  This paper advances the state of the art by extending the study of the
analogy between the spacetime fabric and elasticity.As no prior work exists
about a potential spacetime thermal expansion coeff Lambda, we explore the
analogy of GR with the elasticity theory by considering the cosmological
constant Lambda as an additional space curvature of the space frame due to a
thermal gradient coming from the cosmic web and the cold vacuum and we propose
((AlphaxDeltaT)/e)^2=(1/Ro)^2=Lambda with Ro 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 Lp curved by this thermal
gradient DeltaT a possible thermal expansion coefficient of the equivalent
elastic medium modeling the space AlphaS=(LpxLambda^(1/2))/DeltaT of the order
of Alphas(QFT)=1.16x10-6 K-1.As space-time and not only space must be
considered in GR, this paper also proposes an innovative approach which
consists in introducing into the interval ds^2 of special relativity a temp
effect T,(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
t:cxt/cxnxtau=(kBxt)/nxhxDeltaT=AlphatxDeltaT.With T=10^6 K, n=1, the associate
time interval is 4.8x10^-17s and Alphat=1.0x10^-6K^-1.The consequence of these
hypothesis is that dark energy potentially becomes a thermal space-time
curvature ((AlphafxT)/Lp)^2 with f equal to s or t depending of the
temperature, the thermal entropy variation of the universe, the Planck
thickness and time, that increases since the Bigbang, depending on thermal
expansion coefficients for space-time Alphas and Alphat as a function
respectively of Lambda, kB/hxt, in opposition to space-time curvature gravity
due to mass/energy density as described in GR.
