Brane cosmology and motion of test particles in five-dimensional warped product spacetimes

In the “braneworld scenario” ordinary standard model matter and non-gravitational fields are confined by some trapping mechanism to the 4-dimensional universe constituting the D3-branes which are embedded in a (4 + n)-dimensional manifold referred to as the ‘bulk’ (n being the number of extra dimensions). The notion of particle confinement is necessary for theories with non-compact extra dimensions, otherwise, the particles would escape from our 4-dimensional world along unseen directions. In this paper, we have considered a five-dimensional warped product space-time having an exponential warping function which depends both on time as well as on the extra coordinates and a non-compact fifth dimension. Assuming that the lapse function may either be a constant or a function of both time and of the extra coordinates, we have studied the nature of the geodesics of test particles and photons and have analyzed the conditions of stability in this geometrical framework. We have also discussed the possible cosmology of the corresponding (3 + 1)-dimensional hypersurfaces.     

The cosmological ‘constant’ and quantization in five dimensions

Campbell?s theorem ensures that all vacuum space-times in general relativity can be embedded in five dimensions, with the 4D scalar curvature expressed as an effective cosmological ‘constant’ Λ which depends on the extra coordinate. This Λ-landscape can be used to give insight to certain physical phenomena, such as the big bang and quantized particles.     

Cosmological baryon-number domain structure and the first order phase transition of a vacuum

If CP-nonconservation arises from spontaneous symmetry breaking in the very early universe, the universe will have a domain structure of baryon number. We propose a model of the early universe in which domains are stretched exponentially and the radius of the domains is much greater than that of the horizon of the standard big bang model, provided that the grand unified theory undergoes a first order phase transition. If the size of the stretched domains is sufficiently big to avoid pair annihilations of baryon and antibaryon domains, the difficulties of the baryon symmetric universe may be removed.     

Instability of the Randall-Sundrum Model and Exact Bulk Solutions

Five dimensional geodesic equation is used to study the gravitational force acted on a test particle in the bulk of the Randall-Sundrum two-brane model. This force could be interpreted as the gravitational attraction from matters on the two branes and may cause the model to be unstable. By analogy with star models in astrophysics, a fluid RS model is proposed in which the bulk is filled with a fluid and this fluid has an anisotropic pressure to balance the gravity from the two branes. Thus a class of exact bulk solutions is obtained which shows that any 4D Einstein solution with a perfect fluid source can be embedded in y = constant hypersurfaces in the bulk to form an equilibrium state of the brane model. By requiring a 4D effective curvature to have a minimum, the compactification size of the extra dimension is discussed.     

Entropy of anisotropic universe and fractional branes

We obtain the entropy of a homogeneous anisotropic universe applicable, by assumption, to the fractional branes in the universe in the model of Chowdhury and Mathur. The entropy for the 3 or 4 charge fractional branes thus obtained is not of the expected form or E ². One way the expected form is realised is if p → ρ for the transverse directions and if the compact directions remain constant in size. These conditions are likely to be enforced by brane decay and annihilation, and by the S, T, U dualities. T duality is also likely to exclude high entropic cases, found in the examples, which arise due to the compact space contracting to zero size. Then the 4 charge fractional branes may indeed provide a detailed realisation of the maximum entropic principle we proposed recently to determine the number (3 + 1) of large spacetime dimensions.     

Principle of limitation of physical quantities and cyclic universe

A close study of Heisenberg uncertainty principles reveals many significant facts, and all four major physical quantities, energy, time, momentum and length, have both lower and upper limits. Now, many questions come up. What are these limits? Some answers may lead to the understanding of the development of our universe. What is the shortest limit of time? At the beginning of big bang, there exists a tremendously short time, the Planck time. This may be just the shortest time limit in our universe. The longest time limit might be the lifetime of our universe. The longest length might be the final diameter of our expanding universe. All these lead to a finite universe. Two more coupling formulae are formed for the other two pairs of physical quantities, mass and speed, thermal energy and temperature. These four physical quantities must also have limits. We already knew that speed has upper limit and temperature has lower limit. By these two formulae, Planck and Einstein equations are derived directly. Since most other physical quantities are somewhat related to these major physical quantities, it seems that there exists a principle of limitation of physical quantities. A quantitative sketch of big bang is described. It also shows that our universe will contract back to another big bang. The principle of limitation opens up some fields of investigation. It may bring nature back to the harmony and determined world described by classical physics.     

Everything is entangled

We show that big bang cosmology implies a high degree of entanglement of particles in the universe. In fact, a typical particle is entangled with many particles far outside our horizon. However, the entanglement is spread nearly uniformly so that two randomly chosen particles are unlikely to be directly entangled with each other – the reduced density matrix describing any pair is likely to be separable.     

Infrared hierarchy,thermal brane inflation and superstrings as superheavy dark matter

In theories with TeV scale quantum gravity the standard model particles live on a brane propagating in large extra dimensions. Branes may be stabilized at large (sub-millimeter) distances from each other, either due to weak Van der Waals type interactions, or due to an infrared analog of Witten's inverse hierarchy scenario. In particular, this infrared stabilization may be responsible for a large size of extra dimensions. In either case, thermal effects can drive a brief period of the late inflation necessary to avoid the problems with high reheating temperature and the stable unwanted relics. The main reason is that the branes which repel each other at zero temperature can be temporarily glued together by thermal effects. It is crucial that the temperature needed to stabilize branes on top of each other can be much smaller than the potential energy of the bound-state, which drives inflation. After 10–15 e-foldings bound-states cool below the critical temperature and decay ending inflation. The parallel brane worlds get separated at this stage and superstrings (of a sub-millimeter size) get stretched between them. These strings can have the right density in order to serve as a superheavy dark matter.     

Superweakly interacting massive particles

We investigate a new class of dark matter: superweakly interacting massive particles (super-WIMPs). As with conventional WIMPs, super-WIMPs appear in well motivated particle theories with naturally the correct relic density. In contrast to WIMPs, however, super-WIMPs are impossible to detect in all conventional dark matter searches. We consider the concrete examples of gravitino and graviton cold dark matter in models with supersymmetry and universal extra dimensions, respectively, and show that super-WIMP dark matter satisfies stringent constraints from big bang nucleosynthesis and the cosmic microwave background.     

Cosmological constraints on bulk neutrinos

Recent models invoking extra space-like dimensions inhabited by (bulk) neutrinos are shown to have significant cosmological effects if the size of the largest extra dimension is R greater, similar 1 fm. We consider effects on cosmic microwave background anisotropies, big bang nucleosynthesis, deuterium and 6Li photoproduction, diffuse photon backgrounds, and structure formation. The resulting constraints can be stronger than either bulk graviton overproduction constraints or laboratory constraints.     

General relativity with a background metric

An attempt is made to remove singularities arising in general relativity by modifying it so as to take into account the existence of a fundamental rest frame in the universe. This is done by introducing a background metric γ_μν (in addition to g_μν) describing a spacetime of constant curvature with positive spatial curvature. The additional terms in the field equations are negligible for the solar system but important for intense fields. Cosmological models are obtained without singular states but simulating the “big bang.” The field of a particle differs from the Schwarzschild field only very close to, and inside, the Schwarzschild sphere. The interior of this sphere is unphysical and impenetrable. A star undergoing gravitational collapse reaches a state in which it fills the Schwarzschild sphere with uniform density (and pressure) and has the geometry of a closed Einstein universe. Any charge present is on the surface of the sphere. Elementary particles may have similar structures.     

The Effect of Spatial Curvature in Scalar-Tensor Theory

We investigate the effect of the spatial curvature in extra six dimensions of ten dimensional scalar-tensor theory. As a scalar-tensor theory both string theory effective action and Brans-Dicke type action are considered. For Brans-Dicke type action with positive spatial curvature (k=1) we obtain accelerating expansion of the spacetime for specific value of the Brans-Dicke parameter ω. The value, however, is negative and far from the present universe which requires big number.     

Quantum Oscillations Can Prevent the Big Bang Singularity in an Einstein-Dirac Cosmology

We consider a spatially homogeneous and isotropic system of Dirac particles coupled to classical gravity. The dust and radiation dominated closed Friedmann-Robertson-Walker space-times are recovered as limiting cases. We find a mechanism where quantum oscillations of the Dirac wave functions can prevent the formation of the big bang or big crunch singularity. Thus before the big crunch, the collapse of the universe is stopped by quantum effects and reversed to an expansion, so that the universe opens up entering a new era of classical behavior. Numerical examples of such space-times are given, and the dependence on various parameters is discussed. Generically, one has a collapse after a finite number of cycles. By fine-tuning the parameters we construct an example of a space-time which satisfies the dominant energy condition and is time-periodic, thus running through an infinite number of contraction and expansion cycles.     

The big bang is not needed

Recent computer simulations indicate that a system ofn gravitating masses breaks up, even when the total energy is negative. As a result, almost any initial phase-space distribution results in a universe that eventually expands under the Hubble law. Hence Hubble expansion implies little regarding an initial cosmic state. Especially it does not imply the singularly dense superpositioned state used in the big bang model.     

The universe dynamics from topological considerations

We explore the possibility that the dynamics of the universe can be reproduced choosing appropriately the initial global topology of the Universe. In this work we start with two concentric spherical three-dimensional branes S ³, with radius a ₁ < a ₂ immersed in a five-dimensional space-time. The novel feature of this model is that in the interior brane there exist only spin-zero fundamental fields (scalar fields), while in the exterior one there exist only spin-one fundamental interactions. As usual, the bulk of the universe is dominated by gravitational interactions. In this model, like in the Ekpyrotic one, the Big Bang is consequence of the collision of the branes and causes the existence of the particles predicted by the standard model in the exterior brane (our universe). The scalar fields on the interior brane interact with the spin-one fields on the exterior one only through gravitation, they induce the effect of Scalar Field Dark Matter with an ultra-light mass on the exterior one. We discuss two different regimes where the energy density and the brane tension are compared, with the aim to obtain the observed dynamics of the universe after the collision of the branes.     

Higgs boson cosmology

The discovery of the Standard Model Higgs boson opens up a range of speculative cosmological scenarios, from the formation of structure in the early universe immediately after the big bang, to relics from the electroweak phase transition one nanosecond after the big bang, on to the end of the present-day universe through vacuum decay. Higgs physics is wide ranging, and gives an impetus to go beyond the Standard Models of particle physics and cosmology to explore the physics of ultra-high energies and quantum gravity.     

Vacuum cosmological solution in a 6D universe

A simple vacuum cosmological solution that is a function ofct, Gm/c ² andeG ^1/2/C² is obtained in the 6D space-time-mass-charge universe which is proposed by Wesson [1] with the introduction of the sixth coordinate of charge in order to obtain a unified theory of gravity and electromagnetism along the line of his original 5D space-time-mass universe [2]. It reduces to a similar solution to that of the radiation era in the 4D FRW universe through the compactifications of the extra dimensions. The trajectory of a test particle in the 6D universe is also studied by using the solution.     

Negative mass in general relativity

Mechanics is considered in a universe containing negative mass. Demanding (i) conservation of momentum, (ii) principle of equivalence, (iii) no runaway motions, (iv) no Schwarzschild black holes, and (v) the inertial and active gravitational masses of a body shall have the same sign, we find thatall mass must be negative. Some properties of such a universe are investigated. We show that a neutral spherical body of arbitrarily small size is possible, and observers external to it can communicate with each other by light rays without horizon problems. There are no cosmological models with a power-law big bang, and there is an abundance of nonsingular models. Like electric charges would attract each other, and unlike ones would repel. This could produce stars and galaxies held together by charge and not gravity. The investigation does not suggest any reason why mass in the real universe should be positive.     

Big bang as the collapse of an ordered spin system

The entropy of a spin system interacting with a free particle representing the inertia of the universe in the early stages is calculated. The conversion from a state of minimum entropy and minimum inertia with maximum spin order to a state of maximum entropy andmaximum inertia is analogized to the big bang.