Fantappiè's group as an extension of special relativity on ε(∞) Cantorian space–time

Archaic Universe and Cosmological Model: “Big-Bang” as Nucleation by Vacuum

“…Since F is constant by definition (as we can define it as the energy actually liberated at the "following" big bang), P can depend on x 0 only through T [8]. So, generally speaking, T is a function of x 0 and we can postulate that T is indeed nothing but x 0 , converted through the relation: (11) in which only fundamental constants appear which, as is known, play the role of conversion factors. The formal temperature T assumes an initial value of infinity on the hypersphere equator, then to decrease as x 0 increases (and this is the "special role" of the x 0 axis: basically, it is an axis of temperatures) until it reaches the minimum value c/kr = E dB /k at the extreme x 0 = r; E dB = c/r is the de Broglie energy.…”

“…The framework thus outlined bears a very close resemblance to the Hartle-Hawking solution [8,11], though it differs from it in a number of aspects, e.g. for its independence from any reasoning in terms of quantum gravity.…”

Irreversible processes and a new model for the Universe

“…(2.1) is needed in order to clarify if it is a necessary extension from the viewpoint of El Naschie E-infinity theory [27][28][29][30][31], Iovane stochastic and self similar Universe [32][33][34][35], Nottale scale relativity [36][37][38][39] and Sidharth fractal Universe [40]. We note indeed that it is problematic to explain the present acceleration of the Universe as the effect of a model with an El Naschie E-infinity cantorian spacetime, a scaling law on Newtonian cosmology and a certain dependent gravitational constant G. On the contrary, if we use the fractal self-similarity of the G varying relativistic Friedmann model experimental data can be explained [41].…”

A projective approach to dynamical systems, applications in cosmology and connections with El Naschie ϵ(∞) Cantorian space–time

“…We showed that gravitational lensing could be a good tool in investigating the inner nature of spacetime according to the presented model [1]. As reported in [4] FantappièÕs starting point was the study of the spacetime of classical and relativistic physics; he noted that general relativity follows an extraneous approach of mathematical physics: it does not follow the group structure of physics. Following this idea, we consider a new group of transformations which has PoincarèÕs group as its limit.…”