Dynamic freeze-in: impact of thermal masses and cosmological phase transitions on dark matter production
HJE
Dynamic freeze-in: impact of thermal masses and cosmological phase transitions on dark matter production
Michael J. Baker 0 1 3
Moritz Breitbach 0 1 2
Joachim Kopp 0 1 2
Lukas Mittnacht 0 1 2
Johannes Gutenberg University 0 1
Field Theory
0 Staudingerweg 7 , 55099 Mainz , Germany
1 8057 Zurich , Switzerland
2 PRISMA Cluster of Excellence & Mainz Institute for Theoretical Physics
3 Physik-Institut, Universitat Zurich
The cosmological abundance of dark matter can be signi cantly in uenced by the temperature dependence of particle masses and vacuum expectation values. We illustrate this point in three simple freeze-in models. The rst one, which we call kinematically induced freeze-in, is based on the observation that the e ective mass of a scalar temporarily becomes very small as the scalar potential undergoes a second order phase transition. This opens dark matter production channels that are otherwise forbidden. The second model we consider, dubbed vev-induced freeze-in, is a fermionic Higgs portal scenario. Its scalar sector is augmented compared to the Standard Model by an additional scalar singlet, S, which couples to dark matter and temporarily acquires a vacuum expectation value (a twostep phase transition or \vev ip- op"). While hSi 6= 0, the modi ed coupling structure in the scalar sector implies that dark matter production is signi cantly enhanced compared to the hSi = 0 phases realised at very early times and again today. The third model, which we call mixing-induced freeze-in, is similar in spirit, but here it is the mixing of dark sector fermions, induced by non-zero hSi, that temporarily boosts the dark matter production rate. For all three scenarios, we carefully dissect the evolution of the dark sector in the early Universe. We compute the DM relic abundance as a function of the model parameters, emphasising the importance of thermal corrections and the proper treatment of phase transitions in the calculation.
Beyond Standard Model; Cosmology of Theories beyond the SM; Thermal
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1 Introduction
thresholds
2.1
2.2
2.3
3.1
3.2
3.3
Toy model
The e ective potential
Results and discussion
3
Vev-induced production with a vev ip- op
Toy Model
The e ective potential & the vev ip- op
Dark matter freeze-in and relic abundance
4
5
Vev-induced mixing with a vev ip- op
Summary and conclusions
A Computation of the e ective potential
B Boltzmann equations
B.1 Freeze-in via decay: B1 !
B2
B.2 Freeze-in via annihilation: B1B2 !
B3
2
Kinematically induced freeze-in: temperature-dependent masses and
1
Introduction
\In order for the light to shine so brightly, the darkness must be present." This quote,
attributed to Sir Francis Bacon, subsumes much of modern day cosmology. The Universe
as we know it, with its abundance of bright galaxies, could not have formed without the
presence of large amounts of dark matter (DM). DM drives the formation of structure; the
gravitational collapse of primordial density
uctuations leads to dense objects like galaxy
clusters, galaxies, and stars, with at least one of the latter harbouring life. Even though
one of the lifeforms likes to describe itself as intelligent, it is still very much in the dark
about dark matter, its origin and its nature.
For a long time, the best-motivated scenario to understand DM has been the Weakly
Interacting Massive Particle (WIMP) scenario: DM particles are hypothesised to be heavy
(mDM & 100 GeV) and to have weak, but non-negligible interactions with Standard Model
(SM) particles. In the very early Universe, these interactions keep the DM and SM sectors
{ 1 {
multi-pronged search program [2{8], motivates the study of alternative mechanisms [9{20].
Freeze-in models assume that the initial DM abundance after in ation was zero and that
DM particles couple so weakly to the particles in the thermal bath that they never reach
thermal equilibrium [17{21]. Consequently, DM annihilation does not determine the relic
abundance. Instead, the observed abundance is the result of processes with DM in the nal
state, typically at x ' 1{5. The small coupling between DM and SM particles also implies
a signi cantly greater challenge for all experimental probes of the nature of DM.
In this paper, we consider the impact of nite temperature e ects on the DM abundance
in freeze-in models. Such e ects are manifold: rst, particle masses receive corrections from
thermal loops, implying that the kinematics of DM production is in general T -dependent.
Certain production channels may be open during some epochs of cosmological history, but
kinematically closed during others. Closely related to this e ect is the T dependence of
the e ective scalar potential V e , which implies that not only scalar masses (the second
derivatives of V e ), but also their vacuum expectation values (vevs) change with time in the
early Universe. These vevs, in turn, will a ect gauge boson and fermion masses (of course,
gauge boson and fermion masses also receive direct correct (...truncated)