The Lemaître model and the generalisation of the cosmic mass

We consider the spherically symmetric metric with a comoving perfect fluid and non-zero pressure—the Lemaître metric—and present it in the form of a calculational algorithm. We use it to review the definition of mass, and to look at the apparent horizon relations on the observer’s past null cone. We show that the introduction of pressure makes it difficult to separate the mass from other physical parameters in an invariant way. Under the usual mass definition, the apparent horizon relation, that relates the diameter distance to the cosmic mass, remains the same as in the Lemaître–Tolman case.     

Cosmological expansion and local systems: a Lemaître–Tolman–Bondi model

We propose a Lemaître–Tolman–Bondi system mimicking a two-body system to address the problem of the cosmological expansion versus local dynamics. This system is strongly bound but participates in the cosmic expansion and is exactly comoving with the cosmic substratum.     

Gravitational radiation of the Lemaître primordial atom

A non-traditional secondary quantizing of a strong gravitational field is realized. Using an earlier developed gravitational analog of the non-stationary perturbation theory it is shown that the Lema?tre primordial atom can generate hard gravitational radiation under spontaneous transitions of an effective Planckian particle in its discrete energy spectrum. Thus, the Lema?tre atom can be considered as a regular Big Bang model. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 59–65, February, 2009.     

Georges Lemaître,Pioneer of Modern Theoretical Cosmology

No other scientist may have had a greater impact on modern cosmology than the Belgian physicist, astronomer and priest Georges Lemaître. In 1927 he predicted the expansion of the universe on the basis of the cosmological field equations; and four years later he proposed what he called the primeval-atom hypothesis, the first version of the later big bang universe. In all his work on cosmology the cosmological constant Λ played a significant role. A recognized expert in the theory of general relativity, Lemaître also contributed significantly to the theoretical clarification of local and global singularity problems. Still, when he died in 1968, at a time when the standard big bang model celebrated its first victories, he was largely forgotten or recalled only as a somewhat shadowy figure of the past. This essay reviews in a historical context the scientific work of Lemaître with particular attention to his seminal contributions in the decade between 1925 and 1934.     

Radial asymptotics of Lemaître–Tolman–Bondi dust models

We examine the radial asymptotic behavior of spherically symmetric Lemaître–Tolman–Bondi dust models by looking at their covariant scalars along radial rays, which are spacelike geodesics parametrized by proper length ?, orthogonal to the 4-velocity and to the orbits of SO(3). By introducing quasi-local scalars defined as integral functions along the rays, we obtain a complete and covariant representation of the models, leading to an initial value parametrization in which all scalars can be given by scaling laws depending on two metric scale factors and two basic initial value functions. Considering regular “open” LTB models whose space slices allow for a diverging ?, we provide the conditions on the radial coordinate so that its asymptotic limit corresponds to the limit as ? → ∞. The “asymptotic state” is then defined as this limit, together with asymptotic series expansion around it, evaluated for all metric functions, covariant scalars (local and quasi-local) and their fluctuations. By looking at different sets of initial conditions, we examine and classify the asymptotic states of parabolic, hyperbolic and open elliptic models admitting a symmetry center. We show that in the radial direction the models can be asymptotic to any one of the following spacetimes: FLRW dust cosmologies with zero or negative spatial curvature, sections of Minkowski flat space (including Milne’s space), sections of the Schwarzschild–Kruskal manifold or self-similar dust solutions.     

Unified dark energy from Chiral-Quintom model with a mixed potential in Friedmann–Lemaître–Robertson–Walker cosmology

The European Physical Journal C - The NANOGrav collaboration has published a suspected stochastic gravitational wave (GW) background signal in its analysis of 12.5 years PTA data, so in this work,...     

Functional Renormalization Group Flows on Friedman–Lemaître–Robertson–Walker backgrounds

We revisit the construction of the gravitational functional renormalization group equation tailored to the Arnowitt–Deser–Misner formulation emphasizing its connection to the covariant formulation. The results obtained from projecting the renormalization group flow onto the Einstein–Hilbert action are reviewed in detail and we provide a novel example illustrating how the formalism may be connected to the causal dynamical triangulations approach to quantum gravity.     

Dirac Equation in Lemaįtre—Tolman—Bondi Models

The Dirac equation is studied for a sufficiently large class of Lematre—Tolman—Bondi cosmological models. While the angular equation (whose solution is known) separates directly, the spatial and temporal dependence de-couples only after a suitable separation procedure. The separated time equation is integrated by series. The separated spatial equation still depends on an arbitrary function relative to the integration of the cosmological model.     

Formation of Gyrs old black holes in the centers of galaxies within the Lema?tre–Tolman model

In this article we present a model of formation of a galaxy with a black hole in the center. It is based on the Lema?tre–Tolman solution and is a refinement of an earlier model. The most important improvement is the choice of the interior geometry of the black hole allowing for the formation of Gyrs old black holes. Other refinements are the use of an arbitrary Friedmann model as the background (unperturbed) initial state and the adaptation of the model to an arbitrary density profile of the galaxy. Our main interest was the M87 galaxy (NGC 4486), which hosts a supermassive black hole of mass 3.2 × 10⁹ M⊙. It is shown that for this particular galaxy, within the framework of our model and for the initial state being a perturbation of the ΛCDM model, the age of the black hole can be up to 12.7 Gyrs. The dependence of the model on the chosen parameters at the time of last scattering was also studied. The maximal age of the black hole as a function of the Ω _m and Ω_Λ parameters for the M87 galaxy can be 3.717 or 12.708 Gyr.     

Geometric Equations of State in Friedmann-Lemaître Universes Admitting Matter and Ricci Collineations

As a rule in General Relativity the spacetime metric fixes the Einstein tensor and through the Field Equations (FE) the energy-momentum tensor. However one cannot write the FE explicitly until a class of observers has been considered. Every class of observers defines a decomposition of the energy-momentum tensor in terms of the dynamical variables energy density (), the isotropic pressure (p), the heat flux q ^a and the traceless anisotropic pressure tensor _ab . The solution of the FE requires additional assumptions among the dynamical variables known with the generic name equations of state. These imply that the properties of the matter for a given class of observers depends not only on the energy-momentum tensor but on extra a priori assumptions which are relevant to that particular class of observers. This makes difficult the comparison of the physics observed by different classes of observers for the same spacetime metric. One way to overcome this unsatisfactory situation is to define the extra condition required among the dynamical variables by a geometric condition, which will be based on the metric and not to the observers. Among the possible and multiple conditions one could use the consideration of collineations. We examine this possibility for the Friedmann-Lemaître-Robertson-Walker models admitting matter and Ricci collineations and determine the equations of state for the comoving observers. We find linear and non-linear equations of state, which lead to solutions satisfying the energy conditions, therefore describing physically viable cosmological models.     

Energy spectrum and mass composition of primary cosmic rays in the vicinity of the “knee” in a model with two types of sources

An analysis of the data on the spectra of cosmic rays in the context of the proposed model with two types of sources suggests that the main contribution to the spectrum of all particles in the range of 10⁵?10⁷ GeV is made by the sources in which the exponent in the spectrum of particles’ generation p ≈ 2.85. The complex structure of the spectrum in the vicinity of the “knee” may arise owing to the presence of an additional supernova-type source that accelerates the particles to the energies of ～3 × 10⁴ Z GeV if the energy output of this source is ～2 × 10⁴⁸ erg/source.     

Influence of cosmic rays and cosmic dust on the atmosphere and Earth’s climate

The results of studying the cosmic ray fluxes in the Earth’s atmosphere and their influence on the atmospheric electricity, as well as the effect of cosmic dust entering the terrestrial atmosphere from the interplanetary space on the Earth’s climate are briefly discussed. A forecast of the climate cooling in the forthcoming 50 years is given.     

Spin 3/2 Field Equation: Separation and Solution in a Class of Lema?tre–Tolman–Bondi Cosmologies

The spin 3/2 field equation is studied in the general Lema?tre–Tolman–Bondi (LTB) space-time. The equation is separated by variable separation. The angular dependence factors out at the level of the general LTB metric. Due to spherical symmetry the separated angular equations coincide with those, previously integrated, relative to the Robertson–Walker and Schwarzschild metric. Separation of time and radial dependence is possible within a class of LTB cosmological models for which the physical radius is a product of a time and a radial function, the last one being further selected by the consistency condition of the radial equations. The separated time dependence, that can be integrated by series, results essentially unique. Instead the radial dependence can be reduced to two independent second order ordinary differential equations that still depend on an arbitrary radial function that is an integration function of the cosmological model. The generalization of the scheme to arbitrary spin field equation is suggested.     

Statistical errors in Weizscker-Skyrme mass model

The statistical uncertainties of 13 model parameters in the Weizscker-Skyrme(WS*) mass model are investigated for the first time with an efficient approach,and the propagated errors in the predicted masses are estimated.The discrepancies between the predicted masses and the experimental data,including the new data in AME 2016,are almost all smaller than the model errors.For neutron-rich heavy nuclei,the model errors increase considerably,and go up to a few MeV when the nucleus approaches the neutron drip line.The most sensitive model parameter which causes the largest statistical error is analyzed for all bound nuclei.We find that the two coefficients of symmetry energy term significantly influence the mass predictions of extremely neutron-rich nuclei,and the deformation energy coefficients play a key role for well-deformed nuclei around the β-stability line.     

Study of K（892） mass and width splitting caused by model difference

According to the new K^＊（892）^0 and K^＊（892）^- masses reported by the BELLE experiment and the K^＊（892）^0 mass reported by the FOCUS experiment, mass splitting between neutral and charged K^＊（892） becomes very small. This is significantly different from the current world average values given by the Particle Data Group 2008. We find that there are differences between models used to fit the K^＊（892） decay invariant mass spectra in different measurements and study the model dependence in the measurement of K^＊（892） parameters. We refit the K^＊（892）^0 mass spectra of the BELLE and FOCUS experiments with the formula used by BELLE in fitting K^＊（892）^- to get new mass and width. After refitting, the K^＊（892）^0 mass of the BELLE experiment becomes 1.4 MeV/c^2 larger than the initial value and that of the FOCUS experiment is 1 MeV/c^2 smaller than the initial value. We also fit the spectra of some other experiments to extract the K^＊ （892） parameters using the BELLE K^＊ （892）^- parametrization.