cosmos0

Hello, I just wrote the following manuscript: http://fr.calameo.com/books/000145333298884fdee60. By deriving the standard formula of the luminosity distance, I obtain a time varying speed of light (from light propagation). Therefore, a new definition of the luminosity distance is provided. Given this new definition, the Hubble constant must remain unchanged in order to fit the supernovae data. Your comments and ideas are welcome...

Hello everybody, I am proposing a heat-diffusion model in spherical coordinates applied to the earth. The main idea is that the earth was a hot ball of homogeneous temperature when the earth formed, that did cool down over time due to heat-diffusion. As we know earth formed from an accretion disk, therefore, the homogeneous temperature at earth formation assumption appears to be reasonable. The model provides the temperature-depth profile of the earth at different ages. The model makes two predictions: (1) 4.4 billion years after earth formation, the temperature gradient in the first kilometer of the earth's crust is about 3 degree Celsius per 100 meters. This is well in agreement with current estimates. (2) 4.4 billion years after earth formation, the earth crust thickness is around 70-80 km. This is in agreement with the maxima of the continental crust; however, most of the continental crust is 40-45 km thick, and oceanic crust 7-10 km thick. The challenge is to explain the gap from prediction (2). Please find enclosed the link to the manuscript: http://fr.calameo.com/books/000145333b9055bc4b717 Your comments and ideas are welcome..

In light travel distances this would mean that if we consider three points aligned in space, the distance between the two extremes is not the sum of the two sub-segments.. Let me explain. The idea is that the Hubble coefficient in the light travel distance (LTD) framework is expressed as a function of LTD: the recession speed is Ho*c*T where T is the distance in LTD and c the celerity of light. The Hubble coefficient is in the Euclidean framework is expressed as a function of Eclidean distances: the recession speed is He*y where y is the Euclidean distance. The rationale is to find a time-varying Hubble coefficient in the Euclidean framework, such that Ho*c*T = He(t)*y. Because space is expanding, the expansion is added to the overall distance the photon has to travel to reach the observer, therefore we obtain two differential equations describing the distance between the observer and the photon: (1) In the LTD Framework at any time t > 0: dy/dt = -c + Ho*c*(Tb - t) with boundary conditions: y(Tb-T) = yo, and y(Tb) = 0, where Tb is the time of the Big Bang and y the Euclidean distance. (2) In the Euclidean Framework: dy/dt = -c + He(t)*y Now let us consider the nth order Hubble coefficient in the Euclidean framework of the form He = n/t with t the time from the Big Bang. Therefore the differential equation becomes: dy/dt = -c + n/t*y (this is a first order non homogeneous differential equation). By solving the math for both differential equations we find that the solution is the same when n=2 (read the paper http://fr.calameo.com/books/00014533338c183febd92 for the details about the math). This is the proof that an apparently steady Hubble in the LTD framework is equivalent to a time-varying Hubble coefficient in the Euclidean framework of order two (i.e. Universe expanding at a steady acceleration). Now using kinetics, I will show why a second order time-varying Hubble coefficient means that the Universe is expanding at a steady accelerated pace in the Euclidean framework. Assuming that the time-varying Euclidean Hubble behaves according to the same Hubble law than in the LTD framework, leads to He(t) =v(t)/x(t), where v(t) is the Universe expansion velocity and x(t) the scale factor. Let us consider the following form for the time-varying Hubble coeficient in the Euclidean framework: He(t) =n/t, where n is the order of the time-varying Euclidean Hubble, and t the time from the big bang. (1) Considering the simple scenario of a Universe expanding at a constant velocity, we obtain: v(t) = v and x(t) = v * t. Hence, the time-varying Hubble coefficient from equation is He(t) =1/t. A first order time-varying Hubble coefficient is recognised. (2) Considering a Universe expanding at a steady accelerated rate, and with an initial expansion velocity null, we obtain: v(t) = a*t and x(t) = a*t^2/2, where a is the expansion acceleration. Hence, the time-varying Hubble coefficient from is He(t) = 2/t. A second order time-varying Hubble coefficient is recognised. This is to show that a second order time-varying Hubble coefficient in the Euclidean framework, means that the Universe is expanding at a steady accelerated pace. This would have great implication on the calculation of the age of the Universe!

13.7 billion years (1/Ho) is the distance to the Hubble sphere.. the age of the Universe has to be recalculated.. Let me explain. If the recession speed due to space expansion exceeds the speed of light, the photon would never reach the observer, this is why there exists a horizon of the visible Universe (the Hubble sphere), beyond which light would never reach us. Historically the age of the Universe was computed from the loockback time between a redshift zero and infinity, which yields 1/Ho. Note that this measure gives the lookback time to the Hubble sphere because the redshift must converge towards infinity at the horizon of the visible Universe. Here is a reference showing the calculations with a De Sitter Universe (http://www.jrank.org...-back-time.html). Another reference where the age of the Universe is computed with the look-back time between a redshift of zero and infinity: http://www.mpifr-bon...DiplWebap1.html. See A.36 et A.37. Using another approach we can show that an apparently steady Hubble coefficient in the light travel distance framework is equivalent to a time-varying Hubble coefficient in the Euclidean framework of order two (i.e. Universe expanding at a steady acceleration pace). This approach gives an age of the Universe of about 20-25 billion years. This figure is compatible with the age of the Universe obtained from the datation of old stars. According to Chaboyer (1995) who analysed metal-rich and metal-poor globular clusters, the absolute age of the oldest globular clusters are found to lie in the range 11-21 Gyr. Bolte et al. (1995) estimated the age of the M92 globular cluster to be 15.8 Gyr. Th/Eu dating yields stellar ages of up to 18.9 Gyr (Truran et al., 2001). A paper describing this appoach is available online: http://fr.calameo.co...33338c183febd92