This advantage of the proposed formula 3. The other extension, assuming a negative spatial curvature, is also characterized by the potential of a point-like inhomogeneity, similar to the Yukawa one, so the average value of the total potential is again zero [ 2 ]. We have proven that for some matter distributions at the late stage of the Universe evolution see, e. This situation is absolutely inadmissible, so in order to resolve this challenge we have cut off the gravitational potential and with the help of the modified formula 3.

Evidently, it is valid not only for the considered concrete density profile but also for an arbitrary one. It is important to stress that our conclusion is correct provided that the made assumptions concerning the FLRW geometry as an average one and the comoving volume averaging as an appropriate averaging procedure are valid.

Then the suggested application of the finite-range potentials instead of the infinite-range ones can improve the quality and precision of the cosmological simulations with respect to their representation of the physical reality. The work of M. Eingorn and B. We would like to thank the referee for critical remarks which have considerably improved the discussion parts of the manuscript. Vlahovic are also grateful to V. Gurzadyan and S. Matinyan for useful discussions and valuable comments underlying the given investigation.

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Maxim Eingorn, Email: moc. Maxim Brilenkov, Email: moc. Branislav Vlahovic, Email: ude. National Center for Biotechnology Information , U. The European Physical Journal. C, Particles and Fields. Published online Aug Author information Article notes Copyright and License information Disclaimer. Corresponding author. Received Apr 6; Accepted Aug 3. This article has been cited by other articles in PMC. Abstract We point out a weak side of the commonly used determination of scalar cosmological perturbations lying in the fact that their average values can be nonzero for some matter distributions.

Infinite- and finite-range gravitational potentials In the case of the infinite-range gravitational potential 2. Open in a separate window. The finite-range gravitational potential as a function of the radial distance. Conclusion We have proven that for some matter distributions at the late stage of the Universe evolution see, e. Acknowledgments The work of M. Contributor Information Maxim Eingorn, Email: moc.

References 1. Eingorn, A. Zhuk, Remarks on mechanical approach to observable Universe.

## Frontiers of Inflationary Cosmology

JCAP 05 , Zhuk, Hubble flows and gravitational potentials in observable Universe. JCAP 09 , Kudinova, A. Zhuk, Dynamics of astrophysical objects against the cosmological background. JCAP 04 , Villa, S. Matarrese, D. Maino, Cosmological dynamics: from the Eulerian to the Lagrangian frame. Part I. Seller Inventory BD Publisher: World Scientific , This specific ISBN edition is currently not available. View all copies of this ISBN edition:. Synopsis About this title This book is written from the viewpoint of a deep connection between cosmology and particle physics.

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About AbeBooks. Other Popular Editions of the Same Title. Search for all books with this author and title. Customers who bought this item also bought. Stock Image. Published by World Scientific New Quantity Available: 1. Seller Rating:. Gorbunov, Valery A. New Paperback Quantity Available: 1. Maino, Cosmological dynamics: from the Eulerian to the Lagrangian frame.

Part I. Newtonian approximation. JCAP 06 , Umeh, C. Clarkson, R. Maartens, Nonlinear relativistic corrections to cosmological distances, redshift and gravitational lensing magnification. Chisari, M. Zaldarriaga, Connection between Newtonian simulations and general relativity. D 83 , Adamek, D.

Daverio, R. Durrer, M. Kunz, General relativistic N -body simulations in the weak field limit. D 88 , Theory of cosmological perturbations. Introduction to the theory of the Early Universe: cosmological perturbations and inflationary theory.

Singapore: World Scientific; Landau, E. Lifshitz, The classical theory of fields Course of theoretical physics series, V. Oxford Pergamon Press, Oxford Peebles PJE. The large-scale structure of the Universe.

## Theory of Cosmological Perturbations and Applications to Superstring Cosmology

Princeton: Princeton University Press; MNRAS , Rubakov, A. Vlasov, What do we learn from CMB observations. Mars, F.

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