Trials to Resolve Black Holes Instabilities in Brane World Cosmology Models

In this letter, we report on our trials to remove the instability of black holes in brane world cosmological models consisting of two branes and a bulk. In order to resolve this problem, general types of interaction potentials were employed. Careful analyses have shown that although the black holes instabilities were removed, a sort of arbitrariness adherent to the motion of the two branes towards each other has taken place leading to an unstable system. Thus, the models seem to us rather paradoxical.

Casimir effect for a Cavity in the Spacetime with an Extra Dimension

We reexamine the Casimir effect for the rectangular cavity with two or three equal edges in the presence of compactified universal extra dimension. We derive the expressions for the Casimir energy and discuss the nature of Casimir force. We show analytically the extra-dimension corrections to the standard Casimir effect to put forward a new method of exploring the existence of extra dimensions of the Universe.

Casimir Effect at Finite Temperature in the Presence of Compactified Universal Extra Dimensions

We analyse the Casimir effect for parallel plates at finite temperature in the presence of compactified universal extra dimensions and analytically show the thermal corrections to the effect in detail. The Casimir effect for different sizes of universal extra dimensions is investigated to test the five-dimensional Kaluza-Klein theory.

M理论及其哲学意义

M理论是 2 1世纪基本物理学研究的重要前沿阵地。本文从M理论的基本内容出发 ,阐述其带来的一些自然哲学问题。

Brane世界中的宇宙学方程

首先介绍了相关概念———外赋曲率,引入Brane世界宇宙模型.然后由Brane度规和五维能动张量推得五维爱因斯坦方程,积分得到Brane边界条件,应用到爱因斯坦方程得到与Friedmann类似的方程.由爱因斯坦方程和能动张量守恒方程得到Brane宇宙标度因子的演化规律.最后,在将Brane张量和体宇宙学常数进行微调后,分别在高能和低能范围里讨论修正了的Friedmann方程的解及其中各项的意义.

Eliminating Black Holes Singularity in Brane World Cosmology

In recent works, a construction was proposed resulting in emergent universes inside black holes. This result can be obtained from a 4D black hole embedded in a 5D spacetime with the fifth dimension compactified on a circle [0, 2] (0 and 2 are identified) such that the two branes are at 0 and 1. In the present work, we study this setup by deriving particles’ equations of motion in the new universes, based on redefining energy and angular momentum. This leads to disappearance of the singularity in centers of black holes in classical General Relativity.

Brane world black holes in teleparallel theory equivalent to general relativity and their Killing vectors,energy,momentum and angular momentum

The energy--momentum tensor, which is coordinate-independent, is used to calculate energy, momentum and angular momentum of two different tetrad fields. Although, the two tetrad fields reproduce the same space--time their energies are different. Therefore, a regularized expression of the gravitational energy--momentum tensor of the teleparallel equivalent of general relativity （TEGR）, is used to make the energies of the two tetrad fields equal. The definition of the gravitational energy--momentum is used to investigate the energy within the external event horizon. The components of angular momentum associated with these space--times are calculated. In spite of using a static space--time, we get a non-zero component of angular momentum! Therefore, we derive the Killing vectors associated with these space--times using the definition of the Lie derivative of a second rank tensor in the framework of the TEGR to make the picture more clear.

Fermion field in the vicinity of a brane

A mechanism that enables fermions to live outside of but be localized near a brane is proposed based on the field-theoretical framework. Two types of fermion fields are considered: one is localized to the brane through the Yukawa interaction, and another is localized through the fermion interaction. It is shown that, besides the well-localized zero-mode, there exists a light mode continuum of which oscillating components are delocalized. As a consequence it is possible to assume existence of invisible material particles that live outside the brane on which we reside and beleaguer visible particles. A possible extension to the mind-body problem is discussed.

Alignment of Quasar Polarizations on Large Scales Explained by Warped Cosmic Strings. PART II: The Second Order Contribution

We find an azimuthal-angle dependent approximate wave like solution to second order on a warped five-dimensional manifold with a self-gravitating U(1) scalar gauge field (cosmic string) on the brane using the multiple-scale method. The spectrum of the several orders of approximation show maxima of the energy distribution dependent on the azimuthal-angle and the winding numbers n of the subsequent orders of scalar field. This breakup of the quantized flux quanta does not lead to instability of the asymptotic wavelike solution, due to the suppression of the n-dependency in the energy mo-mentum tensor components by the warp factor. This effect is triggered by the contribution of the five dimensional Weyl tensor on the brane. This con-tribution can be understood as dark energy and can trigger the self-acceleration of the universe without the need of a cosmological constant. There is a striking relation between the symmetry breaking of the Higgs field described by the winding number and the SO(2) breaking of the axially symmetric configuration into a discrete subgroup of rotations about 180°. The discrete sequence of non-axially symmetric deviations, cancelled by the emission of gravitational waves in order to restore the SO(2) symmetry, triggers the pressure Tzz for discrete values of the azimuthal-angle. There can be a possible relation between the recently discovered angle-preferences of polarization axes of quasars on large scales and our theoretical predicted angle-dependency and can be an evidence for the existence of cosmic strings. The discovery of the increase of polarization rate in smaller subgroups of the several large-quasar groups (LQGs), the red shift dependency and the relative orientation of the spin axes with respect to the major axes of their host LQGs, point at a fractional azimuthal structure, were also found in our cosmic string model. This peculiar discontinuous large scale structure, i.e., polarizations directions of multiples of, for example, π/2 orπ/4, can be explained by the spectrum of azimuthal-angle dependent wavelike modes without the need of conventional density perturbations in standard 4D cosmological models. Carefully com-parison of the spectrum of extremal values of the first and second order φ-dependency and the distribution of the alignment of the quasar polarizations is necessary. This can be accomplished when more observational data become available.

Extra Dimensions, Brane Worlds, and the Vanishing of Axion Contributions to Inflation

We examine from first principles the implications of the 5th Randall Sundrum Brane world dimension in terms of setting initial conditions for chaotic inflationary physics. Our model pre-supposes that the inflationary potential pioneered by Guth is equivalent in magnitude in its initial inflationary state to the effective potential presented in the Randall-Sundrum model. We also consider an axion contribution to chaotic inflation (which may have a temperature dependence) which partly fades out up to the point of chaotic inflation being matched to a Randall-Sundrum effective potential. If we reject an explicit axion mass drop off to infinitesimal values at high temperatures, we may use the Bogomolnyi inequality to re-scale and reset initial conditions for the chaotic inflationary potential. One of the potential systems embedded in the Randall-Sundrum brane world is a model with a phase transition bridge from a tilted washboard potential to the chaotic inflationary model pioneered by Guth which is congruent with the slow roll criteria. If, as written up earlier, the axion wall contribution is due to di-quarks, which is equivalent to tying in baryogenesis to the formation of chaotic inflation initial conditions, with the Ran-dall-Sundrum brane world effective potential delineating the end of the dominant role of di-quarks, and the beginning of inflation.

Limit Treatment of Space-Time Foam Calculations If Non Pathological Big Bang Singularity Is Accessible to Modified Einstein Equations

When initial radius if Stoica actually derived Einstein equations in a formalism which removes the big bang singularity pathology, then the reason for Planck length no longer holds. We follow what Ng derived as limit calculations as to a space time length factor Without the drop off of the vacuum energy as given by is at least the value of . We review the work by Ng as to quantum foam as to how that affects a general expression as to energy when , with determined at least approximately by arguments he presented in 2008 in the Dark side of the universe conference. Well before certain effects make themselves apparent, in ways which are illustrated in the manuscript. Having at a point singularity would remove expansion by the scale factor, so that the extreme version of Stoica’s treatment in an isolated 4-dimensional universe would be no expansion at all.

Alignment of Quasar Polarizations on Large Scales Explained by Warped Cosmic Strings

The recently discovered alignment of quasar polarizations on very large scales could possibly be explained by considering cosmic strings on a warped five dimensional spacetime. Compact objects, such as cosmic strings, could have tremendous mass in the bulk, while their warped manifestations in the brane can be consistent with general relativity in 4D. The self-gravitating cosmic string induces gravitational wavelike disturbances which could have effects felt on the brane, i.e., the massive effective 4D modes (Kaluza-Klein modes) of the perturbative 5D graviton. This effect is amplified by the time dependent part of the warp factor. Due to this warp factor, disturbances don’t fade away during the expansion of the universe. From a nonlinear perturbation analysis it is found that the effective Einstein 4D equations on an axially symmetric spacetime, contain a “back-reaction” term on the righthand side caused by the projected 5D Weyl tensor and can act as a dark energy term. The propagation equations to first order for the metric components and scalar-gauge fields contain -dependent terms, so the approximate wave solutions are no longer axially symmetric. The disturbances, amplified by the warp factor, can possess extremal values for fixed polar angles. This could explain the two preferred polarization vectors mod .

Gravitational Waves and Extra Dimensions: A Short Review

We give a brief review on the recent development of gravitational waves in extra-dimensional theories of gravity.Studying extra-dimensional theories with gravitational waves provides a new way to constrain extra dimensions.After a flash look at the history of gravitational waves and a brief introduction to several major extra-dimensional theories, we focus on the sources and spectra of gravitational waves in extra-dimensional theories.It is shown that one can impose limits on the size of extra dimensions and the curvature of the universe by researching the propagations of gravitational waves and the corresponding electromagnetic waves.Since gravitational waves can propagate throughout the bulk, how the amplitude of gravitational waves decreases determines the number of extra dimensions for some models.In addition, we also briefly present some other characteristics of gravitational waves in extra-dimensional theories.

Warm Standard Scalar Field Modified Chaplygin Gas Inflation Inspired by Generalized Dissipative Coefficient on the Brane

We discuss the warm inflation in the presence of standard scalar field model and modified Chaplyggin gas in brahe-world scenario. We consider weak and strong dissipative regimes with generalized dissipative coefficient. We extract various inflationary parameters. For example, we analyze the behavior of different ratios （ratio of dissipative co-efficient and Hubble parameter Г/3H, ratio of temperature and Hubble parameter T/ H, scalar-to-tensor ratio ＇r） with respect to spectral index ns for the weak and strong dissipative regimes through parametric plotting. It is found that T/H and Г/3H satisfied the required conditions in both dissipative regimes. It is also noted that the spectral index （ns） ns=0.96＋0.10-0.10 It is remarked here that our results are consistence with observational data WMAP7, WMAP9, and recent Planck data.

Quark-hadron phase transition in DGP including BD brane

A Dvali–Gabadadze–Porrati(DGP)brane-world model with perfect fluid brane matter including a Brans-Dicke(BD)scalar field on brane was utilized to investigate the problem of the quark-hadron phase(QHP)transition in early evolution of the Universe.The presence of the BD scalar field arises with several modified terms in the Friedmann equation.Because the behavior of the phase transition strongly depends on the basic evolution equations,even a small change in these relations might lead to interesting results about the time of transition.The phase transition is investigated in two scenarios,namely the first-order phase transition and smooth crossover phase transition.For the first-order scenario,which is used for the intermediate temperature regime,the evolution of the physical quantities,such as temperature and scale factor,are investigated before,during,and after the phase transition.The results show that the transition occurs in about a micro-second.In the following part,the phenomenon is studied by assuming a smooth crossover transition,where the lattice QCD data is utilized to obtain a realistic equation for the state of the matter.The investigation for this part is performed in the high and low-temperature regimes.Using the trace anomaly in the high-temperature regime specifies a simple equation of state,which states that the quark-gluon behaves like radiation.However,in the low-temperature regime,the trace anomaly is affected by discretization effects,and the hadron resonance gas model is utilized instead.Using this model,a more realistic equation of state is found in the low-temperature regime.The crossover phase transition in both regimes is considered.The results determine that the transition lasts around a few micro-seconds.Further,the transition in the low-temperature regime occurs after the transition in the high-temperature regime.

Study of Branes with Variable Tension

In this work we study a brane world model with variable tension, which gives rise to four-dimensional cosmologies. The brane worlds obtained correspond to E?tv?s branes whose(internal) geometry can be casted as either a four-dimensional(A)dS_4 or a standard radiation period cosmology. The matter dominated period is discussed as well.

A new unified theory of electromagnetic and gravitational interactions

In this paper we present a new unified theory of electromagnetic and gravitational interactions. By considering a four-dimensional spacetime as a hypersurface embedded in a five-dimensional bulk spacetime, we derive the complete set of field equations in the four-dimensional spacetime from the five-dimensional Einstein field equation. Besides the Einstein field equation in the four-dimensional spacetime, an electromagnetic field equation is obtained: del F-a(ab) - xi R-b (a)A(a) = -4 pi J(b) with xi = -2, where F-ab is the antisymmetric electromagnetic field tensor defined by the potential vector A(a), R-ab is the Ricci curvature tensor of the hypersurface, and J(a) is the electric current density vector. The electromagnetic field equation differs from the Einstein-Maxwell equation by a curvature-coupled term xi R-b (a)A(a), whose presence addresses the problem of incompatibility of the Einstein-Maxwell equation with a universe containing a uniformly distributed net charge, as discussed in a previous paper by the author [L.-X. Li, Gen. Relativ. Gravit. 48, 28 (2016)]. Hence, the new unified theory is physically different from Kaluza-Klein theory and its variants in which the Einstein-Maxwell equation is derived. In the four-dimensional Einstein field equation derived in the new theory, the source term includes the stress-energy tensor of electromagnetic fields as well as the stress-energy tensor of other unidentified matter. Under certain conditions the unidentified matter can be interpreted as a cosmological constant in the four-dimensional spacetime. We argue that, the electromagnetic field equation and hence the unified theory presented in this paper can be tested in an environment with a high mass density, e.g., inside a neutron star or a white dwarf, and in the early epoch of the universe.