Unitarity limits on thermal dark matter in (non-)standard cosmologies
Disha Bhatia, Satyanarayan Mukhopadhyay
Abstract
A bstract Using the upper bound on the inelastic reaction cross-section implied by S-matrix unitarity, we derive the thermally averaged maximum dark matter (DM) annihilation rate for general k → 2 number-changing reactions, with k ≥ 2, taking place either entirely within the dark sector, or involving standard model fields. This translates to a maximum mass of the particle saturating the observed DM abundance, which, for dominantly s -wave annihilations, is obtained to be around 130 TeV, 1 GeV, 7 MeV and 110 keV, for k = 2 , 3 , 4 and 5, respectively, in a radiation dominated Universe, for a real or complex scalar DM stabilized by a minimal symmetry. For modified thermal histories in the pre-big bang nucleosynthesis era, with an intermediate period of matter domination, values of reheating temperature higher than $$ \mathcal{O}(200) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:mn>200</mml:mn> </mml:mfenced> </mml:math> GeV for k ≥ 4, $$ \mathcal{O}(1) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:mn>1</mml:mn> </mml:mfenced> </mml:math> TeV for k = 3 and $$ \mathcal{O}(50) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:mn>50</mml:mn> </mml:mfenced> </mml:math> TeV for k = 2 are strongly disfavoured by the combined requirements of unitarity and DM relic abundance, for DM freeze-out before reheating.