In the presence of the gravitational field, the energy density of matter no longer coincides with its mass density. A discrepancy exists, of course, also between the associated power spectra. Within the Λ CDM model, we derive a formula that relates the power spectrum of the energy density to that of the mass density and test it with the help of N-body simulations run in comoving boxes of 2.816 Gpc/h. The results confirm the validity of the derived formula and simultaneously show that the power spectra diverge significantly from one another at large cosmological scales.

United States

Maxim Eingorn

Germany

Türkiye

Ezgi Yilmaz

A. Emrah Yükselci

Ukraine

Alexander Zhuk

Mass density vs. energy density at cosmological scales

We investigate the backreaction of nonlinear perturbations on the global evolution of the Universe within the cosmic screening approach. To this end, we have considered the second-order scalar perturbations. An analytical study of these perturbations followed by a numerical evaluation shows that, first, the corresponding average values have a negligible backreaction effect on the Friedmann equations and, second, the second-order correction to the gravitational potential is much less than the first-order quantity. Consequently, the expansion of perturbations into orders of smallness in the cosmic screening approach is correct.

Brianna O'Briant

Adjaratou Diouf

Backreaction in cosmic screening approach

Defect characterizes the depth of factorization of terms in differential (cyclotomic) expansions of knot polynomials, i.e. of the non-perturbative Wilson averages in the Chern-Simons theory. We prove the conjecture that the defect can be alternatively described as the degree in  $$q^{\pm 2}$$  <math> <msup> <mi>q</mi> <mrow> <mo>±</mo> <mn>2</mn> </mrow> </msup> </math>   of the fundamental Alexander polynomial, which formally corresponds to the case of no colors. We also pose a question if these Alexander polynomials can be arbitrary integer polynomials of a given degree. A first attempt to answer the latter question is a preliminary analysis of antiparallel descendants of the 2-strand torus knots, which provide a nice set of examples for all values of the defect. The answer turns out to be positive in the case of defect zero knots, what can be observed already in the case of twist knots. This proved conjecture also allows us to provide a complete set of C-polynomials for the symmetrically colored Alexander polynomials for defect zero. In this case, we achieve a complete separation of representation and knot variables.

Russia

E. Lanina

A. Morozov

Defect and degree of the Alexander polynomial

We investigate the effect of peculiar velocities of inhomogeneities and the spatial curvature of the universe on the shape of the gravitating potential. To this end, we consider scalar perturbations of the FLRW metric. The gravitational potential satisfies a Helmholtz-type equation which follows from the system of linearized Einstein equations. We obtain analytical solutions of this equation in the cases of open and closed universes, filled with cold dark matter in presence of the cosmological constant. We demonstrate that, first, peculiar velocities significantly affect the screening length of the gravitational interaction and, second, the form of the gravitational potential depends on the sign of the spatial curvature.

Ezgi Canay

Andrew McLaughlin

A. Savaş Arapoğlu

Effect of peculiar velocities of inhomogeneities on the shape of gravitational potential in spatially curved universe

We compare two competing relativistic approaches to the N-body simulation of the Universe large-scale structure. To this end, employing the corresponding alternative computer codes (“gevolution” and “screening”), we conduct a series of cosmological simulations in boxes of different sizes and calculate the power spectra of the scalar perturbation Φ, the frame-dragging vector potential B and the difference between scalar modes <math><mi>χ</mi><mo>=</mo><mi>Φ</mi><mo>−</mo><mi>Ψ</mi></math>. We demonstrate that the corresponding power spectra are in very good agreement between the compared schemes. For example, the relative difference of the power spectra for Φ is 0.04% maximum. Since the perturbed Einstein equations have much simpler form in the screening approach, the simulation with this code consumes less computational time, saving almost 40% of CPU hours.

Screening vs. gevolution: In chase of a perfect cosmological simulation code

In this paper we study the group theoretic structures of colored HOMFLY polynomials in a specific limit. The group structures arise in the perturbative expansion of <math><mi>S</mi><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> Chern-Simons Wilson loops, while the limit is <math><mi>N</mi><mo>→</mo><mn>0</mn></math>. The result of the paper is twofold. First, we explain the emergence of Kadomsev-Petviashvily (KP) τ-functions. This result is an extension of what we did in [1], where a symbolic correspondence between KP equations and group factors was established. In this paper we prove that integrability of the colored Alexander polynomial is due to it's relation to soliton τ-functions. Mainly, the colored Alexander polynomial is embedded in the action of the KP generating function on the soliton τ-function. Secondly, we use this correspondence to provide a rather simple combinatoric description of the group factors in term of Young diagrams, which is otherwise described in terms of chord diagrams, where no simple description is known. This is a first step providing an explicit description of the group theoretic data of Wilson loops, which would effectively reduce them to a purely topological quantity, mainly to a collection of Vassiliev invariants.

V. Mishnyakov

A. Sleptsov

Perturbative analysis of the colored Alexander polynomial and KP soliton -functions

We study a three-component universe filled with dust-like matter in the form of discrete inhomogeneities (e.g., galaxies) and perfect fluids characterized by linear and nonlinear equations of state. Within the cosmic screening approach, we develop the theory of scalar and vector perturbations. None of the energy density contrasts associated with the distinct components is treated as small. Consequently, the derived equations are valid at both sub- and super-horizon scales and enable simulations for a variety of cosmological models.

Netherlands

Ruslan Brilenkov

A. Arapoğlu

Scalar and vector perturbations in a universe with nonlinear perfect fluid

We consider a universe filled with perfect fluid with the constant equation of state parameter ω. In the theory of scalar perturbations, we study the effect of peculiar velocities on the gravitational potential. For radiation with <math><mi>ω</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>3</mn></math>, we obtain the expression for the gravitational potential in the integral form. Numerical calculation clearly demonstrates the modulation of the gravitational potential by acoustic oscillations due to the presence of peculiar velocities. We also show that peculiar velocities affect the gravitational potential in the case of the frustrated network of cosmic strings with <math><mi>ω</mi><mo>=</mo><mo>−</mo><mn>1</mn><mo>/</mo><mn>3</mn></math>.

Alvina Burgazli

China

Valerii Shulga

Effect of peculiar velocities on the gravitational potential in cosmological models with perfect fluids

We describe predictions for top quark pair differential distributions at hadron colliders, by combining the next-to-next-to-leading order quantum chromodynamics calculations and next-to-leading order electroweak corrections with double resummation at the next-to-next-to-leading logarithmic accuracy of threshold logarithms and small-mass logarithms. To the best of our knowledge, this is the first study to present such a combination, which incorporates all known perturbative information. Numerical results are presented for the invariant-mass distribution, transverse-momentum distribution, and rapidity distributions.

Michał Czakon

Andrea Ferroglia

United Kingdom

Alexander Mitov

Davide Pagani

Andrew S. Papanastasiou

Benjamin D. Pecjak

Darren J. Scott

Sweden

Ioannis Tsinikos

Xing Wang

Li Lin Yang

Italy

Marco Zaro

Top quark pair production at complete NLO accuracy with NNLO+NNLL′ corrections in QCD L. L. Yang and X. Wang are supported in part by the National Natural Science Foundation of China (11975030, 11635001, 11575004). X. Wang is also supported in part by the Cluster of Excellence PRISMA+ (project ID 39083149). D. J. S. is supported under the ERC grant ERC-STG2015-677323. The work of D. P. and I. T. is supported by the Alexander von Humboldt Foundation, in the framework of the Sofja Kovalevskaja Award Project "Event Simulation for the Large Hadron Collider at High Precision". D. P. is also supported by the Deutsche Forschungsgemeinschaft (DFG) under Germany’s Excellence Strategy – EXC 2121"Quantum Univers" – 390833306. I. T. is also supported by the Swedish Research Council under contract number 2016-05996. The research of A. M. and A. P. has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (683211) as well as from UK STFC grants ST/L002760/1 and ST/K004883/1. The work of M. C. was supported in part by a grant of the BMBF and by the Deutsche Forschungs-gemeinschaft under grant 396021762 - TRR 257
						

We study the effects associated with nonlinearity of f(R) gravity and of the background perfect fluid manifested in the Kaluza–Klein model with spherical compactification. The background space-time is perturbed by a massive gravitating source which is pressureless in the external space but has an arbitrary equation of state (EoS) parameter in the internal space. As characteristics of a nonlinear perfect fluid, the squared speeds of sound are not equal to the background EoS parameters in the external and internal spaces. In this setting, we find exact solutions to the linearized Einstein equations for the perturbed metric coefficients. For nonlinear models with $$f^{\prime \prime }(R_0)\ne 0$$ <math><mrow><msup><mi>f</mi><mo>″</mo></msup><mrow><mo>(</mo><msub><mi>R</mi><mn>0</mn></msub><mo>)</mo></mrow><mo>≠</mo><mn>0</mn></mrow></math> , we show that these coefficients acquire correction terms in the form of two summed Yukawa potentials and that in the degenerated case, the solutions are reduced to a single Yukawa potential with some “corrupted” prefactor (in front of the exponential function), which, in addition to the standard 1/r term, contains a contribution independent of the three-dimensional distance r. In the linear $$f''(R)=0$$ <math><mrow><msup><mi>f</mi><mrow><mo>′</mo><mo>′</mo></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mrow></math>  model, we generalize the previous studies to the case of an arbitrary nonlinear perfect fluid. We also investigate the particular case of the nonlinear background perfect fluid with zero speed of sound in the external space and demonstrate that a non-trivial solution exists only in the case of $$f''(R_0)=0$$ <math><mrow><msup><mi>f</mi><mrow><mo>′</mo><mo>′</mo></mrow></msup><mrow><mo>(</mo><msub><mi>R</mi><mn>0</mn></msub><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mrow></math> .

Effects of nonlinearity of f(R) gravity and perfect fluid in Kaluza–Klein models with spherical compactification