A NEW COSMOLOGICAL MODEL: RED-SHIFT AND SCALE FACTORS MOHAMMAD SHYFUR RAHMAN CHOWDHURY Lecturer, Department of Business Administration, International Islamic University, Chittagong, Bangladesh ABSTRACT A new cosmological model is considered which doesn‟t require dark energy. The expansion of the universe is reinterpreted as a „rescaling‟ whereby the whole universe can change scale, yet appear static. Rescaling is a symmetry whereby there is a simultaneous change of every length in the universe and all physical constants which contain length dimensions. It is shown that this interpretation of expansion of the universe, can lead to a Hubble law, due to changing of Hubble constant with time. Also an interpretation of expansion of the universe by red-shift of light, due to a changing of Plancks constant with time. This results in a new relationship between scale factor of the universe and red-shift. The misunderstanding of the true relationship is the cause of the apparent dark energy phenomenon. In this paper we have discussed about the angular size of the distance that subtend at our location. Also we have discussed about the apparent brightness is related to the luminosity of the galaxy and its distance from us in the expanding universe described by the Robertson-Walker space-time and A related result is the variation of apparent surface brightness with red-shift. Finally it includes the predictions for the magnitudes of supernovae against red-shift are made and found to be in good agreement with supernovae data, without dark energy. KEYWORDS: Cosmology, Hubble Law, Red-Shift, Distance Scale, Luminosity Distance, Dark Energy 1. INTRODUCTION On large scales the Universe in homogeneous and isotropic, at least to a good approximation. This means that the Universe does not possess any privileged positions or directions. This idea is of such importance in cosmology that it has been elevated to the status of a Principle, and is usually known as the Cosmological Principle. We shall discuss the observational evidence for it later. There are various approaches one can take to this principle. One is philosophical, and is characterized by the work of Milne in the 1930s and later by Bondi & Gold and Hoyle in 1948. This line of reasoning is based, to a large extent, on the aesthetic appeal of the cosmological principle. Ultimately this appeal stems from the fact that it would indeed be very difficult for us to understand the Universe if physical conditions, or even the laws of physics themselves, were to very dramatically from place to place. These thoughts have been further leading to the Perfect Cosmological Principle in which the Universe is the same not only in all places and in all directions, but also at all times. This stronger version of the cosmological principle was formulated by Bondi & Gold (1948) [23,24] and it subsequently led Hoyle (1948) and Hoyle & Narlikar (1968, 1964) to develop the Steady State Cosmology. This theory implies, amongst other things, the continuous creation of matter to keep the density of the expanding Universe constant. The Steady State universe was abandoned in the 1960s because of the properties of the cosmic microwave background, radio sources and the cosmological helium abundance which are more readily explained in a Big Bang model than in a Steady State. Nowadays the latter is only of historical interest. International Journal of Applied Mathematics & Statistical Sciences (IJAMSS) ISSN 2319-3972 Vol. 2, Issue 4, Sep 2013, 15-26 © IASET