We consider Kaluza-Klein models with background matter in the form of a multicomponent perfect fl... more We consider Kaluza-Klein models with background matter in the form of a multicomponent perfect fluid. This matter provides spherical compactification of the internal space with an arbitrary number of dimensions. The gravitating source has the dust-like equation of state in the external/our space and an arbitrary equation of state (with the parameter \Omega) in the internal space. In the single-component case, tension (\Omega=-1/2) is the necessary condition to satisfy both the gravitational tests in the solar system and the thermodynamical observations. In the multicomponent case, we propose two models satisfying both of these observations. One of them also requires tension \Omega=-1/2, but the second one is of special interest because is free of tension, i.e. \Omega=0. To get this result, we need to impose certain conditions.
In the six-dimensional Kaluza-Klein model with the multidimensional cosmological constant \Lambda... more In the six-dimensional Kaluza-Klein model with the multidimensional cosmological constant \Lambda_6, we obtain the black brane with spherical compactification of the internal space. The matter source for this exact solution consists of two parts. First, it is a fine-tuned homogeneous perfect fluid which provides spherical compactification of the internal space. Second, it is a gravitating massive body with the dustlike equation of state in the external space and tension \hat p_1=-(1/2)\hat\varepsilon in the internal space. This solution exists both in the presence and absence of \Lambda_6. In the weak-field approximation, we also get solutions of the linearized Einstein equations for the model with spherical compactification. Here, the gravitating matter source has the dustlike equation of state in the external space and an arbitrary equation of state \hat p_1=\Omega \hat\varepsilon in the internal space. In the case \Lambda_6>0 and \Omega\neq -1/2, these approximate solutions tend asymptotically to the weak-field limit of the exact black brane solution. Both the exact and asymptotic black branes satisfy the gravitational experiments at the same level of accuracy as general relativity.
In Kaluza-Klein model with toroidal extra dimensions, we obtain the metric coefficients in a weak... more In Kaluza-Klein model with toroidal extra dimensions, we obtain the metric coefficients in a weak-field approximation for delta-shaped matter sources. These metric coefficients are applied to calculate the formulas for frequency shift, perihelion shift, deflection of light and parameterized post-Newtonian (PPN) parameters. In the leading order of approximation, the formula for frequency shift coincides with well-known general relativity expression. However, for perihelion shift, light deflection and PPN parameter \gamma we obtain formulas D\pi r_g/[(D-2)a(1-e^2)], (D-1)r_g/[(D-2)\rho] and 1/(D-2) respectively, where D is a total number of spatial dimensions. These expressions demonstrate good agreement with experimental data only in the case of ordinary three-dimensional (D=3) space. This result does not depend on the size of the extra dimensions. Therefore, in the considered multidimensional Kaluza-Klein models the point-like masses cannot produce the gravitational field which corresponds to the classical gravitational tests.
In Kaluza-Klein models with an arbitrary number of toroidal internal spaces, we investigate solit... more In Kaluza-Klein models with an arbitrary number of toroidal internal spaces, we investigate soliton solutions which describe the gravitational field of a massive compact object. We single out the physically interesting solution corresponding to a point-like mass. For the general solution we obtain equations of state in the external and internal spaces. These equations demonstrate that the point-like mass soliton has dust-like equations of state in all spaces. We also obtain the PPN parameters, which give the possibility to obtain the formulas for perihelion shift, deflection of light and time delay of radar echoes. Additionally, the gravitational experiments lead to a strong restriction on the parameter of the model: \tau = -(2.1\pm 2.3)\times 10^{-5}. The point-like mass solution contradicts this restriction. The condition \tau=0 satisfies the experimental limitation and defines a new class of solutions which are indistinguishable from general relativity. We call such solutions latent solitons. Black strings and black branes belong to this class. Moreover, the condition of stability of the internal spaces singles out black strings/branes from the latent solitons and leads uniquely to the black string/brane equations of state p_i=-\epsilon/2, in the internal spaces and to the number of the external dimensions d_0=3. The investigation of multidimensional static spherically symmetric perfect fluid with dust-like equation of state in the external space confirms the above results.
In Kaluza-Klein models, we investigate soliton solutions of Einstein equation. We obtain the form... more In Kaluza-Klein models, we investigate soliton solutions of Einstein equation. We obtain the formulas for perihelion shift, deflection of light, time delay of radar echoes and PPN parameters. We find that the solitonic parameter k should be very big: |k|\geq 2.3\times10^4. We define a soliton solution which corresponds to a point-like mass source. In this case the soliton parameter k=2, which is clearly contrary to this restriction. Similar problem with the observations takes place for static spherically symmetric perfect fluid with the dust-like equation of state in all dimensions. The common for both of these models is the same equations of state in our three dimensions and in the extra dimensions. All dimensions are treated at equal footing. To be in agreement with observations, it is necessary to break the symmetry between the external/our and internal spaces. It takes place for black strings which are particular examples of solitons with k\to \infty. For such k, black strings are in concordance with the observations. Moreover, we show that they are the only solitons which are at the same level of agreement with the observations as in general relativity. Black strings can be treated as perfect fluid with dust-like equation of state p_0=0 in the external/our space and very specific equation of state p_1=-(1/2)\epsilon in the internal space. The latter equation is due to negative tension in the extra dimension. We also demonstrate that dimension 3 for the external space is a special one. Only in this case we get the latter equation of state. We show that the black string equations of state satisfy the necessary condition of the internal space stabilization. Therefore, black strings are good candidates for a viable model of astrophysical objects (e.g., Sun) if we can provide a satisfactory explanation of negative tension for particles constituting these objects.
It is found the exact solution of the Poisson equation for the multidimensional space with topolo... more It is found the exact solution of the Poisson equation for the multidimensional space with topology M_{3+d}=\mathbb{R}^3\times T^d. This solution describes smooth transition from the newtonian behavior 1/r_3 for distances bigger than periods of tori (the extra dimension sizes) to multidimensional behavior 1/r^{1+d}_{3+d} in opposite limit. In the case of one extra dimension d=1, the gravitational potential is expressed via compact and elegant formula. It is shown that the corrections to the gravitational constant in the Cavendish-type experiment can be within the measurement accuracy of Newton's gravitational constant G_N. It is proposed models where the test masses are smeared over some (or all) extra dimensions. In 10-dimensional spacetime with 3 smeared extra dimensions, it is shown that the size of 3 rest extra dimensions can be enlarged up to submillimeter for the case of 1TeV fundamental Planck scale M_{Pl(10)}. In the models where all extra dimensions are smeared, the gravitational potential exactly coincides with the newtonian one. Nevertheless, the hierarchy problem can be solved in these models.
A multidimensional cosmological model with space-time consisting of n(n ≥ 2) Ein-stein spaces M i... more A multidimensional cosmological model with space-time consisting of n(n ≥ 2) Ein-stein spaces M i is investigated in the presence of a cosmological constant Λ and a homogeneous minimally coupled scalar field ϕ(t) as a matter source. Classical and quantum wormhole solutions are obtained for Λ < 0 and all M i being Ricci-flat. Classical wormhole solutions are also found for Λ < 0 and only one of the M i being Ricci-flat for the case of spontaneous compactification of the internal dimensions with fine tuning of parameters.
We investigate time dependent solutions (S-brane solutions) for product manifolds consisting of f... more We investigate time dependent solutions (S-brane solutions) for product manifolds consisting of factor spaces where only one of them is non-Ricci-flat. Our model contains a minimally coupled free scalar field as a matter source. We discuss a possibility of generating late-time acceleration of the Universe. The analysis is performed in conformally related Brans-Dicke and Einstein frames. Dynamical behavior of our Universe is described by its scale factor. Since the scale factors of our Universe are described by different variables in both frames, they can have different dynamics. Indeed, we show that with our S-brane ansatz in the Brans-Dicke frame the stages of accelerating expansion exist for all types of the external space (flat, spherical, and hyperbolic). However, applying the same ansatz for the metric in the Einstein frame, we find that a model with flat external space and hyperbolic compactification of the internal space is the only one with the stage of the accelerating expansion. A scalar field can prevent this acceleration. It is shown that the case of hyperbolic external space in the Brans-Dicke frame is the only model which can satisfy experimental bounds for the fine-structure constant variations. We obtain a class of models where a pair of dynamical internal spaces have fixed total volume. This results in a fixed fine-structure constant. However, these models are unstable and external space is nonaccelerating.
A multidimensional cosmological model with space-time consisting of n (n>1) Einstein spaces M_i i... more A multidimensional cosmological model with space-time consisting of n (n>1) Einstein spaces M_i is investigated in the presence of a cosmological constant Lambda and m homogeneous minimally coupled scalar fields as a matter source. Classes of the models integrable at classical as well as quantum levels are found. These classes are equivalent to each other. Quantum wormhole solutions are obtained for them and the procedure of the third quantization is performed. An inflationary universe arising from classically forbidden Euclidean region is investigated for a model with a cosmological constant.
Multidimensional cosmological model with the topology M=RxM_1xM_2x...xM_n where M_i (i=1,... ,n) ... more Multidimensional cosmological model with the topology M=RxM_1xM_2x...xM_n where M_i (i=1,... ,n) undergo a chain splitting into arbitrary number of compact spaces is considered. It is shown that equations of motion can be solved exactly because they depend only on the effective curvatures and dimensions and "forget" about inner topological structure. It is proved that effective cosmological action for the model with n=1 in the case of infinite splitting of the internal space coincides with the tree-level effective action for a bosonic string.
Multidimensional cosmological model with the topology M=RxM_1xM_2x...xM_n where M_i (i=1,... ,n) ... more Multidimensional cosmological model with the topology M=RxM_1xM_2x...xM_n where M_i (i=1,... ,n) undergo a chain splitting into arbitrary number of compact spaces is considered. It is shown that equations of motion can be solved exactly because they depend only on the effective curvatures and dimensions and "forget" about inner topological structure. It is proved that effective cosmological action for the model with n=1 in the case of infinite splitting of the internal space coincides with the tree-level effective action for a bosonic string.
It is shown that a transition from a multidimensional cosmological model with one internal space ... more It is shown that a transition from a multidimensional cosmological model with one internal space (of the dimension d1) to the effective tree-level bosonic string corresponds to an infinite number of the internal dimensions: d1 → ∞.
An open homogenous isotropic Universe is examined, with De Sitter phase at the yearly stage of it... more An open homogenous isotropic Universe is examined, with De Sitter phase at the yearly stage of its evolution. A spontaneous breackdown of the symmetry of the masless self-acting scalar field is occuring for all realistic values of the self-action constant "lambda". The taking into account of the back action of that spontaneously breacked field on the metric lead to avoiding of the initial singularity in Cosmology for "lambda" = 10^-2, ...10^-12 for z>= 10^29, where Z^3 is the Entropy of the Universe at the present moment to the Entropy of Universe at the beggining of the inflationary phase ratio. Bibliography: 4
A multidimensional cosmological model with space-time consisting of n (n ≥ 2) Einstein spaces M i... more A multidimensional cosmological model with space-time consisting of n (n ≥ 2) Einstein spaces M i is investigated in the presence of a cosmological constant Λ and m (m ≥ 1) homogeneous minimally coupled scalar fields as a matter source. Classes of the models integrable at classical as well as quantum levels are found. These classes are equivalent to each other. Quantum wormhole solutions are obtained for them and the procedure of the third quantization is performed. An inflationary universe arising from classically forbidden Euclidean region is investigated for a model with a cosmological constant. *
A multidimensional cosmological model with space-time consisting of n (n>1) Einstein spaces M_i i... more A multidimensional cosmological model with space-time consisting of n (n>1) Einstein spaces M_i is investigated in the presence of a cosmological constant Lambda and m homogeneous minimally coupled scalar fields as a matter source. Classes of the models integrable at classical as well as quantum levels are found. These classes are equivalent to each other. Quantum wormhole solutions are obtained for them and the procedure of the third quantization is performed. An inflationary universe arising from classically forbidden Euclidean region is investigated for a model with a cosmological constant.
We investigate a possibility for construction of the conventional Friedmann cosmology for our obs... more We investigate a possibility for construction of the conventional Friedmann cosmology for our observable Universe if underlying theory is multidimensional Kaluza-Klein model endowed with a perfect fluid. We show that effective Friedmann model obtained by dynamical compactification of the multidimensional one is faced with too strong variations of the fundamental "constants". From other hand, models with stable compactification of the internal space are free from this problem and also result in conventional 4D cosmological behavior for our Universe. We prove a no-go theorem which shows that stable compactification of the internal spaces is possible only if equations of state in the external and internal spaces are properly adjusted to each other. With a proper choice of parameters (fine tuning), effective cosmological constant in this model provides the late time acceleration of the Universe. The fine tuning problem is resolved in the case of the internal spaces in the form of orbifolds with branes in fixed points. However, in this case the effective potential is too flat (mass gravexcitons is very small) to provide necessary constancy of the effective fundamental "constants".
We consider dilatonic brane world models with a non-minimal coupling between a dilaton and usual ... more We consider dilatonic brane world models with a non-minimal coupling between a dilaton and usual matter on a brane. We demonstrate that variation of the fundamental constants on the brane due to such interaction leads to strong restrictions on parameters of models. In particular, the experimental bounds on variation of the fine structure constant rule out non-minimal dilatonic models with a Liouville-type coupling potential
It is shown that most important closed Robertson-Walkcr-Friedmann universe models with a perfect ... more It is shown that most important closed Robertson-Walkcr-Friedmann universe models with a perfect fluid have an anaI~uc continuation into the Euclidean region with a wormhole-iype topology. Permanent address: Department of Physics, Universiiy ot~the effective gravitational constant problem in the Odessa, 2 Petra Velikogo, 270100 Odessa. Ukraine. model with a conformal scalar field. 1 76 Elsevier Science Publishers B.V. Volume 176, number 3,4 PHYSICS LETTERS A
We consider Kaluza-Klein models with background matter in the form of a multicomponent perfect fl... more We consider Kaluza-Klein models with background matter in the form of a multicomponent perfect fluid. This matter provides spherical compactification of the internal space with an arbitrary number of dimensions. The gravitating source has the dust-like equation of state in the external/our space and an arbitrary equation of state (with the parameter \Omega) in the internal space. In the single-component case, tension (\Omega=-1/2) is the necessary condition to satisfy both the gravitational tests in the solar system and the thermodynamical observations. In the multicomponent case, we propose two models satisfying both of these observations. One of them also requires tension \Omega=-1/2, but the second one is of special interest because is free of tension, i.e. \Omega=0. To get this result, we need to impose certain conditions.
In the six-dimensional Kaluza-Klein model with the multidimensional cosmological constant \Lambda... more In the six-dimensional Kaluza-Klein model with the multidimensional cosmological constant \Lambda_6, we obtain the black brane with spherical compactification of the internal space. The matter source for this exact solution consists of two parts. First, it is a fine-tuned homogeneous perfect fluid which provides spherical compactification of the internal space. Second, it is a gravitating massive body with the dustlike equation of state in the external space and tension \hat p_1=-(1/2)\hat\varepsilon in the internal space. This solution exists both in the presence and absence of \Lambda_6. In the weak-field approximation, we also get solutions of the linearized Einstein equations for the model with spherical compactification. Here, the gravitating matter source has the dustlike equation of state in the external space and an arbitrary equation of state \hat p_1=\Omega \hat\varepsilon in the internal space. In the case \Lambda_6>0 and \Omega\neq -1/2, these approximate solutions tend asymptotically to the weak-field limit of the exact black brane solution. Both the exact and asymptotic black branes satisfy the gravitational experiments at the same level of accuracy as general relativity.
In Kaluza-Klein model with toroidal extra dimensions, we obtain the metric coefficients in a weak... more In Kaluza-Klein model with toroidal extra dimensions, we obtain the metric coefficients in a weak-field approximation for delta-shaped matter sources. These metric coefficients are applied to calculate the formulas for frequency shift, perihelion shift, deflection of light and parameterized post-Newtonian (PPN) parameters. In the leading order of approximation, the formula for frequency shift coincides with well-known general relativity expression. However, for perihelion shift, light deflection and PPN parameter \gamma we obtain formulas D\pi r_g/[(D-2)a(1-e^2)], (D-1)r_g/[(D-2)\rho] and 1/(D-2) respectively, where D is a total number of spatial dimensions. These expressions demonstrate good agreement with experimental data only in the case of ordinary three-dimensional (D=3) space. This result does not depend on the size of the extra dimensions. Therefore, in the considered multidimensional Kaluza-Klein models the point-like masses cannot produce the gravitational field which corresponds to the classical gravitational tests.
In Kaluza-Klein models with an arbitrary number of toroidal internal spaces, we investigate solit... more In Kaluza-Klein models with an arbitrary number of toroidal internal spaces, we investigate soliton solutions which describe the gravitational field of a massive compact object. We single out the physically interesting solution corresponding to a point-like mass. For the general solution we obtain equations of state in the external and internal spaces. These equations demonstrate that the point-like mass soliton has dust-like equations of state in all spaces. We also obtain the PPN parameters, which give the possibility to obtain the formulas for perihelion shift, deflection of light and time delay of radar echoes. Additionally, the gravitational experiments lead to a strong restriction on the parameter of the model: \tau = -(2.1\pm 2.3)\times 10^{-5}. The point-like mass solution contradicts this restriction. The condition \tau=0 satisfies the experimental limitation and defines a new class of solutions which are indistinguishable from general relativity. We call such solutions latent solitons. Black strings and black branes belong to this class. Moreover, the condition of stability of the internal spaces singles out black strings/branes from the latent solitons and leads uniquely to the black string/brane equations of state p_i=-\epsilon/2, in the internal spaces and to the number of the external dimensions d_0=3. The investigation of multidimensional static spherically symmetric perfect fluid with dust-like equation of state in the external space confirms the above results.
In Kaluza-Klein models, we investigate soliton solutions of Einstein equation. We obtain the form... more In Kaluza-Klein models, we investigate soliton solutions of Einstein equation. We obtain the formulas for perihelion shift, deflection of light, time delay of radar echoes and PPN parameters. We find that the solitonic parameter k should be very big: |k|\geq 2.3\times10^4. We define a soliton solution which corresponds to a point-like mass source. In this case the soliton parameter k=2, which is clearly contrary to this restriction. Similar problem with the observations takes place for static spherically symmetric perfect fluid with the dust-like equation of state in all dimensions. The common for both of these models is the same equations of state in our three dimensions and in the extra dimensions. All dimensions are treated at equal footing. To be in agreement with observations, it is necessary to break the symmetry between the external/our and internal spaces. It takes place for black strings which are particular examples of solitons with k\to \infty. For such k, black strings are in concordance with the observations. Moreover, we show that they are the only solitons which are at the same level of agreement with the observations as in general relativity. Black strings can be treated as perfect fluid with dust-like equation of state p_0=0 in the external/our space and very specific equation of state p_1=-(1/2)\epsilon in the internal space. The latter equation is due to negative tension in the extra dimension. We also demonstrate that dimension 3 for the external space is a special one. Only in this case we get the latter equation of state. We show that the black string equations of state satisfy the necessary condition of the internal space stabilization. Therefore, black strings are good candidates for a viable model of astrophysical objects (e.g., Sun) if we can provide a satisfactory explanation of negative tension for particles constituting these objects.
It is found the exact solution of the Poisson equation for the multidimensional space with topolo... more It is found the exact solution of the Poisson equation for the multidimensional space with topology M_{3+d}=\mathbb{R}^3\times T^d. This solution describes smooth transition from the newtonian behavior 1/r_3 for distances bigger than periods of tori (the extra dimension sizes) to multidimensional behavior 1/r^{1+d}_{3+d} in opposite limit. In the case of one extra dimension d=1, the gravitational potential is expressed via compact and elegant formula. It is shown that the corrections to the gravitational constant in the Cavendish-type experiment can be within the measurement accuracy of Newton's gravitational constant G_N. It is proposed models where the test masses are smeared over some (or all) extra dimensions. In 10-dimensional spacetime with 3 smeared extra dimensions, it is shown that the size of 3 rest extra dimensions can be enlarged up to submillimeter for the case of 1TeV fundamental Planck scale M_{Pl(10)}. In the models where all extra dimensions are smeared, the gravitational potential exactly coincides with the newtonian one. Nevertheless, the hierarchy problem can be solved in these models.
A multidimensional cosmological model with space-time consisting of n(n ≥ 2) Ein-stein spaces M i... more A multidimensional cosmological model with space-time consisting of n(n ≥ 2) Ein-stein spaces M i is investigated in the presence of a cosmological constant Λ and a homogeneous minimally coupled scalar field ϕ(t) as a matter source. Classical and quantum wormhole solutions are obtained for Λ < 0 and all M i being Ricci-flat. Classical wormhole solutions are also found for Λ < 0 and only one of the M i being Ricci-flat for the case of spontaneous compactification of the internal dimensions with fine tuning of parameters.
We investigate time dependent solutions (S-brane solutions) for product manifolds consisting of f... more We investigate time dependent solutions (S-brane solutions) for product manifolds consisting of factor spaces where only one of them is non-Ricci-flat. Our model contains a minimally coupled free scalar field as a matter source. We discuss a possibility of generating late-time acceleration of the Universe. The analysis is performed in conformally related Brans-Dicke and Einstein frames. Dynamical behavior of our Universe is described by its scale factor. Since the scale factors of our Universe are described by different variables in both frames, they can have different dynamics. Indeed, we show that with our S-brane ansatz in the Brans-Dicke frame the stages of accelerating expansion exist for all types of the external space (flat, spherical, and hyperbolic). However, applying the same ansatz for the metric in the Einstein frame, we find that a model with flat external space and hyperbolic compactification of the internal space is the only one with the stage of the accelerating expansion. A scalar field can prevent this acceleration. It is shown that the case of hyperbolic external space in the Brans-Dicke frame is the only model which can satisfy experimental bounds for the fine-structure constant variations. We obtain a class of models where a pair of dynamical internal spaces have fixed total volume. This results in a fixed fine-structure constant. However, these models are unstable and external space is nonaccelerating.
A multidimensional cosmological model with space-time consisting of n (n>1) Einstein spaces M_i i... more A multidimensional cosmological model with space-time consisting of n (n>1) Einstein spaces M_i is investigated in the presence of a cosmological constant Lambda and m homogeneous minimally coupled scalar fields as a matter source. Classes of the models integrable at classical as well as quantum levels are found. These classes are equivalent to each other. Quantum wormhole solutions are obtained for them and the procedure of the third quantization is performed. An inflationary universe arising from classically forbidden Euclidean region is investigated for a model with a cosmological constant.
Multidimensional cosmological model with the topology M=RxM_1xM_2x...xM_n where M_i (i=1,... ,n) ... more Multidimensional cosmological model with the topology M=RxM_1xM_2x...xM_n where M_i (i=1,... ,n) undergo a chain splitting into arbitrary number of compact spaces is considered. It is shown that equations of motion can be solved exactly because they depend only on the effective curvatures and dimensions and "forget" about inner topological structure. It is proved that effective cosmological action for the model with n=1 in the case of infinite splitting of the internal space coincides with the tree-level effective action for a bosonic string.
Multidimensional cosmological model with the topology M=RxM_1xM_2x...xM_n where M_i (i=1,... ,n) ... more Multidimensional cosmological model with the topology M=RxM_1xM_2x...xM_n where M_i (i=1,... ,n) undergo a chain splitting into arbitrary number of compact spaces is considered. It is shown that equations of motion can be solved exactly because they depend only on the effective curvatures and dimensions and "forget" about inner topological structure. It is proved that effective cosmological action for the model with n=1 in the case of infinite splitting of the internal space coincides with the tree-level effective action for a bosonic string.
It is shown that a transition from a multidimensional cosmological model with one internal space ... more It is shown that a transition from a multidimensional cosmological model with one internal space (of the dimension d1) to the effective tree-level bosonic string corresponds to an infinite number of the internal dimensions: d1 → ∞.
An open homogenous isotropic Universe is examined, with De Sitter phase at the yearly stage of it... more An open homogenous isotropic Universe is examined, with De Sitter phase at the yearly stage of its evolution. A spontaneous breackdown of the symmetry of the masless self-acting scalar field is occuring for all realistic values of the self-action constant "lambda". The taking into account of the back action of that spontaneously breacked field on the metric lead to avoiding of the initial singularity in Cosmology for "lambda" = 10^-2, ...10^-12 for z>= 10^29, where Z^3 is the Entropy of the Universe at the present moment to the Entropy of Universe at the beggining of the inflationary phase ratio. Bibliography: 4
A multidimensional cosmological model with space-time consisting of n (n ≥ 2) Einstein spaces M i... more A multidimensional cosmological model with space-time consisting of n (n ≥ 2) Einstein spaces M i is investigated in the presence of a cosmological constant Λ and m (m ≥ 1) homogeneous minimally coupled scalar fields as a matter source. Classes of the models integrable at classical as well as quantum levels are found. These classes are equivalent to each other. Quantum wormhole solutions are obtained for them and the procedure of the third quantization is performed. An inflationary universe arising from classically forbidden Euclidean region is investigated for a model with a cosmological constant. *
A multidimensional cosmological model with space-time consisting of n (n>1) Einstein spaces M_i i... more A multidimensional cosmological model with space-time consisting of n (n>1) Einstein spaces M_i is investigated in the presence of a cosmological constant Lambda and m homogeneous minimally coupled scalar fields as a matter source. Classes of the models integrable at classical as well as quantum levels are found. These classes are equivalent to each other. Quantum wormhole solutions are obtained for them and the procedure of the third quantization is performed. An inflationary universe arising from classically forbidden Euclidean region is investigated for a model with a cosmological constant.
We investigate a possibility for construction of the conventional Friedmann cosmology for our obs... more We investigate a possibility for construction of the conventional Friedmann cosmology for our observable Universe if underlying theory is multidimensional Kaluza-Klein model endowed with a perfect fluid. We show that effective Friedmann model obtained by dynamical compactification of the multidimensional one is faced with too strong variations of the fundamental "constants". From other hand, models with stable compactification of the internal space are free from this problem and also result in conventional 4D cosmological behavior for our Universe. We prove a no-go theorem which shows that stable compactification of the internal spaces is possible only if equations of state in the external and internal spaces are properly adjusted to each other. With a proper choice of parameters (fine tuning), effective cosmological constant in this model provides the late time acceleration of the Universe. The fine tuning problem is resolved in the case of the internal spaces in the form of orbifolds with branes in fixed points. However, in this case the effective potential is too flat (mass gravexcitons is very small) to provide necessary constancy of the effective fundamental "constants".
We consider dilatonic brane world models with a non-minimal coupling between a dilaton and usual ... more We consider dilatonic brane world models with a non-minimal coupling between a dilaton and usual matter on a brane. We demonstrate that variation of the fundamental constants on the brane due to such interaction leads to strong restrictions on parameters of models. In particular, the experimental bounds on variation of the fine structure constant rule out non-minimal dilatonic models with a Liouville-type coupling potential
It is shown that most important closed Robertson-Walkcr-Friedmann universe models with a perfect ... more It is shown that most important closed Robertson-Walkcr-Friedmann universe models with a perfect fluid have an anaI~uc continuation into the Euclidean region with a wormhole-iype topology. Permanent address: Department of Physics, Universiiy ot~the effective gravitational constant problem in the Odessa, 2 Petra Velikogo, 270100 Odessa. Ukraine. model with a conformal scalar field. 1 76 Elsevier Science Publishers B.V. Volume 176, number 3,4 PHYSICS LETTERS A
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