Constraints on Tsallis Cosmology from Big Bang Nucleosynthesis and the Relic Abundance of Cold Dark Matter Particles

Understand

By employing Tsallis' extensive but non-additive $\delta$-entropy, we formulate the first two laws of thermodynamics for gravitating systems.

• By invoking Carath\'{e}odory's principle, we pay particular attention to the integrating factor for the heat one-form.
• We show that the latter factorizes into the product of thermal and entropic parts, where the entropic part cannot be reduced to a constant, as is the case in conventional thermodynamics, due to the non-additive nature of $S_{\delta}$.
• The ensuing two laws of thermodynamics imply a Tsallis cosmology, which is then applied to a radiation-dominated universe to address the Big Bang nucleosynthesis and the relic abundance of cold dark matter particles.