In the presence of a light weakly interacting massive particle , a WIMP with mass m _ { \chi } \lesssim 30 { MeV } , there are degeneracies among the nature of the WIMP ( fermion or boson ) , its couplings to the standard model particles ( to electrons , positrons , and photons , or only to neutrinos ) , its mass m _ { \chi } , and the number of equivalent ( additional ) neutrinos , \Delta { N } _ { \nu } .
These degeneracies can not be broken by the cosmic microwave background ( CMB ) constraint on the effective number of neutrinos , { N } _ { eff } .
However , since big bang nucleosynthesis ( BBN ) is also affected by the presence of a light WIMP and equivalent neutrinos , complementary BBN and CMB constraints can help to break some of these degeneracies .
In a previous paper [ 1 ] the combined BBN and Planck [ 2 ] CMB constraints were used to explore the allowed ranges for m _ { \chi } , \Delta { N } _ { \nu } , and { N } _ { eff } in the case where the light WIMPs annihilate electromagnetically ( EM ) to photons and/or e ^ { \pm } pairs .
In this paper the BBN predictions for the primordial abundances of deuterium and ^ { 4 } He ( along with ^ { 3 } He and ^ { 7 } Li ) in the presence of a light WIMP that only couples ( annihilates ) to neutrinos ( either standard model – SM – only or both SM and equivalent ) are calculated .
Recent observational estimates of the relic abundances of D and ^ { 4 } He are used to limit the light WIMP mass , the number of equivalent neutrinos , the effective number of neutrinos , and the present Universe baryon density ( \Omega _ { B } h ^ { 2 } ) .
Allowing for a neutrino coupled light WIMP and \Delta { N } _ { \nu } equivalent neutrinos , the combined BBN and CMB data provide lower limits to the WIMP mass that depend very little on the nature of the WIMP ( Majorana or Dirac fermion , real or complex scalar boson ) , with a best fit m _ { \chi } \gtrsim 35 { MeV } , equivalent to no light WIMP at all .
The analysis here excludes all neutrino coupled WIMPs with masses below a few MeV , with specific limits varying from 4 to 9 MeV depending on the nature of the WIMP .
In the absence of a light WIMP ( either EM or neutrino coupled ) , BBN alone prefers \Delta { N } _ { \nu } = 0.50 \pm 0.23 , favoring neither the absence of equivalent neutrinos ( \Delta { N } _ { \nu } = 0 ) , nor the presence of a fully thermalized sterile neutrino ( \Delta { N } _ { \nu } = 1 ) .
This result is consistent with the CMB constraint , { N } _ { eff } = 3.30 \pm 0.27 [ 2 ] , constraining “ new physics ” between BBN and recombination .
Combining the BBN and CMB constraints gives \Delta { N } _ { \nu } = 0.35 \pm 0.16 and { N } _ { eff } = 3.40 \pm 0.16 .
As a result , while BBN and the CMB combined require \Delta { N } _ { \nu } \geq 0 at \sim 98 \% confidence , they disfavor \Delta { N } _ { \nu } \geq 1 at > 99 \% confidence .
Adding the possibility of a neutrino-coupled light WIMP extends the allowed range slightly downward for \Delta { N } _ { \nu } and slightly upward for { N } _ { eff } simultaneously , while leaving the best-fit values unchanged .