the disk mass density and energy density, as …
In this report, we discuss the behavior of coordinate-time dependent lapse function of FLRW metric of an accelerated expanding universe in the de Rham-Gabadadze-Tolley massive gravity theory. We find for the conventional dRGT formalism the corresponding lapse function can exhibit unphysical behaviors in the associated parameter space with a negative cosmological-constant-like term that leads to the decelerated universe model. To solve this problem, we introduce the so-called cosmological background density parameter to the perfect fluid stress-energy tensor which induces negative pressure. It …
The quantum theory of the Maxwell free field in Coulomb gauge on the de Sitter expanding universe is completed with the technical elements needed for building a coherent quantum theory of redshift. Paying a special attention to the conserved observables and defining the projection operator selecting the detected momenta it is shown that the expectation values of the energies of the emitted and detected photons comply with the Lema\^ itre rule of Hubble's law. Moreover, the quantum corrections to the dispersions of the principal observables and new uncertainty relations are derived.
The propagators of the Dirac fermions are studied in the configuration representation on the expanding portion of the $(1+3)$-dimensional de Sitter spacetime considering a fixed vacuum of Bunch-Davies type. In this representation the method of Koksma and Prokopec [J. F. Koksma and T. Prokopec, Class. Quant. Grav. {\bf 26}, 125003 (2009)] is applied recovering thus the form of the propagators in the massive case but obtaining a new result for the left-handed massless fermions (neutrinos).
A new type of integral representation is proposed for the propagators of the massive Klein-Gordon field minimally coupled to the gravity of the de Sitter expanding universe. This representation encapsulates the effects of the Heaviside step functions of the Feynman propagators making possible for the first time the calculation of Feynman diagrams involving scalar particles on this background. In order to convince that, a simple example is given outlining the amplitudes in the second order of perturbations of the Compton effect in the de Sitter scalar quantum electrodynamics.
We study the dynamics of a supersonically expanding ring-shaped Bose-Einstein condensate both experimentally and theoretically. The expansion redshifts long-wavelength excitations, as in an expanding universe. After expansion, energy in the radial mode leads to the production of bulk topological excitations -- solitons and vortices -- driving the production of a large number of azimuthal phonons and, at late times, causing stochastic persistent currents. These complex nonlinear dynamics, fueled by the energy stored coherently in one mode, are reminiscent of a type of "preheating" that may have…
We consider a cluster of Primordial Black Holes which is decoupled from the cosmological expansion (Hubble flow) and this region is heated as compared to the surrounding matter. The increased temperature inside the region can be explained by several mechanisms of Primordial Black Holes formation. We study the temperature dynamics of the heated region of Primordial Black Holes cluster.
Our recent results concerning the transformation under isometries of the conserved quantities on de Sitter manifolds, allow us to define the rest frame and study the relative geodesic motion in terms of conserved momentum, revealing thus various relativistic effects [I. I. Cotaescu, arXiv:1701.08499]. Here we discuss the time dilation (of the twin paradox) and the Lorentz contraction on the de Sitter expanding portions, pointing out the dependence of these effects on the position and moment in which the time and lengths are measured.
We analyze the properties of the electric and magnetic fields in different reference frames within a cosmological background space-time. First, we investigate the conformal properties of the electromagnetic fields and charge currents, discussing how the spatial curvature of the universe affects the field on different scales. Then, we analyze the effects of the expansion of the universe on local electromagnetic sources using Fermi coordinates. In particular, we investigate the energy balance and Poynting flux in this locally defined reference frame. We show that a charge following the Hubble fl…
The Faulty Assumptions of the Expanding-Universe Model vs. the Simple and Consistent Principles of a Flat-Universe Model -- with Moving Pisa Tower Experiment which Tests General Relativity
We investigate the formation, gravitational clustering and interactions of solitons in a self-interacting, non-relativistic scalar field in an expanding universe. Rapid formation of large number of solitons is driven by attractive self-interactions of the field, whereas the slower clustering of solitons is driven by gravitational forces. Driven closer together by gravity, we see a rich plethora of dynamics in the soliton "gas" including mergers, scatterings and formation of soliton binaries. The numerical simulations are complemented by analytic calculations and estimates of (i) the relevant i…
We studied the superradiance effect of a charge black hole immersed in an expanding Universe. We considered a test massive charged scalar field scattered off the horizon of the charge McVittie black hole. We carried out a detailed analysis of the electric energy extracted from the horizon of McVittie black hole in two different epochs of the expansion of the Universe, the dust dominated and radiation dominated epochs. We found that we have the superradiance effect in both epochs of the expansion of the Universe. Our study also provides evidence that we have extraction of energy from the horizo…
The spherical symmetry Black holes are considered in expanding background. The singularity line and the marginally trapped tube surface behavior are discussed. In particular, we address the conditions of whether a dynamical horizon forms for these cosmological black holes. We also discuss the cosmological constant effect on these black holes and the redshift of the light which comes from the marginally trapped tube surface.
The Renyi entropy coprises a group of data estimates that sums up the well-known Shannon entropy, acquiring a considerable lot of its properties. It appears as unqualified and restrictive entropy, relative entropy, or common data, and has found numerous applications in information theory. in the Renyi's argument, the area law of the black hole entropy plays a significant role. However, the total entropy can be modified by some quantum effects, motivated by the randomness of a system. In this note, by employing this modified entropy relation, we have derived corrections to Newton's law of gravi…
