The Cosmological Models with Jump Discontinuities

The article is dedicated to one of the most undeservedly overlooked properties of the cosmological models: the behaviour at, near and due to a jump discontinuity. It is most interesting that while the usual considerations of the cosmological dynamics deals heavily in the singularities produced by the discontinuities of the second kind (a.k.a. the essential discontinuities) of one (or more) of the physical parameters, almost no research exists to date that would turn to their natural extension/counterpart: the singularities induced by the discontinuities of the first kind (a.k.a. the jump discontinuities). It is this oversight that this article aims to amend. In fact, it demonstrates that the inclusion of such singularities allows one to produce a number of very interesting scenarios of cosmological evolution. For example, it produces the cosmological models with a finite value of the equation of state parameter $w=p/\rho$ even when both the energy density and the pressure diverge, while at the same time keeping the scale factor finite. Such a dynamics is shown to be possible only when the scale factor experiences a finite jump at some moment of time. Furthermore, if it is the first derivative of the scale factor that experiences a jump, then a whole new and different type of a sudden future singularity appears. Finally, jump discontinuities suffered by either a second or third derivatives of a scale factor lead to cosmological models experiencing a sudden dephantomization -- or avoiding the phantomization altogether. This implies that theoretically there should not be any obstacles for extending the cosmological evolution beyond the corresponding singularities; therefore, such singularities can be considered a sort of a cosmological phase transition.Comment: 27 pages, 5 figures. Inserted additional references; provided in Introduction a specific example of a well-known physical field leading to a cosmological jump discontinuity; seriously expanded the discussion of possible physical reasons leading to the jump discontinuities in view of recent theoretical and experimental discoverie

The Big Trip and Wheeler-DeWitt equation

Of all the possible ways to describe the behavior of the universe that has undergone a big trip the Wheeler-DeWitt equation should be the most accurate -- provided, of course, that we employ the correct formulation. In this article we start by discussing the standard formulation introduced by Gonz\'alez-D\'iaz and Jimenez-Madrid, and show that it allows for a simple yet efficient method of the solution's generation, which is based on the Moutard transformation. Next, by shedding the unnecessary restrictions, imposed on aforementioned standard formulation we introduce a more general form of the Wheeler-DeWitt equation. One immediate prediction of this new formula is that for the universe the probability to emerge right after the big trip in a state with $w=w_0$ will be maximal if and only if $w_0=-1/3$.Comment: accepted in Astrophysics and Space Scienc

The d-Dimensional Cosmological Constant and the Holographic Horizons

This article is dedicated to establishing a novel approach to the cosmological constant, in which it is treated as an eigenvalue of a certain Sturm–Liouville problem. The key to this approach lies in the proper formulation of physically relevant boundary conditions. Our suggestion in this regard is to utilize the “holographic boundary condition”, under which the cosmological horizon can only bear a natural (i.e., non-fractional) number of bits of information. Under this framework, we study the general d-dimensional problem and derive the general formula for the discrete spectrum of a positive energy density of vacuum. For the particular case of two dimensions, the resultant problem can be analytically solved in the degenerate hypergeometric functions, so it is possible to define explicitly a self-action potential, which determines the fields of matter in the model. We conclude the article by taking a look at the d-dimensional model of a fractal horizon, where the Bekenstein’s formula for the entropy gets replaced by the Barrow entropy. This gives us a chance to discuss a recently realized problem of possible existence of naked singularities in the D≠3 models

The <i>d</i>-Dimensional Cosmological Constant and the Holographic Horizons

This article is dedicated to establishing a novel approach to the cosmological constant, in which it is treated as an eigenvalue of a certain Sturm–Liouville problem. The key to this approach lies in the proper formulation of physically relevant boundary conditions. Our suggestion in this regard is to utilize the “holographic boundary condition”, under which the cosmological horizon can only bear a natural (i.e., non-fractional) number of bits of information. Under this framework, we study the general d-dimensional problem and derive the general formula for the discrete spectrum of a positive energy density of vacuum. For the particular case of two dimensions, the resultant problem can be analytically solved in the degenerate hypergeometric functions, so it is possible to define explicitly a self-action potential, which determines the fields of matter in the model. We conclude the article by taking a look at the d-dimensional model of a fractal horizon, where the Bekenstein’s formula for the entropy gets replaced by the Barrow entropy. This gives us a chance to discuss a recently realized problem of possible existence of naked singularities in the D≠3 models

On the Question of the Bäcklund Transformations and Jordan Generalizations of the Second Painlevé Equation

We demonstrate the way to derive the second Painlevé equation P2 and its Bäcklund transformations from the deformations of the Nonlinear Schrödinger equation (NLS), all the while preserving the strict invariance with respect to the Schlesinger transformations. The proposed algorithm allows for a construction of Jordan algebra-based completely integrable multiple-field generalizations of P2 while also producing the corresponding Bäcklund transformations. We suggest calling such models the JP-systems. For example, a Jordan algebra JMat(N,N) with the Jordan product in the form of a semi-anticommutator is shown to generate an integrable matrix generalization of P2, whereas the VN algebra produces a different JP-system that serves as a generalization of the Sokolov’s form of a vectorial NLS

The Cosmological Arrow of Time and the Retarded Potentials

We demonstrate that the cosmological arrow of time is the cause for the arrow of time associated with the retarded radiation. This implies that the proposed mathematical model serves to confirm the hypothesis of Gold and Wheeler that the stars radiate light instead of consuming it only because the universe is expanding—just like the darkness of the night sky is a side-effect of the global cosmological expansion

The Cauchy Problem for the Generalized Hyperbolic Novikov–Veselov Equation via the Moutard Symmetries

We begin by introducing a new procedure for construction of the exact solutions to Cauchy problem of the real-valued (hyperbolic) Novikov&ndash;Veselov equation which is based on the Moutard symmetry. The procedure shown therein utilizes the well-known Airy function Ai(&xi;) which in turn serves as a solution to the ordinary differential equation d2zd&xi;2=&xi;z. In the second part of the article we show that the aforementioned procedure can also work for the n-th order generalizations of the Novikov&ndash;Veselov equation, provided that one replaces the Airy function with the appropriate solution of the ordinary differential equation dn&minus;1zd&xi;n&minus;1=&xi;z

Secondary structure of the human mitochondrial genome affects formation of deletions

Acknowledgements: We acknowledge Filipe Pereira and Joana Damas for discussion of the MitoBreak database, Maria Falkenberg for the discussion of the potential structure of mtDNA, and Nariman Battulin for the discussion of mtDNA Hi-C data. We acknowledge Scott Lujan and Bill Copeland for providing the metadata of the principal component analysis from their paper, Maxim Ri for editing and improving the manuscript.Funder: EPFL LausanneBackground: Aging in postmitotic tissues is associated with clonal expansion of somatic mitochondrial deletions, the origin of which is not well understood. Such deletions are often flanked by direct nucleotide repeats, but this alone does not fully explain their distribution. Here, we hypothesized that the close proximity of direct repeats on single-stranded mitochondrial DNA (mtDNA) might play a role in the formation of deletions. Results: By analyzing human mtDNA deletions in the major arc of mtDNA, which is single-stranded during replication and is characterized by a high number of deletions, we found a non-uniform distribution with a “hot spot” where one deletion breakpoint occurred within the region of 6–9 kb and another within 13–16 kb of the mtDNA. This distribution was not explained by the presence of direct repeats, suggesting that other factors, such as the spatial proximity of these two regions, can be the cause. In silico analyses revealed that the single-stranded major arc may be organized as a large-scale hairpin-like loop with a center close to 11 kb and contacting regions between 6–9 kb and 13–16 kb, which would explain the high deletion activity in this contact zone. The direct repeats located within the contact zone, such as the well-known common repeat with a first arm at 8470–8482 bp (base pair) and a second arm at 13,447–13,459 bp, are three times more likely to cause deletions compared to direct repeats located outside of the contact zone. A comparison of age- and disease-associated deletions demonstrated that the contact zone plays a crucial role in explaining the age-associated deletions, emphasizing its importance in the rate of healthy aging. Conclusions: Overall, we provide topological insights into the mechanism of age-associated deletion formation in human mtDNA, which could be used to predict somatic deletion burden and maximum lifespan in different human haplogroups and mammalian species