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We analyze how predictions of cosmological models depend on a choice of described observational data, restrictions on flatness, and how this choice can alleviate the $H_0$ tension. These effects are demonstrated in the $w$CDM model in comparison with the standard $\Lambda$CDM model. We describe the Pantheon sample observations of Type Ia supernovae, 31 Hubble parameter data points $H(z)$ from cosmic chronometers, the extended sample with 57 $H(z)$ data points and observational manifestations of cosmic microwave background radiation (CMB). For the $w$CDM and $\Lambda$CDM models in the flat case and with spatial curvature we calculate $\chi^2$ functions for all observed data in different combinations, estimate optimal values of model parameters and their expected intervals. For both considered models the results essentially depend on a choice of data sets. In particular, for the $w$CDM model with $H(z)$ data, supernovae and CMB the $1\sigma$ estimations may vary from $H_0=67.52^{+0.96}_{-0.95}$ km\,/(s$\cdot$Mpc) (for all $N_H=57$ Hubble parameter data points) up to $H_0=70.87^{+1.63}_{-1.62}$ km\,/(s$\cdot$Mpc) for the flat case ($k=0$) and $N_H=31$. These results might be a hint how to alleviate the problem of $H_0$ tension: different estimates of the Hubble constant may be connected with filters and a choice of observational data., Comment: 15 pages, 6 figures, submitted to Mathematical Modelling and Geometry

We explore recent estimations of the Hubble parameter $H$ depending on redshift $z$, which include 31 $H(z)$ data points measured from differential ages of galaxies and 26 data points, obtained with other methods. We describe these data together with Union 2.1 observations of Type Ia supernovae and observed parameters of baryon acoustic oscillations with 2 cosmological models: the standard cold dark matter model with the $\Lambda$ term ($\Lambda$CDM) and the model with generalized Chaplygin gas (GCG). For these models with different sets of $H(z)$ data we calculate two-parameter and one-parameter distributions of $\chi^2$ functions for all observed effects, estimate optimal values of model parameters and their $1\sigma$ errors. For both considered models the results appeared to be strongly depending on a choice of Hubble parameter data sets if we use all 57 $H(z)$ data points or only 31 data points from differential ages. This strong dependence can be explained in connection with 4 $H(z)$ data points with high redshifts $z>2$., Comment: 15 pages, 5 figures, published in Mathematical Modelling and Geometry, http://mmg.tversu.ru

Observational manifestations of accelerated expansion of the universe, in particular, recent data for Type Ia supernovae, baryon acoustic oscillations, for the Hubble parameter $H(z)$ and cosmic microwave background constraints are described with different cosmological models. We compare the $\Lambda$CDM, the models with generalized and modified Chaplygin gas and the model with quadratic equation of state. For these models we estimate optimal model parameters and their permissible errors with different approaches to calculation of sound horizon scale $r_s(z_d)$. Among the considered models the best value of $\chi^2$ is achieved for the model with quadratic equation of state, but it has 2 additional parameters in comparison with the $\Lambda$CDM and therefore is not favored by the Akaike information criterion., Comment: 20 pages, 4 figures, revised version for JCAP

For different gravitational models we consider limitations on their parameters coming from recent observational data for type Ia supernovae, baryon acoustic oscillations, and from 34 data points for the Hubble parameter $H(z)$ depending on redshift. We calculate parameters of 3 models describing accelerated expansion of the universe: the $\Lambda$CDM model, the model with generalized Chaplygin gas (GCG) and the multidimensional model of I. Pahwa, D.~Choudhury and T.R.~Seshadri. In particular, for the $\Lambda$CDM model $1\sigma$ estimates of parameters are: $H_0=70.262\pm0.319$ km\,c${}^{-1}$Mpc${}^{-1}$, $\Omega_m=0.276_{-0.008}^{+0.009}$, $\Omega_\Lambda=0.769\pm0.029$, $\Omega_k=-0.045\pm0.032$. The GCG model under restriction $\alpha\ge0$ is reduced to the $\Lambda$CDM model. Predictions of the multidimensional model essentially depend on 3 data points for $H(z)$ with $z\ge2.3$., Comment: 18 pages, 4 figures

Various string models of mesons and baryons include a string carrying 2 or 3 massive points (quarks or antiquarks). Rotational states (planar uniform rotations) of these systems generate quasilinear Regge trajectories and may be used for describing excited hadron states on these trajectories. For different string models of baryon we are to solve the problem of choice between them and the stability problem for their rotational states. An unexpected result is that for the Y string baryon model these rotations are unstable with respect to small disturbances on the classical level. This instability has specific feature, disturbances grow linearly, whereas for the linear string baryon model they grow exponentially and may increase predictions for baryon's width $\Gamma$. The classical instability of rotational states and nonstandard Regge slope are the arguments in favor of the stable simplest model of string with massive ends both for baryons and mesons. Rotational states of this model with two types of spin-orbit correction are used to describe Regge trajectories for light, strange, charmed, bottom mesons and for $N$, $\Delta$, $\Sigma$, $\Lambda$ and $\Lambda_c$ baryons., Comment: 8 pages, 6 figures. arXiv admin note: text overlap with arXiv:1004.1518

We consider the gravitational model with additional spatial dimensions and anisotropic pressure which is nonzero only in these dimensions. Cosmological solutions in this model include accelerated expansion of the Universe at late age of its evolution and dynamical compactification of extra dimensions. This model describes observational data for Type Ia supernovae on the level or better than the $\Lambda$CDM model. We analyze two equations of state resulting in different predictions for further evolution, but in both variants the acceleration epoch is finite., Comment: 9 pages, 6 figures

We consider various hadron models with a string carrying $n=3$ massive points (quarks): Y configuration, linear baryon model $q$-$q$-$q$ and the closed string. For these models classical rotational states (planar uniform rotations) are tested for stability with respect to small disturbances. It is shown that rotations of all mentioned models are unstable, but nature of this instability is different. For the model Y the instability results from existence of multiple real frequencies in the spectrum of small disturbances, but for the linear model and the closed string the similar spectra contain complex frequencies, corresponding to exponentially growing modes of disturbances. This classical rotational instability is important for describing excited hadrons, in particular, for the linear model and the closed string it results in additional contribution in width of hadron states., Comment: 12 pages, 7 figures, REVTeX

For the closed string carrying 2 or 3 point-like masses the stability problem for central and linear rotational states is considered. This problem is important for applications of these model to describing baryons, glueballs or other exotic hadrons. The linear rotational state correspond to an uniform rotation of the system with rectilinear string segments, connecting massive points. The state is named ``central'' one, if there is a massive point at the rotational center. It is shown that the linear rotational states with 2 massive points are stable with respect to small disturbances. But the central rotational states with 3 masses are not stable, if the central mass it less than energy of the string with other massive points. This effect may change properties of excited hadron states, in particular, increase their width., Comment: 17 pages, 6 figures

The closed string carrying $n$ point-like masses is considered as the model of a baryon ($n=3$), a glueball ($n=2$ or 3) or another exotic hadron. For this system the rotational states are obtained and classified. They correspond to exact solutions of dynamical equations, describing an uniform rotation of the string with massive points. These rotational states result in a set of quasilinear Regge trajectories with different behavior. The stability problem for the so called central rotational states (with a mass at the rotational center) is solved with using the analysis of small disturbances. These states turned out to be unstable, if the central mass is less than some critical value., Comment: 19 pages, 3 figures

The closed relativistic string carrying two point-like masses is considered as the model of a glueball with two constituent gluons. Here the gluon-gluon interaction is simulated by a pair of strings. For this system exact solutions of classical equations of motions are obtained. They describe rotational states of the string resulting in the set of quasilinear Regge trajectories with different behavior., Comment: 11 pages, no figures

The stability problem for the hypocycloidal rotational states of the closed relativistic string with a point-like mass is solved with the help of analysis of small disturbances of these states. Both analytical and numerical investigations showed an unexpected result: the mentioned states turned out to be unstable. This conclusion is based upon the presence of roots with positive imaginary parts (increments) in the spectrum of frequencies of small disturbances. But these increments were small enough, so this instability had not been detected in previous numerical experiments. For the linear rotational states (the particular case of hypocycloidal states) the stability was confirmed. These results are important for applications of this model in hadron spectroscopy., Comment: 9 pages, 4 figures

The closed relativistic string carrying a point-like mass in the space with nontrivial geometry is considered. For rotational states of this system (resulting in non-trivial Regge trajectories) the stability problem is solved. It was shown that rotations of the folded string with the massive point placed at the rotational center are stable (with respect to small disturbances) if the mass exceeds some critical value: $m>m_{cr}$. But these rotational states are unstable in the opposite case $m

For the closed relativistic string carrying a pointlike mass the exact solutions of the dynamical equations are obtained and studied. These solutions describe states of the mentioned system moving in Minkowski space and also in the space that is the direct product of Minkowski space and a compact manifold (torus)., Comment: 7 pages, no figures, LaTeX

For the relativistic string with massive ends arbitrary small disturbances of the uniform rotation of the rectilinear string are investigated. There are two classes of these oscillations with different spectra of frequencies. They are stationary waves oscillating in the rotational plane and in the orthogonal direction. These states are presented in the form of Fourier series that helps to quantize string excitations in the linear vicinity of the classical rotation. These string oscillations may be applied to describing daughter Regge trajectories in the framework of the considered model, Comment: 12 pages, no figures, LaTeX, submitted to Theor. Math. Phys

For the relativistic string with massive ends the small disturbances of its rotational motion (quasirotational states) are investigated. They are presented in the form of Fourier series with the two types of oscillatory modes. They have the form of stationary waves correspondently in the rotational plane and in the orthogonal direction. The calculated values of the energy and angular momentum of these states give us possibility to describe higher radial excitations for hadrons with the help of the planar quasirotational oscillatory modes of the string with massive ends., Comment: 10 pages, no figures, LaTeX

For the linear string baryon model $q$-$q$-$q$ the small disturbances of its rotational motion (quasirotational states) are investigated. The spectrum of these states is obtained in the form of Fourier series and the complex eigenfrequencies are found in this spectrum. So the classic rotational motions of the linear string baryon model are unstable (unlike the similar motions for the string with massive ends). This instability differs from its analog for the three-string baryon model., Comment: 9 pages, no figures, LaTeX

For the linear string baryon model with three material points (three quarks) joined sequentially by the relativistic strings, the class of motions admitting linearizable boundary conditions is investigated. These motions may be represented as the Fourier series with eigenfunctions of some boundary-value problem. The two types of rotational motions are found among the mentioned class of solutions., Comment: 6 pages, no figures, LaTeX

In $D$-dimensional dilaton gravitational model stationary Schwarzschild type solutions (centrally symmetrical solutions in vacuum) are obtained. They contain the two-parameter set of solutions: the first parameter is proportional to a central mass and the second one describes intensity of the dilaton field. If the latter parameter equals zero we have pure Schwarzschild solution with the black hole and constant dilaton field. But when the mentioned parameter is non-zero and the dilaton is non-constant, the black hole horizon vanishes., Comment: 5 pages, LaTeX, 1 gif figure. Talk given at XVth International Workshop QFTHEP'2000 Tver, Russia, 14-20 September 2000

For the relativistic string with massive ends, the three-string baryon model and other string models of the baryon the small disturbances of well known rotational motions are considered. For the string meson model the two types of these disturbances (quasirotational motions) are obtained. They are oscillatory motions in the form of stationary waves in the rotational plane and in the orthogonal direction. These solutions may be used for describing more wide spectrum of hadron excitations and for the quantization of this nonlinear system. For three-string baryon model or Y configuration these quasirotational motions are more complicated and contain the branch with growing amplitudes. This consideration proves that for the three-string model with both massless and massive ends the rotational motions are unstable on the classical level., Comment: 9 pages, no figures, LaTeX. Talk given at XXIII International Colloquium on Group Theoretical Methods in Physics, Dubna, July 31 to August 05, 2000

The relativistic string with massive ends (the meson model) and four various string baryon models: q-qq, q-q-q, Y and $\Delta$ are considered. In particular, the rotational motions for all these systems are applied to describing the leading Regge trajectories, and also the classical dynamics beyond the usual rectilinear string rotations is studied. For the string meson model the two types of quasirotational motions (disturbances of the planar uniform rotations) are obtained. They are oscillatory motions in the form of stationary waves in the rotational plane and in the orthogonal direction. The analysis of the stability problem for the rotational motions for all mentioned string configurations shows that these motions for the Y and q-q-q models are unstable on the classical level., Comment: 5 pages, no figures, LaTeX. Talk given at International Conference on Quantization, Gauge Theory, and Strings dedicated to the memory of E.S. Fradkin, Moscow, 5-10 June 2000

For the relativistic string with massive ends (the meson model) and four various string baryon models (q-qq, q-q-q, Y and $\Delta$) we consider the classical quasirotational motions, which are small disturbances of the planar uniform rotations of these systems. For the string meson model the two types of these solutions are obtained. They describe oscillatory motions in the form of stationary waves in the rotational plane and in the orthogonal direction. This approach and the suggested method of determining an arbitrary motion of the system on the base of initial data let us solve the stability problem for the rotational motions for all mentioned string configurations. It is shown that the classic rotational motions are {\it stable} for the string meson model (or its analog q-qq) and for the $\Delta$ baryon configuration, but they are {\it unstable} for the string baryon models Y and q-q-q. For the latter two systems any small asymmetric disturbances grow with growing time. The motion of the q-q-q configuration become more complicated and quasiperiodic but quarks do not merge. In the case of Y model the evolution of disturbances results in falling a quark into the junction. These features of the classic behavior are important for describing the hadron states on the Regge trajectories and for choosing and developing the most adequate QCD-based string hadron models., Comment: 11 pages, 5 figures, RevTeX

The dynamics of baryon string model Y (three-string) is considered with using the approach that implies defining a classical motion of the system on the base of given initial position and initial velocities of string points. The analysis resulted, in particular, in the necessity of regarding more wide (than it was supposed earlier) class of parametrizations of the world surface for the adequate description of the three-string model. This approach let us to ascertain that the classic rotational motions (flat uniform rotations) for this string configuration are unstable. Any small asymmetric disturbances grow and inevitably result in falling a quark into the junction., Comment: 8 pages, 3 figures, LaTeX

We scrutinized hadronic Regge trajectories in a framework of two different models --- string and potential. Our results are compared with broad spectrum of existing theoretical quark models and all experimental data from PDG98. It was recognized that Regge trajectories for mesons and baryons are not straight and parallel lines in general in the current resonance region both experimentally and theoretically, but very often have appreciable curvature, which is flavor-dependent. For a set of baryon Regge trajectories this fact is well described in the considered potential model. The standard string models predict linear trajectories at high angular momenta J with some form of nonlinearity at low J., Comment: 15 pages, 9 figures, LaTeX

In $D$-dimensional dilaton gravitational model with the central charge deficit the generalized Friedmann-type cosmological solutions (spatially homogeneous and isotropic) are obtained and classified., Comment: 10 pages, LaTeX, 4 gif figures

For the string baryon model "triangle" the initial-boundary value problem is stated and solved in general. This problem implies defining a classical motion of the system on the base of given initial position and initial velocities of string points. The presented solution reduces the initial-boundary value problem for the considered model to the system of ordinary differential equations that can be integrated numerically in general. Using this approach we ascertain the stability of the rotational motions (flat uniform rotations) for the "triangle" string configuration., Comment: 11 pages, 4 figures, LaTeX

For the linear baryon string model with three massive points (three quarks) connected sequentially by the relativistic strings the initial-boundary value problem is stated and solved in general. This problem implies defining a classical motion of the system on the base of given initial position and initial velocities of string points. The given solution work reduces the initial-boundary value problem for the considered model to the system of ordinary differential equations that can be integrated numerically in general. The examples of numerical simulation of the system motion are considered, which, in particular, allow to answer to the old question about stability of a flat uniform rotation of the linear string configuration., Comment: 13 pages, 1 figure, LaTeX

Rotational motions for the quark-diquark (q-qq), linear (q-q-q) "three-string" (Y) and "triangle" string baryon models are considered and applied to description of baryonic orbitally exited states on the Regge trajectories. For the model "triangle" (three pointlike masses bounded pairwise by relativistic strings) the rotating closed string has a form of a curvilinear triangle composed of segments of a hypocycloid. The ultrarelativistic asymptotic relation between the energy $E=M$ and the total angular momentum $J$ has the same form $J\simeq\alpha'E^2+\alpha_1E^{1/2}$ for rotational states in all string baryon models. Taking into account some type of quark spin-orbit interaction one can describe the baryonic Regge trajectories by means of all mentioned string baryon configurations under assumption of different effective string tensions for them. Model depending estimations of effective quark masses in this procedure $m_{ud}\simeq 130$ MeV, $m_{s}\simeq 270$ MeV are close for all string configurations., Comment: 5 pages, 2 figures, LaTeX. Talk given at XI International Conference Problems in Quantum Field Theory, Dubna, Russia, July 13-17, 1998

The considered model of baryon consists of three pointlike masses (quarks) bounded pairwise by relativistic strings forming a curvilinear triangle. Classic analytic solutions for this model corresponding to a planar uniform rotation about the system center of mass are found and investigated. These solutions describe a rotating curve composed of segments of a hypocycloid. The curve is a curvilinear triangle or --- a more complicated configuration with a set of internal massless points moving at the speed of light. Different topological types of these motions are classified in connection with different forms of hypocycloids in zero quark mass limit. An application of these solutions to description of baryon states on the Regge trajectories is considered., Comment: 9 pages, 2 figures, LaTeX, to appear in Rhys. Rev. D