_{1}

^{*}

We propose a new interpretation of Hubble law. Waves are observed in the observer space-time. It defines the observer proper time
*T*. Space-time is composed of three spatial dimensions and three temporal parameters: proper-time s of the observed object, proper time
*T* of the observer and integration time
*t* (currently considered as relative time). Time origin is the birth of the universe. So, universe is stable; it can be seen as the comobile space of expansion theory. When changing space-time from the source to the observer, waves are seen cooling; this explains the redshift effect. The distance is defined as the product of the delay time with the local speed of light of the observer. The mistake between
*t* and
*T* can explain why universe is viewed as not only in expansion but also in acceleration whereas we think it is stable.

Up to now, physics laws are based on Einstein relativity, established in 1905. Hubble has discovered the correlation between redshift and distance [

This article proposes a new approach to explain Hubble law. Other alternatives to expansion have been proposed such as Zwicky in 1929 [

First we present the model and then we discuss the interpretation of redshift applied to black body radiation. We compare the proposed model to measured data in the distance modulus―redshift diagram. At the end we explain why, in present interpretation, universe is viewed expanding and moreover accelerating [

Using Euclidean space, the observer position is x_{o}. His proper time is T. Time begins at universe origin. The observer detects light from an object in position x_{e}, with a proper time s. Their separation distance is

Let’s consider light propagating from the object to the observer. The boundary conditions are

On the short term, this result is compatible with relativity (Minkowsky metric) written in times, with

^{9} years from [

In this model, product _{u} is constant. It defines the Euclidean space. All present physics remains locally valid, only long scales interpretations are modified and explained without matter effects. Physical quantities and laws applied to matter in each space-time are universals. This model is compatible with the restricted theory, using

More than speed light,

A distance x is defined as the product of delay time τ by the local space-time relation c(T), with

The black body theory is local. It can be applied to a volume as little as possible. So it is not affected by the proposed theory. The Planck black body radiation law is:

where c is the speed of light in vacuum, h is the Planck constant, k_{B} is the Boltzmann constant, K_{1} is the temperature in Kelvin (˚K), λ is the wavelength in meters (m). ^{2}∙sr∙m).

c = 299792458 m/s; h = 6.62606957 × 10^{−}^{34} J∙s; k_{B} = 1.3806488 × 10^{−}^{23} J/˚K. Constants are from [

We write again the Planck law assuming radiation has been emitted at the proper time s. In Equation (2.2A), we replace c by the local space-time relation at the time s of light emission, so

We make appear the observer proper time T in the above expression.

In the observer space-time

We deduce:

Equation (2.2C) is the source radiation interpreted as a cooling black body in the observer space-time. The temperature decreases from K_{1} to K_{2} with

so

Equation (2.2D) suggests that the product K.T is constant. Today, based on the cosmic background radiation temperature from [^{9} years from [^{18} K.s.

Now, in Equation (2.2C), the factor z + 1 is gathered with wavelength, so we get

In Equation (2.2E), cooling generates two effects:

The first one is the redshift of the source spectrum, wavelengths are divided by the (z + 1) factor.

The second one is the total reduction of the radiance which is divided by the

In the expansion theory, the

In the present expansion theory distance x is related to redshift z using FLWR metric [

L. A. Marosi proposes in [

The fitted curve is:

with a = 44.109769 and b = 0.059883 for

Let us now analyze the Hubble law under the proposed cooling theory. We first deal with the distance. We deduce from Equation (2.2B)

The distance x from object to observer is defined by Equation (2.1D) and using Equation (2.1B)

Using Equation (2.1C) and Equation (2.3C)

Using Equation (2.3E) and Equation (2.3F)

For z ~ 0, Equation (2.3G) and Equation (2.1B) gives

Let’s now deal with the radiation. When measuring a radiation, we assume that it follows a law such as

where L is the intrinsic radiation, x is the distance from object to observer. That is due to the assumption of the energy conservation so the product

where L_{0} is the apparent intrinsic radiation. We deduce from Equation (2.3G), Equation (2.3H) and Equation (2.3I):

So,

The magnitude is defined by

Then

where

The distance modulus μ is defined by μ = m − m_{0}. So,

We note the very good agreement between the two curves. The remaining deviation is less than 0.2 distance modulus. This can be seen as a validation of the proposed theory which uses only time and space-time relationship.

The Hubble parameter H and the acceleration parameter

and

where

We deduce from Equation (3A) and Equation (3C)

so,

But, as we propose in the cooling universe theory, by introducing the observer proper time, at date t = T, Equation (3C) becomes,

We deduce from Equation (3A) and Equation (3F)

Equation (3D) and Equation (3G) are not compatible. Equation (3G) applied into Equation (3B) leads to

T is not the integration time t. No solution can be found when using a metric such as, at first order,

Research is for the moment looking toward expansion and gravitational interpretation of phenomenon. It is using more and more complex gravitation point of view.

We shall not go further on present cosmological metric analysis, because they are only based on gravitational effects. We think that gravitation is a local effect.

We propose a new model to explain the µ-z diagram. This diagram represents time between the observed object and the observer. It can be explained without gravitational effects. Space-time is changing between the light source and the observer.

The proposed model is compatible with the Einstein Universe. When Einstein postulated the constancy of speed of light, the good idea was that the waves are always viewed in the space-time of the observer and so independent with t. Universe is stable, not expanding and not accelerating by the current space-time point of view.

PascalChuroux, (2015) A New Interpretation of the Hubble Law. Journal of Modern Physics,06,1227-1232. doi: 10.4236/jmp.2015.69127