Constraining Tsallis corrections to photon reheating from electron–positron annihilation: a phenomenological approach

Abstract In this work we generalize the entropy transfer from electron–positron annihilation to photons in the early Universe. The generalization is implemented within the Tsallis formalism by using generalized distribution functions derived from Curado–Tsallis constraints. Through this deformation, the entropy density of the electromagnetic sector is modified, while the photon component is kept extensive. Therefore, the nonextensive correction is introduced only in the $$e^-e^+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>-</mml:mo> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>+</mml:mo> </mml:msup> </mml:mrow> </mml:math> pairs. This affects the entropic degrees of freedom before electron–positron annihilation and consequently modifies the temperature ratio $$T_\nu /T_\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>ν</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>γ</mml:mi> </mml:msub> </mml:mrow> </mml:math> . The resulting correction is then mapped into an effective value of $$N_{{\textrm{eff}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>N</mml:mi> <mml:mtext>eff</mml:mtext> </mml:msub> </mml:math> within the instantaneous decoupling approximation. Comparing this effective thermodynamic estimate with CMB+BAO data, and using BBN only as an illustrative Gaussian comparison, we obtain an order-of-magnitude phenomenological interval for the nonextensive parameter. The result should not be interpreted as a precision neutrino decoupling constraint, since a full treatment would require solving the kinetic evolution of the neutrino sector, including non-instantaneous decoupling, finite-temperature QED effects and possible spectral distortions.