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

By employing Tsallis’ extensive but non-additive [Formula: see text]-entropy, we formulate the first two laws of thermodynamics for gravitating systems. By invoking Carathéodory’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 [Formula: see text]. 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. It is demonstrated that the Tsallis cosmology with the scaling exponent [Formula: see text] ∼1.499 (or equivalently, the anomalous dimension [Formula: see text] ∼0.0013) consistently describes both the abundance of cold dark matter particles and the formation of primordial light elements, such as deuterium [Formula: see text] and helium [Formula: see text]. Salient issues, including the zeroth law of thermodynamics for the [Formula: see text]-entropy and the lithium [Formula: see text] problem, are also briefly discussed.