On the Zero-Energy Universe

We consider the energy of the Universe, from the pseudo-tensor point of view (Berman, M.Sc. thesis, 1981). We find zero values, when the calculations are well-done. The doubts concerning this subject are clarified, with the novel idea that the justification for the calculation lies in the association of the equivalence principle, with the nature of co-motional observers, as demanded in Cosmology. In Sect. 4, we give a novel calculation for the zero-total energy result.     

On the Periodicity Conjecture for Y-systems

The conjecture in question (due ultimately to Alexei Zamolodchikov) asserts the periodicity of all the solutions to the so-called Y-systems. Those systems are naturally associated to pairs of indecomposable Cartan matrices of finite type, and the conjectured period is equal to twice the sum of the respective Coxeter numbers. This conjecture has so far been proven only if one of the ranks equals one, in which case the Y-systems are intrinsically related to Fomin-Zelevinsky’s cluster algebras. In this paper, I use elementary projective geometry to prove the case when the two Cartan matrices involved are of type A with both ranks arbitrary.     

On the Crepant Resolution Conjecture in the Local Case

In this paper we analyze four examples of birational transformations between local Calabi–Yau 3-folds: two crepant resolutions, a crepant partial resolution, and a flop. We study the effect of these transformations on genus-zero Gromov–Witten invariants, proving the Coates–Iritani–Tseng/Ruan form of the Crepant Resolution Conjecture in each case. Our results suggest that this form of the Crepant Resolution Conjecture may also hold for more general crepant birational transformations. They also suggest that Ruan’s original Crepant Resolution Conjecture should be modified, by including appropriate “quantum corrections”, and that there is no straightforward generalization of either Ruan’s original Conjecture or the Cohomological Crepant Resolution Conjecture to the case of crepant partial resolutions. Our methods are based on mirror symmetry for toric orbifolds.     

On the Birth of a Closed Hyperbolic Universe

We clarify and develop the results of a previous paper on the birth of a closed universe of negative spatial curvature and multiply connected topology. In particular we discuss the initial instanton and the second topology change in more detail. This is followed by a short discussion of the results.     

On the anomalous large-scale flows in the Universe

Recent combined analyses of the CMB and galaxy cluster data reveal unexpectedly large and anisotropic peculiar velocity fields at large scales. We study cosmic models with included vorticity, acceleration and total angular momentum of the Universe in order to understand the phenomenon. The Zel’dovich model is used to mimic the low redshift evolution of the angular momentum. Solving coupled evolution equations of the second order for density contrast in corrected Ellis–Bruni covariant and gauge-invariant formalism one can properly normalize and evaluate integrated Sachs–Wolfe effect and peculiar velocity field. The theoretical results compared to the observations favor a much larger matter content of the Universe than that of the concordance model. Large-scale flows appear anisotropic with dominant components placed in the plane perpendicular to the axis of vorticity (rotation). The integrated Sachs–Wolfe term has a negative contribution to the CMB fluctuations for the negative cosmological constant and it can explain the observed small power of the CMB TT spectrum at large scales. The rate of the expansion of the Universe may be substantially affected by the angular momentum if its magnitude is large enough.     

On the Energy-Momentum Problem in Static Einstein Universe

The energy-momentum distributions of Einstein＇s simplest static geometrical model for an isotropic and homogeneous universe are evaluated. For this purpose, Einstein, Bergmann-Thomson, Landau-Lifshitz （LL）, Moller and Papapetrou energy-momentum complexes are used in general relativity. While Einstein and Bergmann-Thomson complexes give exactly the same results, LL and Papapetrou energy-momentum complexes do not provide the same energy densities. The Moller energy-momentum density is found to be zero everywhere in Einstein＇s universe. Also, several spacetimes are the limiting cases considered here.     

Theory of Gravitational-Inertial Field of Universe. II. On Critical Systems in Universe

Application of the equations of the gravitational-inertial field to the problem of free motion in the inertial field (to the cosmologic problem) leads to results according to which 1. all Galaxies in the Universe “disperse” from each other according to Hubble's law, 2. the “dispersion” of bodies represents a free motion in the inertial field and Hubble's law represents a law of motion of free body in the inertial field, 3. for arbitrary mean distribution densities of space masses different from zero the space is Lobachevskian. All critical systems (with Schwarzschild radius) are specific because they exist in maximalinertial and gravitational potentials. The Universe represents a critical system, it exists under the Schwarzschild radius. In high-potential inertial and gravitational fields the material mass in a static state or in motion with deceleration is subject to an inertial and gravitational “annihilation”. At the maximal value of inertial and gravitational potentials (= c²) the material mass is being completely “evaporated” transforming into radiation mass. The latter is being concentrated in the “horizon” of the critical system. All critical systems-black holes-represent geon systems, i.e. local formations of gravitational-electromagnetic radiations, held together by their own gravitational and inertial fields. The Universe, being a critical system, is “wrapped” in a geon crown.     

On a remarkable electromagnetic field in the Einstein Universe

We present a time-dependent solution of the Maxwell equations in the Einstein universe, whose electric and magnetic fields, as seen by the stationary observers, are aligned with the Clifford parallels of the 3-sphere \(S^3\). The conformal equivalence between Minkowski’s spacetime and (a region of) the Einstein cylinder is then exploited in order to obtain a knotted, finite energy, radiating solution of the Maxwell equations in flat spacetime. We also discuss similar electromagnetic fields in expanding closed Friedmann models, and compute the matter content of such configurations.     

On Combinatorial Expansion of the Conformal Blocks Arising from AGT Conjecture

In their recent paper, Alday et al. (Lett Math Phys 91:167–197, 2010) proposed a relation between \({\mathcal{N}=2}\) four-dimensional supersymmetric gauge theories and two-dimensional conformal field theories. As part of their conjecture they gave an explicit combinatorial formula for the expansion of the conformal blocks inspired by the exact form of the instanton part of the Nekrasov partition function. In this paper we study the origin of such an expansion from a CFT point of view. We consider the algebra \({\mathcal{A}={\sf Vir} \otimes\mathcal{H}}\) which is the tensor product of mutually commuting Virasoro and Heisenberg algebras and discover the special orthogonal basis of states in the highest weight representations of \({\mathcal{A}}\). The matrix elements of primary fields in this basis have a very simple factorized form and coincide with the function called \({Z_{{\sf bif}}}\) appearing in the instanton counting literature. Having such a simple basis, the problem of computation of the conformal blocks simplifies drastically and can be shown to lead to the expansion proposed in Alday et al. (2010). We found that this basis diagonalizes an infinite system of commuting Integrals of Motion related to Benjamin–Ono integrable hierarchy.     

On the Consequences of Retaining the General Validity of Locality in Physical Theory

The empirical validity of the locality (LOC) principle of relativity is used to argue in favour of a local hidden variable theory (HVT) for individual quantum processes. It is shown that such a HVT may reproduce the statistical predictions of quantum mechanics (QM), provided the reproducibility of initial hidden variable states is limited. This means that in a HVT limits should be set to the validity of the notion of counterfactual definiteness (CFD). This is supported by the empirical evidence that past, present, and future are basically distinct. Our argumentation is contrasted with a recent one by Stapp resulting in the opposite conclusion, i.e. nonlocality or the existence of faster-than-light influences. We argue that Stapps argumentation still depends in an implicit, but crucial, way on both the notions of hidden variables and of CFD. In addition, some implications of our results for the debate between Bohr and Einstein, Podolsky and Rosen are discussed.     

Locality Hypothesis and the Speed of Light

The locality hypothesis is generally considered necessary for the study of the kinematics of non-inertial systems in special relativity. In this paper we discuss this hypothesis, showing the necessity of an improvement, in order to get a more clear understanding of the various concepts involved, like coordinate velocity and standard velocity of light. Concrete examples are shown, where these concepts are discussed.     

Entropy of the Universe

After a discussion on several limiting cases where General Relativity turns into less sophisticated theories, we find that in the correct thermodynamical and cosmological weak field limit of Einstein’s field equations the entropy of the Universe is R ^3/2-dependent, where R stands for the radius of the causally related Universe. Thus, entropy grows in the Universe, contrary to Standard Cosmology prediction.     

On Effective Approximation of the Power Spectrum of Large-Scale Structure of the Universe

Russian Physics Journal - The article is focused on statistical properties of spatial distribution of galaxies in the Universe on scales exceeding 5 Мpc. The investigation aims at finding an...     

Theory of Gravitational-Inertial Field of Universe. IV. The Universe and the Microcosm

On basis of principle of discreteness of the space and time the following relations are obtained Λ_oM_oc = 2π?, τ_oE_o = 2π? and c² = 2GM_o/Λ_o giving the values of fundamental elements of length Λ_o ≈ (?G/c³)^1/2, mass M_o ≈ (?c/G)^1/2, time τ_o ≈ (?G/c⁵)^1/2 and energy E_o ≈ (?c⁵/G)^1/2. The geon crown of any critical system and the crown of the Universe must have a thickness equal to the fundamental length Λ_o = 2(π?G/c³)^1/2 = 5.74. 10^?33 cm. Each critical system has its specific (most probable) quantum with an average invariant mass which in the case of the Universe is equal to (2π²?H_u/Gc)^1/3 ≈ 300 m_e where H_u is Hubble's constant. There are all reasons to consider the universal virtual quanta of an invariant mass m_u ≈ 300 m_e as carriers of gravitational, electromagnetic and nuclear fields in the Universe.