Black holes in the varying speed of light theory

We consider the effect of the \emph{Varying Speed of Light} theory on non-rotating black holes. We show that in any varying-$c$ theory, the Schwarzschild solution is neither static nor stationary. For a no-charged black hole, the singularity in the Schwarzschild horizon cannot be removed by coordinate transformation. Hence, no matter can enter the horizon, and the interior part of the black hole is separated from the rest of the Universe. If $\dot{c}<0$, then the size of the Schwarzschild radius increases with time. The higher value of the speed of light in the very early Universe may have caused a large reduction in the probability of the creation of the primordial black holes and their population.The same analogy is also considered for the charged black holes.Comment: 5 page

Dynamical System Approach to Cosmological Models with a Varying Speed of Light

Methods of dynamical systems have been used to study homogeneous and isotropic cosmological models with a varying speed of light (VSL). We propose two methods of reduction of dynamics to the form of planar Hamiltonian dynamical systems for models with a time dependent equation of state. The solutions are analyzed on two-dimensional phase space in the variables $(x, \dot{x})$ where $x$ is a function of a scale factor $a$. Then we show how the horizon problem may be solved on some evolutional paths. It is shown that the models with negative curvature overcome the horizon and flatness problems. The presented method of reduction can be adopted to the analysis of dynamics of the universe with the general form of the equation of state $p=\gamma(a)\epsilon$. This is demonstrated using as an example the dynamics of VSL models filled with a non-interacting fluid. We demonstrate a new type of evolution near the initial singularity caused by a varying speed of light. The singularity-free oscillating universes are also admitted for positive cosmological constant. We consider a quantum VSL FRW closed model with radiation and show that the highest tunnelling rate occurs for a constant velocity of light if $c(a) \propto a^n$ and $-1 < n \le 0$. It is also proved that the considered class of models is structurally unstable for the case of $n < 0$.Comment: 18 pages, 5 figures, RevTeX4; final version to appear in PR

A scalar-tensor cosmological model with dynamical light velocity

The dynamical consequences of a bimetric scalar-tensor theory of gravity with a dynamical light speed are investigated in a cosmological setting. The model consists of a minimally-coupled self-gravitating scalar field coupled to ordinary matter fields in the standard way through the metric: \metric_{\mu\nu}+B\partial_\mu\phi\partial_\nu\phi. We show that in a universe with matter that has a radiation-dominated equation of state, the model allows solutions with a de Sitter phase that provides sufficient inflation to solve the horizon and flatness problems. This behaviour is achieved without the addition of a potential for the scalar field, and is shown to be largely independent of its introduction. We therefore have a model that is fundamentally different than the potential-dominated, slowly-rolling scalar field of the standard models inflationary cosmology. The speed of gravitational wave propagation is predicted to be significantly different from the speed of matter waves and photon propagation in the early universe.Comment: 12 pages, uses amsart and amssymb. Minor corrections, to appear in Phys. Lett.

Comments on "Note on varying speed of light theories"

In a recent note Ellis criticizes varying speed of light theories on the grounds of a number of foundational issues. His reflections provide us with an opportunity to clarify some fundamental matters pertaining to these theories

Cosmic Numbers: A Physical Classification for Cosmological Models

We introduce the notion of the cosmic numbers of a cosmological model, and discuss how they can be used to naturally classify models according to their ability to solve some of the problems of the standard cosmological model.Comment: 3 pages, no figures. v2: Two references added, cosmetic changes. Version to appear in Phys. Rev. D (Brief reports

Photon-axion conversion in intergalactic magnetic fields and cosmological consequences

Photon-axion conversion induced by intergalactic magnetic fields causes an apparent dimming of distant sources, notably of cosmic standard candles such as supernovae of type Ia (SNe Ia). We review the impact of this mechanism on the luminosity-redshift relation of SNe Ia, on the dispersion of quasar spectra, and on the spectrum of the cosmic microwave background. The original idea of explaining the apparent dimming of distant SNe Ia without cosmic acceleration is strongly constrained by these arguments. However, the cosmic equation of state extracted from the SN Ia luminosity-redshift relation remains sensitive to this mechanism. For example, it can mimic phantom energy.Comment: (14 pages, 9 eps figures) Contribution to appear in a volume of Lecture Notes in Physics (Springer-Verlag) on Axion

Variable-Speed-of-Light Cosmology from Brane World Scenario

We argue that the four-dimensional universe on the TeV brane of the Randall-Sundrum scenario takes the bimetric structure of Clayton and Moffat, with gravitons traveling faster than photons instead, while the radion varies with time. We show that such brane world bimetric model can thereby solve the flatness and the cosmological constant problems, provided the speed of a graviton decreases to the present day value rapidly enough. The resolution of other cosmological problems such as the horizon problem and the monopole problem requires supplementation by inflation, which may be achieved by the radion field provided the radion potential satisfies the slow-roll approximation.Comment: 18 pages, LaTeX, revised version to appear in Phys. Rev.

Non-Minimal Warm Inflation and Perturbations on the Warped DGP Brane with Modified Induced Gravity

We construct a warm inflation model with inflaton field non-minimally coupled to induced gravity on a warped DGP brane. We incorporate possible modification of the induced gravity on the brane in the spirit of $f(R)$-gravity. We study cosmological perturbations in this setup. In the case of two field inflation such as warm inflation, usually entropy perturbations are generated. While it is expected that in the case of one field inflation these perturbations to be removed, we show that even in the absence of the radiation field, entropy perturbations are generated in our setup due to non-minimal coupling and modification of the induced gravity.Comment: 29 pages, 7 figures, Accepted by Gen. Rel Gravi

About Bianchi I with VSL

In this paper we study how to attack, through different techniques, a perfect fluid Bianchi I model with variable G,c and Lambda, but taking into account the effects of a $c$-variable into the curvature tensor. We study the model under the assumption,div(T)=0. These tactics are: Lie groups method (LM), imposing a particular symmetry, self-similarity (SS), matter collineations (MC) and kinematical self-similarity (KSS). We compare both tactics since they are quite similar (symmetry principles). We arrive to the conclusion that the LM is too restrictive and brings us to get only the flat FRW solution. The SS, MC and KSS approaches bring us to obtain all the quantities depending on \int c(t)dt. Therefore, in order to study their behavior we impose some physical restrictions like for example the condition q<0 (accelerating universe). In this way we find that $c$ is a growing time function and Lambda is a decreasing time function whose sing depends on the equation of state, w, while the exponents of the scale factor must satisfy the conditions $\sum_{i=1}^{3}\alpha_{i}=1$ and $\sum_{i=1}^{3}\alpha_{i}^{2}<1,$ $\forall\omega$, i.e. for all equation of state$,$ relaxing in this way the Kasner conditions. The behavior of $G$ depends on two parameters, the equation of state $\omega$ and $\epsilon,$ a parameter that controls the behavior of $c(t),$ therefore $G$ may be growing or decreasing.We also show that through the Lie method, there is no difference between to study the field equations under the assumption of a $c-$var affecting to the curvature tensor which the other one where it is not considered such effects.Nevertheless, it is essential to consider such effects in the cases studied under the SS, MC, and KSS hypotheses.Comment: 29 pages, Revtex4, Accepted for publication in Astrophysics & Space Scienc

Bianchi II with time varying constants. Self-similar approach

We study a perfect fluid Bianchi II models with time varying constants under the self-similarity approach. In the first of the studied model, we consider that only vary $G$ and $\Lambda.$ The obtained solution is more general that the obtained one for the classical solution since it is valid for an equation of state $\omega\in(-1,\infty)$ while in the classical solution $\omega\in(-1/3,1) .$ Taking into account the current observations, we conclude that $G$ must be a growing time function while $\Lambda$ is a positive decreasing function. In the second of the studied models we consider a variable speed of light (VSL). We obtain a similar solution as in the first model arriving to the conclusions that $c$ must be a growing time function if $\Lambda$ is a positive decreasing function.Comment: 10 pages. RevTeX