Analogy of space time as un elastic medium -- Can we establish a thermal expansion coefficient of space from the cosmological constant Lambda?

TL;DR

This paper explores the analogy between spacetime and elastic media to propose a thermal expansion coefficient of space related to the cosmological constant Lambda, suggesting a thermal origin for dark energy and extending GR concepts.

Contribution

It introduces a novel analogy between spacetime and elasticity, proposing a thermal expansion coefficient of space derived from Lambda, and incorporates thermal effects into spacetime intervals.

Findings

Proposes a thermal expansion coefficient of space AlphaS ≈ 1.16×10^-6 K^-1.

Suggests dark energy as a thermal space-time curvature related to temperature variations.

Introduces a thermal effect T into the spacetime interval, linking entropy variations to time laps.

Abstract

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.