Is Time Inhomogeneous ?

In this article, we discuss probability of inhomogeneous time in high or low energy scale of physics. Consequently, the possibility was investigated of using theories such as varying speed of light (VSL) and fractal mathematics to build a framework within which answers can be found to some of standard cosmological problems and physics theories on the basis of time non-homogeneity.


Motivation
The possibility of breaking physical symmetry in certain positions in the quantum gravity mechanism has opened a new aspects onto this realm of physics.This study connect on phenomenological concepts such as Lorentz invariance violation, in an effort to further investigate the breaking of principle symmetries in general theory of relativity.As we know, violation of Lorentz invariance in high-energy quantum fields theory is predictable [1].In other words, Lorentz invariance cannot be a perfect symmetry at all energy scales.Our main goal in this research is that maybe the effects of CPT/Lorentz invariance violation can be consideration in nature.In this case, a new fundamental theory in physics should be favorable which takes into account the symmetry breaking.On the other hand, egress of new theories in physics, for example, varying speed of light theory [5] in physics or fractals mathematic theories [6], has prompted researchers to study the subject more seriously.Recently ,the possibility of fractal method (non-integer) dimensions is emphasized.For example, possibility, spatial dimensions are fractal structures, e.g., volume might be 3D and surface may be considered to have 2.1D .It should be insisted here that when we considering fractal dimensions or mass contents, we are concerned ourself only with very large or very small scales in physics.In other view point, fractal method in cosmology is a set of minority cosmological theories which state that the content of matter in the Universe, or the structure of the universe itself, is a fractal structure.More generally, A main issue in this field is the fractal dimension of the Universe or of matter content within it, when study at very large or very small scales.One A analyze of the SDSS data in 2004 found The power spectrum is not actually characterized by a single power law potential but clearly shows curvature [2].Their analysis shows that a fractal structure of galaxies in the universe.In this regard, theories like Quantum gravity theory [3] are fractal in some position, for example in the ultra-small near the Planck scale.More interesting,in July 2008, Scientific American published an article on Causal dynamical [4] written by the three scientists who proposed the theory, which consider the universe maybe have a fractal structure.

Time Non-homogeneity ?
The main idea in this article is that although the non-homogeneity of time can be directly obtained from the theory of relativity, we should instead, according some astronomical observation data, we can use fractal calculations for cosmological evolution.Moreover, fractal calculations can also be explain other physical phenomena such as black holes.Generally, fractal mathematics can be used for explaining some physical phenomena that cannot be describing by non-fractal functions or analytical formulas.In following , this article is divided into four main parts: 1) fractal calculus method, 2) the varying speed of light theory, 3) fractal cosmological physics and 4) conclusion.

Fractal mathematics
Fractal equations and, in especially, differential fractal relations have already been performed in many fields of science.For example, fractal derivatives are used in Classical fluids as good as dynamical systems.The suitable variation method was used by HE [7] for differential relations in control method of engineering [7].The mathematical structure of fractal calculations has been obtained at different levels.The well-known case is Riemann-Liouvilles Integration that give as: where p > 0. The Riemann-Liouville's Fractal derivative is obtained from the following equation: here m is an integer number that define m − 1 ≤ p < m.In other define we have a equation that give as here Γ(x) is Eulers function, and a and b are in interval [0, ∞).In these definitions, always take, m = d + 1 , that d is the integer part of d.
In the following sections, we consider briefly the varying speed of light theory, and then use this theory in Section 3.

Varying Speed of Light theory
In recent years, an interesting new theory, Varying Speed of Light (VSL), has been proposed which assuming varying speed for speed light(c).this model can be used for solving the standard cosmological problems such as Horizon and the cosmological [8].However, in the most general definition of this theory, it claimed that within the framework of this theory, laws of physics may be considered by substituting c (speed of light) in the standard action with the field c = c(x µ ) .As can be seen in this definition, the speed of light is not constant, but depends on a specific time and place in space relation( in some models, only the time dependence is studied for the speed of light).It is more important that by further taking into account the spatial dependence of the speed of light, we would open the way for fractal calculus since in so doing.This means, we actually divide space into fractals structures by unique properties (for more information, see [8]).Usually in this theory, the time dependence of the speed of light is coupled with a parameter of the cosmological scale factor.For example in some models [5,8] speed of light relation given as where a is scale factor and n is a constant.We note that n in above equation determine by observational data fine tuning [8].In following, by using this theory and the fractal calculus methods, we can revisit some of the problems in physics and cosmology.This means by using fractal mathematics and observation data for determination of n in equation( 5) can solve some physics problems in fractal differential framework.

Fractal Physics and Cosmology
In this section, we first present a brief description of the fractal dimensions method for time and space that used in other work.Consequently, we consider the particular case of this method in cosmological relations.As an example, we begin with the basic equations in dynamics of particles, namely, Newton movings Law.It can be shown that upon application in fractal calculus.the well-known form of Newtons relation for gravitational forces is expressed as [9]: Here, the previous integer time and space derivatives are replaced by fractal number that depend on the amount of parameter d.In a generalized case, the Euler equations in classical mechanics equations can be rewritten in fractal form as: The above equation can be shown that physical fields may be reconstructed into their fractal form in which temporal and spatial dimensions are fractal dimension.
In other view point, about impact fractal method and Cosmology, we can point out a interesting answer to anomalies received in the ultrahigh energy cosmic rays (UHECR) and TeV-photon spectra [9].For example, one has proposed an attractive solution that using with general relativity and is consistent with the new form of geometry (Cantorian geometry) of space-time at high-energy scales or equivalent to fractal methods [9].There, the author assumed a new form of dispersion relation for relativistic energy in fractal calculation as E 2β = |p| 2α + (m 0 0 ) 2 and obtained an attractive solution for (UHECR) anomalies in cosmology.Also fractal formalism offer a strong tool for study the ultraviolet region of field theory such as: action mechanism, origin of spin method [6,9].In context of fractal cosmology, previous work [10] have been shown the relation for the relative density of dark contexts.In this regards, the continuity equation in fractal cosmology model takes the form as with v = 1 and L = 4 (where L = 2 + ǫ), we get the standard Friedmann equations in four dimensions.

Summary
At the start of this article, we asked fundamental questions such as Are time and space continuous?, Why is time non-invertible?, and How could time and space dimensions be described?.This research presents a theory on the nature of time and space based on fractal geometry formalism.It is obvious that the fractal dimensions method of space lead to the production of a new define for space-time.In this discussion, we have assumed that space and time are new-define fields specified according to the contents of the Universe.
Based on this proposal, the presented model would be a theory to include all forces within a fractal calculation framework.On the other hand, the principle lows also holds, e.g., by ignoring the temporal fractal corrections in formalism, we can obtain the special theory of relativity.It should be noted that determination of the fractal parts in fractal calculations is to be adjusted through comparison with observational data.For example, through the use of varying speed of light theory, its dependence on space and time fractals.In this way, many thus far unanswered questions in cosmology can be addressed through application of fractal physical fields method.The most significant result of this research is that fractal calculations formalism maybe used to correct all the theories of modern physics.The alternative way would be to convert the fractal equations into integer derivatives without introducing any corrections.