Ideal Gas with a Varying (Negative Absolute) Temperature: an Alternative to Dark Energy?

Abstract

The present work is an attempt to investigate whether the evolutionary history of the Universe from the offset of inflation can be described by assuming the cosmic fluid to be an ideal gas with a specific gas constant but a varying negative absolute temperature (NAT). The motivation of this work is to search for an alternative to the “exotic” and “supernatural” dark energy (DE). In fact, the NAT works as an “effective quintessence” and there is need to deal neither with exotic matter like DE nor with modified gravity theories. For the sake of completeness, we release some clarifications on NATs in Section 3 of the paper.

Appendix A

Proposition

Negative absolute temperatures are hotter than positive absolute temperatures.

Proof

Consider two bodies (1 ∖ & 2) at different temperatures (T₁∖ & T₂)in contact with one another. Suppose there is a transfer of a small amountof heat Q from body 1 to body 2, which changes the entropy of body 1 by− Q/T₁and that ofbody 2 by Q/T₂, so that the total change in entropy is

$$dS=Q\left( \frac{1}{T_{2}}-\frac{1}{T_{1}}\right). $$

The above quantity must be positive according to the second law. Now, if T₁ < 0 and T₂ > 0, then $\frac {1}{T2}-\frac {1}{T1}>0$, which implies that body 1 (with a negative temperature) can transfer heat to body 2 (with a positive temperature), but not the other way around. Hence, negative absolute temperatures are hotter than positive absolute temperatures. □