Analogy of spacetime as an elastic medium—Can we establish a thermal expansion coefficient of space from the cosmological constant Λ?

Abstract

This paper advances the state-of-the-art by extending the study of the analogy between the fabric of spacetime and elasticity. As no prior work exists about a potential spacetime thermal expansion coefficient [Formula: see text], we explore the analogy of general relativity with the theory of elasticity by considering the cosmological constant [Formula: see text] as an additional space curvature of the structure of space due to a thermal gradient coming from the cosmic web and the cold vacuum and we propose [Formula: see text] with [Formula: see text] being the curvature radius of the space fabric. It follows from this analogy and from the supposed space model consisting of thin sheets of Planck thickness [Formula: see text] curved by this thermal gradient [Formula: see text]T a possible thermal expansion coefficient of the equivalent elastic medium modeling the space [Formula: see text] of the order of [Formula: see text][Formula: see text]K[Formula: see text]. As spacetime and not only space must be considered in general relativity, this paper also proposes an innovative approach which consists in introducing into the interval ds2 of special relativity a temperature effect [Formula: see text] (entropy variations correlated with time laps, based on temperature variations affecting always physically the clocks) based on different thermal expansion coefficients for space and time with for the flow of time [Formula: see text]. With [Formula: see text] 106[Formula: see text]K, [Formula: see text], the associate time interval is [Formula: see text][Formula: see text]s and [Formula: see text]. The consequence of this hypothesis is that dark energy potentially becomes a thermal spacetime curvature [Formula: see text] with [Formula: see text] equal to [Formula: see text] or [Formula: see text] depending of the temperature, the thermal entropy variation of the universe, the Planck thickness and time, that increases since the Big bang, depending on thermal expansion coefficients for spacetime [Formula: see text] and [Formula: see text] as a function, respectively, of [Formula: see text], [Formula: see text], in opposition to spacetime curvature gravity due to mass/energy density as described in general relativity.