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Papers by Andrew Billyard
Gravitation & Cosmology, 1998
... 3 ˙H 2 H2 + 3k H2 + 6 ˙H ˙L HL + ˙L 2 L2 + K L2 = Λ+ 2α L4 (21d) where α = 2π (6) G/ e 2 . Cr... more ... 3 ˙H 2 H2 + 3k H2 + 6 ˙H ˙L HL + ˙L 2 L2 + K L2 = Λ+ 2α L4 (21d) where α = 2π (6) G/ e 2 . Cremmer and Scherk [14, 24] presented a six-dimensional Yang-Mills solution simi-lar to the 't Hooft magnetic monopole [25, 26] where L = L0 a constant and k = 0 (see also [27]). ...
We examine generalizations of the five-dimensional canonical metric by including a dependence of ... more We examine generalizations of the five-dimensional canonical metric by including a dependence of the extra coordinate in the four-dimensional metric. We discuss a more appropriate way to interpret the four-dimensional energy-momentum tensor induced from the five-dimensional space-time and show it can lead to quite different physical situations depending on the interpretation chosen. Furthermore, we show that the assumption of five-dimensional
A complete qualitative study of the dynamics of string cosmologies is presented for the class of ... more A complete qualitative study of the dynamics of string cosmologies is presented for the class of isotopic curvature universes. These models are of Bianchi types I, V and IX and reduce to the general class of Friedmann-Robertson-Walker universes in the limit of vanishing shear isotropy. A non-trivial 2-form potential and cosmological constant terms are included in the system. In general, the 2-form potential and spatial curvature terms are only dynamically important at intermediate stages of the evolution. In many of the models, the cosmological constant is important asymptotically and anisotropy becomes dynamically negligible. There also exist bouncing cosmologies.
We examine generalizations of the five-dimensional canonical metric by including a dependence of ... more We examine generalizations of the five-dimensional canonical metric by including a dependence of the extra coordinate in the four-dimensional metric. We discuss a more appropriate way to interpret the four-dimensional energy-momentum tensor induced from the five-dimensional space-time and show it can lead to quite different physical situations depending on the interpretation chosen. Furthermore, we show that the assumption of five-dimensional null trajectories in Kaluza-Klein gravity can correspond to either four-dimensional massive or null trajectories when the path parameterization is chosen properly. Retaining the extra-coordinate dependence in the metric, we show the possibility of a cosmological variation in the rest masses of particles and a consequent departure from four-dimensional geodesic motion by a geometric force. In the examples given, we show that at late times it is possible for particles traveling along 5D null geodesics to be in a frame consistent with the induced matter scenario.
Int. J. Mod. Phys. D, 1995
The augmentation of general relativity's spacetime by one or more dimensions is described... more The augmentation of general relativity's spacetime by one or more dimensions is described by Kaluza-Klein theory and is within testable limits. Should an extra dimension be observable and significant, it would be beneficial to know how physical properties would differ from ``conventional'' relativity. In examining the class of five-dimensional solutions analogous to the four-dimensional Schwarzschild solution, we examine where the
Physical Review D, 1998
We study the qualitative properties of cosmological models in scalar-tensor theories of gravity b... more We study the qualitative properties of cosmological models in scalar-tensor theories of gravity by exploiting the formal equivalence of these theories with general relativity minimally coupled to a scalar field under a conformal transformation and field redefinition. In particular, we investigate the asymptotic behavior of spatially homogeneous cosmological models in a class of scalar-tensor theories which are conformally equivalent to general relativistic Bianchi cosmologies with a scalar field and an exponential potential whose qualitative features have been studied previously. Particular attention is focused on those scalar-tensor theory cosmological models, which are shown to be self-similar, that correspond to general relativistic models that play an important role in describing the asymptotic behavior of more general models ͑e.g., those cosmological models that act as early-time and late-time attractors͒.
Information & Security: An International Journal, 2009
Physical Review D, 2000
A complete global analysis of spatially flat, four-dimensional cosmologies derived from the type ... more A complete global analysis of spatially flat, four-dimensional cosmologies derived from the type IIA string and M-theory effective actions is presented. A non-trivial Ramond-Ramond sector is included. The governing equations are written as a dynamical system. Asymptotically, the form fields are dynamically negligible, but play a crucial role in determining the possible intermediate behavior of the solutions ͑i.e., the nature of the equilibrium points͒. The only past-attracting solution ͑source in the system͒ may be interpreted in the elevendimensional setting in terms of flat space. This source is unstable to the introduction of spatial curvature.
Physical Review D, 1999
A qualitative analysis is presented for spatially flat, isotropic and homogeneous cosmologies der... more A qualitative analysis is presented for spatially flat, isotropic and homogeneous cosmologies derived from the string effective action when the combined effects of a dilaton, modulus, two-form potential and central charge deficit are included. The latter has significant effects on the qualitative dynamics. The analysis is also directly applicable to the anisotropic Bianchi type I cosmology. ͓S0556-2821͑99͒01112-1͔
Physical Review D, 1998
We study the stability of cosmological scaling solutions within the class of spatially homogeneou... more We study the stability of cosmological scaling solutions within the class of spatially homogeneous cosmological models with a perfect fluid subject to the equation of state p ␥ ϭ(␥Ϫ1) ␥ ͑where ␥ is a constant satisfying 0Ͻ␥Ͻ2) and a scalar field with an exponential potential. The scaling solutions, which are spatially flat isotropic models in which the scalar field energy density tracks that of the perfect fluid, are of physical interest. For example, in these models a significant fraction of the current energy density of the Universe may be contained in the scalar field whose dynamical effects mimic cold dark matter. It is known that the scaling solutions are late-time attractors ͑i.e., stable͒ in the subclass of flat isotropic models. We find that the scaling solutions are stable ͑to shear and curvature perturbations͒ in generic anisotropic Bianchi models when ␥ Ͻ2/3. However, when ␥Ͼ2/3, and particularly for realistic matter with ␥у1, the scaling solutions are unstable; essentially they are unstable to curvature perturbations, although they are stable to shear perturbations. We briefly discuss the physical consequences of these results. ͓S0556-2821͑98͒10920-7͔
Physical Review D, 1996
We derive a class of solutions of the field equations of five-dimensional general relativity that... more We derive a class of solutions of the field equations of five-dimensional general relativity that is static and spherically symmetric in ordinary three-dimensional space. In the induced-matter picture, where the extra dimension is responsible for matter in four-dimensional spacetime, the solutions represent centrally condensed clouds with density profiles similar to those of clusters of galaxies. This class of solutions could
Physical Review D, 2000
We investigate spatially flat isotropic cosmological models which contain a scalar field with an ... more We investigate spatially flat isotropic cosmological models which contain a scalar field with an exponential potential and a perfect fluid with a linear equation of state. We include an interaction term, through which the energy of the scalar field is transferred to the matter fields, consistent with a term that arises from scalar-tensor theory under a conformal transformation and field redefinition. The governing ordinary differential equations reduce to a dynamical system when appropriate normalized variables are defined. We analyze the dynamical system and find that the interaction term can significantly affect the qualitative behavior of the models. The late-time behavior of these models may be of cosmological interest. In particular, for a specific range of values for the model parameters there are late-time attracting solutions, corresponding to a novel attracting equilibrium point, which are inflationary and in which the scalar field's energy-density remains a fixed fraction of the matter field's energy density. These scalar field models may be of interest as late-time cosmologies, particularly in view of the recent observations of the current accelerated cosmic expansion. For appropriate values of the interaction coupling parameter, this equilibrium point is an attracting focus, and hence as inflating solutions approach this late-time attractor the scalar field oscillates. Hence these models may also be of importance in the study of inflation in the early universe. PACS number͑s͒: 98.80.Cq pϭ͑␥Ϫ1 ͒, ͑2͒
Modern Physics Letters A, 1997
Modern Physics Letters A, 1997
... 19. T. Chiba and J. Soda, gr-qc/9603056. 20. YM Cho and DH Park, J. Math. Phys. 31, 695 (1996... more ... 19. T. Chiba and J. Soda, gr-qc/9603056. 20. YM Cho and DH Park, J. Math. Phys. 31, 695 (1996). 21. ... Lett. 70, 9 (1993). 23. AA Coley, Ap. J. 427, 585 (1994). 24. AA Coley, to appear in Class. ... 70,2220 (1995). 27. T. Damour and K. Nordtvedt, Phys. Rev. D48, 3436 (1993). 28. ...
Journal of Mathematical Physics, 1999
A qualitative analysis is presented for a class of homogeneous cosmologies derived from the strin... more A qualitative analysis is presented for a class of homogeneous cosmologies derived from the string effective action when a cosmological constant is present in the matter sector of the theory. Such a term has significant effects on the qualitative dynamics. For example, models exist which undergo a series of oscillations between expanding and contracting phases due to the existence of a heteroclinic cycle in the phase space. Particular analytical solutions corresponding to the equilibrium points are also found.
Gravitation & Cosmology, 1998
... 3 ˙H 2 H2 + 3k H2 + 6 ˙H ˙L HL + ˙L 2 L2 + K L2 = Λ+ 2α L4 (21d) where α = 2π (6) G/ e 2 . Cr... more ... 3 ˙H 2 H2 + 3k H2 + 6 ˙H ˙L HL + ˙L 2 L2 + K L2 = Λ+ 2α L4 (21d) where α = 2π (6) G/ e 2 . Cremmer and Scherk [14, 24] presented a six-dimensional Yang-Mills solution simi-lar to the 't Hooft magnetic monopole [25, 26] where L = L0 a constant and k = 0 (see also [27]). ...
We examine generalizations of the five-dimensional canonical metric by including a dependence of ... more We examine generalizations of the five-dimensional canonical metric by including a dependence of the extra coordinate in the four-dimensional metric. We discuss a more appropriate way to interpret the four-dimensional energy-momentum tensor induced from the five-dimensional space-time and show it can lead to quite different physical situations depending on the interpretation chosen. Furthermore, we show that the assumption of five-dimensional
A complete qualitative study of the dynamics of string cosmologies is presented for the class of ... more A complete qualitative study of the dynamics of string cosmologies is presented for the class of isotopic curvature universes. These models are of Bianchi types I, V and IX and reduce to the general class of Friedmann-Robertson-Walker universes in the limit of vanishing shear isotropy. A non-trivial 2-form potential and cosmological constant terms are included in the system. In general, the 2-form potential and spatial curvature terms are only dynamically important at intermediate stages of the evolution. In many of the models, the cosmological constant is important asymptotically and anisotropy becomes dynamically negligible. There also exist bouncing cosmologies.
We examine generalizations of the five-dimensional canonical metric by including a dependence of ... more We examine generalizations of the five-dimensional canonical metric by including a dependence of the extra coordinate in the four-dimensional metric. We discuss a more appropriate way to interpret the four-dimensional energy-momentum tensor induced from the five-dimensional space-time and show it can lead to quite different physical situations depending on the interpretation chosen. Furthermore, we show that the assumption of five-dimensional null trajectories in Kaluza-Klein gravity can correspond to either four-dimensional massive or null trajectories when the path parameterization is chosen properly. Retaining the extra-coordinate dependence in the metric, we show the possibility of a cosmological variation in the rest masses of particles and a consequent departure from four-dimensional geodesic motion by a geometric force. In the examples given, we show that at late times it is possible for particles traveling along 5D null geodesics to be in a frame consistent with the induced matter scenario.
Int. J. Mod. Phys. D, 1995
The augmentation of general relativity's spacetime by one or more dimensions is described... more The augmentation of general relativity's spacetime by one or more dimensions is described by Kaluza-Klein theory and is within testable limits. Should an extra dimension be observable and significant, it would be beneficial to know how physical properties would differ from ``conventional'' relativity. In examining the class of five-dimensional solutions analogous to the four-dimensional Schwarzschild solution, we examine where the
Physical Review D, 1998
We study the qualitative properties of cosmological models in scalar-tensor theories of gravity b... more We study the qualitative properties of cosmological models in scalar-tensor theories of gravity by exploiting the formal equivalence of these theories with general relativity minimally coupled to a scalar field under a conformal transformation and field redefinition. In particular, we investigate the asymptotic behavior of spatially homogeneous cosmological models in a class of scalar-tensor theories which are conformally equivalent to general relativistic Bianchi cosmologies with a scalar field and an exponential potential whose qualitative features have been studied previously. Particular attention is focused on those scalar-tensor theory cosmological models, which are shown to be self-similar, that correspond to general relativistic models that play an important role in describing the asymptotic behavior of more general models ͑e.g., those cosmological models that act as early-time and late-time attractors͒.
Information & Security: An International Journal, 2009
Physical Review D, 2000
A complete global analysis of spatially flat, four-dimensional cosmologies derived from the type ... more A complete global analysis of spatially flat, four-dimensional cosmologies derived from the type IIA string and M-theory effective actions is presented. A non-trivial Ramond-Ramond sector is included. The governing equations are written as a dynamical system. Asymptotically, the form fields are dynamically negligible, but play a crucial role in determining the possible intermediate behavior of the solutions ͑i.e., the nature of the equilibrium points͒. The only past-attracting solution ͑source in the system͒ may be interpreted in the elevendimensional setting in terms of flat space. This source is unstable to the introduction of spatial curvature.
Physical Review D, 1999
A qualitative analysis is presented for spatially flat, isotropic and homogeneous cosmologies der... more A qualitative analysis is presented for spatially flat, isotropic and homogeneous cosmologies derived from the string effective action when the combined effects of a dilaton, modulus, two-form potential and central charge deficit are included. The latter has significant effects on the qualitative dynamics. The analysis is also directly applicable to the anisotropic Bianchi type I cosmology. ͓S0556-2821͑99͒01112-1͔
Physical Review D, 1998
We study the stability of cosmological scaling solutions within the class of spatially homogeneou... more We study the stability of cosmological scaling solutions within the class of spatially homogeneous cosmological models with a perfect fluid subject to the equation of state p ␥ ϭ(␥Ϫ1) ␥ ͑where ␥ is a constant satisfying 0Ͻ␥Ͻ2) and a scalar field with an exponential potential. The scaling solutions, which are spatially flat isotropic models in which the scalar field energy density tracks that of the perfect fluid, are of physical interest. For example, in these models a significant fraction of the current energy density of the Universe may be contained in the scalar field whose dynamical effects mimic cold dark matter. It is known that the scaling solutions are late-time attractors ͑i.e., stable͒ in the subclass of flat isotropic models. We find that the scaling solutions are stable ͑to shear and curvature perturbations͒ in generic anisotropic Bianchi models when ␥ Ͻ2/3. However, when ␥Ͼ2/3, and particularly for realistic matter with ␥у1, the scaling solutions are unstable; essentially they are unstable to curvature perturbations, although they are stable to shear perturbations. We briefly discuss the physical consequences of these results. ͓S0556-2821͑98͒10920-7͔
Physical Review D, 1996
We derive a class of solutions of the field equations of five-dimensional general relativity that... more We derive a class of solutions of the field equations of five-dimensional general relativity that is static and spherically symmetric in ordinary three-dimensional space. In the induced-matter picture, where the extra dimension is responsible for matter in four-dimensional spacetime, the solutions represent centrally condensed clouds with density profiles similar to those of clusters of galaxies. This class of solutions could
Physical Review D, 2000
We investigate spatially flat isotropic cosmological models which contain a scalar field with an ... more We investigate spatially flat isotropic cosmological models which contain a scalar field with an exponential potential and a perfect fluid with a linear equation of state. We include an interaction term, through which the energy of the scalar field is transferred to the matter fields, consistent with a term that arises from scalar-tensor theory under a conformal transformation and field redefinition. The governing ordinary differential equations reduce to a dynamical system when appropriate normalized variables are defined. We analyze the dynamical system and find that the interaction term can significantly affect the qualitative behavior of the models. The late-time behavior of these models may be of cosmological interest. In particular, for a specific range of values for the model parameters there are late-time attracting solutions, corresponding to a novel attracting equilibrium point, which are inflationary and in which the scalar field's energy-density remains a fixed fraction of the matter field's energy density. These scalar field models may be of interest as late-time cosmologies, particularly in view of the recent observations of the current accelerated cosmic expansion. For appropriate values of the interaction coupling parameter, this equilibrium point is an attracting focus, and hence as inflating solutions approach this late-time attractor the scalar field oscillates. Hence these models may also be of importance in the study of inflation in the early universe. PACS number͑s͒: 98.80.Cq pϭ͑␥Ϫ1 ͒, ͑2͒
Modern Physics Letters A, 1997
Modern Physics Letters A, 1997
... 19. T. Chiba and J. Soda, gr-qc/9603056. 20. YM Cho and DH Park, J. Math. Phys. 31, 695 (1996... more ... 19. T. Chiba and J. Soda, gr-qc/9603056. 20. YM Cho and DH Park, J. Math. Phys. 31, 695 (1996). 21. ... Lett. 70, 9 (1993). 23. AA Coley, Ap. J. 427, 585 (1994). 24. AA Coley, to appear in Class. ... 70,2220 (1995). 27. T. Damour and K. Nordtvedt, Phys. Rev. D48, 3436 (1993). 28. ...
Journal of Mathematical Physics, 1999
A qualitative analysis is presented for a class of homogeneous cosmologies derived from the strin... more A qualitative analysis is presented for a class of homogeneous cosmologies derived from the string effective action when a cosmological constant is present in the matter sector of the theory. Such a term has significant effects on the qualitative dynamics. For example, models exist which undergo a series of oscillations between expanding and contracting phases due to the existence of a heteroclinic cycle in the phase space. Particular analytical solutions corresponding to the equilibrium points are also found.