Abstract. In Dantean cosmography the Universe is described as a series of concentric spheres with all the known planets embedded in their rotation motion, the Earth located at the centre and Lucifer at the centre of the Earth. Beyond these “celestial spheres”, Dante represents the “angelic choirs” as other nine spheres surrounding God. The rotation velocity increases with decreasing distance from God, that is with increasing Power (Virtù). We show that, adding Power as an additional fourth dimension to space, the modern equations governing the expansion of a closed Universe (i. e. with the density parameter
0>1) in the space-time, can be applied to the medieval Universe as imaged by Dante in his Divine Comedy. In this representation the Cosmos acquires a unique description and Lucifer is not located at the centre of the hyperspheres.

PACS: 95.90.+v; 98.80.Bp. Keywords: History and philosophy of astronomy – Cosmology.

The Dantean cosmography started about 600 years ago, when the medieval concept of the Universe was already fading away. It is probably not a mere coincidence that the first scholars to deal with the problem at the end of XVth century were two architects who accepted the challenge to visualise those sites, their shapes and sizes which had been poetically described by Dante in his Divine Comedy. The first one was a young Filippo Brunelleschi, who analysed the “site and the size” (il sito e le misure) of all the locations reported in the Divine Comedyi; the second one, Antonio di Tuccio Manettiii,iii a specialist in perspective studies, derived the shape and size of the Hell examining
Dante’s poem. Even if both the architects never published their studies, their conclusions are at the basis of Hell’s iconography which can found in the XVIth century editions of the Divine Comedyiv . This iconography, which continues nowadays, represents the Hell as a cone formed when Lucifer fell from the Sky. The apex of the cone is at the centre of the Earth, where Lucifer remained jammed, with his head and feet respectively in the boreal and austral hemisphere. The issue was so important in the XVIth century that even a young Galileo Galilei got involved and in 1587 he delivered two lectures on the Dante’s Hell at the Accademia Fiorentinav. By a close scrutiny of Dante’s verses, in these lectures Galileo worked out the size of the Hell, as well as Lucifer’s. Although the Hell has been abundantly illustrated for six centuries, it turns out that this is not the case for the Paradise. To our knowledge, Michelangelo Cactanivi in 1855 was the first to publish a series of woodcuts specifically intended to illustrate Dante’s cosmography, Paradise included. It is noticeable that all the ensuing representations faithfully trace Cactani’s scheme (figure 1). In the Divine Comedy Dante figures the Empyrean in a specular manner with respect to the celestial spheres. In the Empyrean the celestial spheres correspond to nine “angelic choirs” orbiting around God with velocities that increase with decreasing distance from the centervii.
At first sight, this is the opposite of what happens for the celestial spheres whose velocities increase with increasing the distance from their center of rotation, the Earth. However, Dante clarifies that
the parameter which drives the rotation speed is, in both cases, the Power, i.e. the distance from God, called by Dante “Virtù”viii. Therefore all the spheres of the Universe, both the celestial and those of the Empyrean, rotate with velocities that increase with decreasing the distance from God.
It has been already recognized that, in order to represent the whole medieval Universe (Earth, planets, Hell, Empyrean and their rotation), Dante was forced to add a fourth spatial dimension to the usual threeix,x.
In this work we have investigated whether the equations of the space-time could be translated into the Dantean space-power.

Dynamics of the expansion of the Universe (Newtonian cosmology) For the time being it is not necessary to make use of General Relativity. Let us consider the expansion of the Universe as it can be derived in Newtonian cosmology: ) ( ) ( 3 4 ) ( t a t G t a 


&&

or equivalently 2 2 2 ) ( ) ( 3 8 Kc t a t G a 


&

where a(t) is the cosmic scale factor, (t) is the mass density, G is the gravitational constant and Kc2 is an integration constant. With a coordinate transformation from space-time to space-power and substituting a with R. It follows that 2 1 2 / 1 1 C C R V R 

where R (V) is the radius of the celestial spheres and the angelic choirs as a function of the power V.

The Dantean Universe in the space-power manifestly corresponds to a closed Universe in the space- time (K>0 case),