> home > APCTP Section
WIMPs with Low Reheating Temperature
Ki-Young Choi
File 1 : Vol28_No4_APCTP Section-1.pdf (0 byte)

DOI: 10.22661/AAPPSBL.2018.28.4.51

WIMPs with Low Reheating Temperature



The early Universe was dominated by hot and dense matters. It is expected that these matters were created after inflation by the decay of heavy particles known as the inflation field. At this stage, weakly interacting massive particles (WIMPs) can be produced and constitute dark matter. In this article, we review the various interesting phenomena of WIMP dark matters related to the reheating phase and observation today.


The homogeneity and isotropy of the present Universe requires that it had an accelerating phase in the early Universe, which is called cosmic inflation [1]. During this epoch, the Universe was cold and the most of the matters were diluted due to the fast expansion. After inflation, the decay of inflation produced light particles and the Universe became hot again. The temperature after inflation is called reheating temperature. The reheating temperature needs to have been several MeV higher than the temperature of big bang nucleosynthesis (BBN), not to disturb the abundance of the light elements such as hydrogen, helium, and lithium [2].

Dark matter is also generated during the reheating process or later from the thermal plasmas in the radiation-dominated epoch [3]. Dark matter plays an essential role for structure formation in the early Universe. Dark matter exists even now, around galaxies and galaxy clusters and its existence can be confirmed through gravitational observations.

The reheating temperature after inflation may change the behavior of the production and evolution of dark matter and consequently affect the evolution of the Universe and the formation of the structures. In other words, the observational constraints on dark matter from cosmological and astrophysical observations may be used to investigate and understand the physics of the early Universe.

In this article, we will focus on the low-reheating temperature and the interesting phenomena related to dark matter. First, we will discuss the non-thermal production of dark matter from the decay of heavy particles, which can explain the appropriate value of dark matter abundance and thus clarifies the present observations. Second, we will explain the mechanism for the generation of isocurvature perturbation at small scales, which is not erased during kinetic decoupling and thus enhances the abundance of small scale structures such as ultra compact mini-halos (UCMHs). Third, we will introduce a new method to constrain the low limit of reheating temperature by considering the dark matter density perturbations and possible astrophysical observations. And finally we will suggest a method for the baryogenesis that can accommodate with the low reheating temperature due to the annihilation of non-thermal dark matter.

Early Matter Domination and Reheating
The Universe is called 'radiation-dominated' (RD), when it was dominated by relativistic particles in the early Universe. However, even before this RD period, the possibility of early matter domination (EMD) existed, driven by heavy unstable particles that are very weakly interacting with thermal plasmas. One example is the inflaton field, which is the source of inflation. After inflation, the inflaton field oscillated and made the Universe matter-dominated. After the decay of the inflaton field into light particles, the Universe became RD again. This process of the transfer of energy of the inflaton field to radiation is called 'reheating'.

Fig. 1: The evolution of the energy density of a heavy particle (scalar) and thermal plasma (radiation) with a scale factor.

There are more examples where EMD could be created by different heavy unstable particles, such as the gravitino, moduli, axino, curvaton, etc. These particles were produced from thermal plasmas, decoupled in the early Universe, and soon dominated the Universe (EMD). After some time, they decayed into light particles. For heavy fields of around 1 TeV mass with gravitational interactions, their lifetime corresponds to around 1 second to 1,000 seconds, which is around BBN and may harm the abundance of light elements.

To avoid this severe problem and to save the Big Bang Universe, bigger mass or larger interactions are required to make the lifetime shorter than 1 second. This would also correspond to the cosmic temperature, which is around 1 MeV. This is another kind of reheating, different from the reheating after inflation. For this very weakly interacting particle, the reheating temperature is relatively small; around a MeV to GeV.

In Fig. 1, we show the evolution of the energy density of a heavy particle (scalar) and the thermal plasma (radiation) with a scale factor. Initially, scalar field dominated Universe and its energy density decreases as a cubic of the scale factor, and after its decay, the Universe is dominated by radiation and the energy density decreases to a fourth of the scale factor.

Dark Matter Production from Heavy Particle Decay
Weakly interacting massive particles (WIMPs) with mass m are initially in the thermal equilibrium and decouple later at a temperature of around T=m/25, when they are non-relativistic. For 100 GeV WIMP, this might give the appropriate value for dark matter and has been studied as a candidate for dark matter [4].

If the reheating temperature is lower then m/25, the WIMPs cannot be in equilibrium any longer and the abundance of WIMPs produced from thermal plasmas is too suppressed to explain the present amounts of dark matter.

However WIMPs can be produced directly from the decay of heavy particles. Since heavy particles dominate the Universe, the number density is big enough to make dark matter re-annihilate, even though the reheating temperature is below the freeze-out temperature of thermal WIMPs. We call this the non-thermal production of WIMPs.

The non-thermal production of WIMPs from a heavy axino was studied [5]. An axino is the supersymmetric partner of an axion field [6], which was introduced to explain the strong Charge-conjugation and Parity (CP) problem. Since axino coupling to the other particles is suppressed by the Peccei-Quinn scale, which is around 1010 GeV, the axinos decoupled early in the Universe when they were relativistic. When the temperature becomes smaller than the axino mass, then axinos can dominate the energy density of the Universe and then decay later. The decay of axinos can produce the lightest supersymmetric particles, e.g., neutralino WIMPs. The non-thermal neutralinos annihilate themselves until the rate becomes smaller than the expansion rate of the Universe, when the new value of the abundance of dark matter is determined with the proper magnitude to explain the relic density of dark matter.

In Fig. 2, we show an example of heavy axino decay and non-thermal neutralino WIMPs as dark matter. We can see that for the Peccei-Quinn scale with 1010 GeV, the axino mass between 100 GeV and 2 TeV might explain dark matter density for the thermal averaged annihilation cross section of WIMPs between 10-6 - 10-8 GeV-2.

Fig. 2: A non-thermal neutralino as dark matter in the plane of reheating temperature and axino mass in the Peccei-Quinn scale with 1010 GeV[5].

Generation of Isocurvature Perturbation and Dark Matter
Thermal WIMP dark matter is produced from thermal plasma and therefore its density perturbation is adiabatic. During the kinetic decoupling of WIMPs from thermal plasma, adiabatic perturbation is erased for scales smaller than the Hubble scale. This scale is related to the smallest size of the structures in the Universe [7].

However, in low-reheating temperature, this popular belief is not valid anymore because the isocurvature perturbation is generated during the early matter domination period when the heavy fields decay [8].

After thermal freeze-out of WIMPs in the early matter-domination epoch, WIMPs are not generated any more, while background radiation is still produced from decay. The ratio of the number density between dark matter and the radiation changes and the isocurvature perturbation of dark matter is generated at smaller scales than the Hubble size.

Fig. 3: The evolution of density perturbation of radiation (red), dark matter (blue) and the entropy perturbation (brown) [8].

In Fig. 3, we show the evolution of the perturbations of radiation (red), dark matter (blue) and the entropy perturbation (brown) [8]. Here we can see that the density perturbation of dark matter grows quickly at the time of reheating and the entropy perturbation grows together. The adiabatic part of dark matter oscillates and disappears; however, the isocurvature still remains constant.

This isocurvature perturbation is not erased during the kinetic decoupling of dark matter. The large isocurvature perturbations still remain and become the source of the formation of structures at small scales. The kinetic decoupling scale is no longer the scale for the smallest size of structure formation.

The isocurvature perturbation of dark matter at small scales can have various observational implications [8]. They enhance the number of structures of small scale objects, such as the ultra compact mini halos that are made of WIMPs. The density of WIMPs in the center of those objects is high and the WIMPs have a greater probability to annihilate and then to produce cosmic rays or gamma-rays. These are good signals to be observed by satellite telescopes. The WIMP annihilations also can produce neutrinos, which can be detected at neutrino detectors like IceCube in Antarctica. The radiation from the annihilations of WIMPs can modify the reionization process to leave an imprint in the cosmic microwave background anisotropy. They even can affect the microlensing light curve or the direct detection of dark matter.

Constraints on Low-Reheating Temperature
Before reheating, in many cases, there exists an early matter domination epoch (EMD), which is driven by the heavy unstable field. One of the properties in the matter domination epoch is that the density perturbation of non-relativistic matter decoupled from thermal plasma grows linearly with a scale factor, while that of relativistic matter just oscillates. The same growth of density perturbation of dark matter happens in the early matter domination epoch.

When dark matter exists during EMD, its density perturbation grows linearly. For WIMPs, during the reheating stage, the isocurvature perturbation is generated as mentioned in the previous section. Those density perturbations are not suppressed at later times in the Universe and help to enhance the formation of structures.

The direct result of the growth of the density perturbations of dark matter is the enhancement of small scale objects in the present Universe. One of these objects is the ultra compact mini halo (UCMH). UCMH has a mass similar to Earth and its inner density of dark matter is higher than the usual density of galactic halo dark matter. Dark matter annihilation into visible objects may affect astrophysical and/or gravitational phenomena in the present Universe.

For WIMP dark matter, their annihilation in the UCMH produces gamma-rays. These gamma rays can be observed by the Fermi Gamma-ray Space Telescope. However, the present non-observation of signals puts a bound on the fractional density of UCMHs. Consequently, this constraint on the number of UCMHs places a bound on the reheating temperature [9].

For very weakly interacting dark matter, which is already decoupled, density perturbation grows until the end of EMD. The growth starts when the scale enters the horizon during EMD. The enhanced density perturbations result in more abundance of UCMHs and can be constrained by the observations.

In Fig. 4, we show the future prospects for constraining the reheating temperature from gravitational lensing and pulsar timing [9]. The regions below the lines are disfavored when the scale of the observation is given as that number on the line. The orange region below is disfavored by BBN and Cosmic Microwave Background (CMB). From this figure we can find that, in the near future, the low-bound of the reheating temperature can be raised to 10 - 100 MeV.

Fig. 4: The low-bound on the reheating temperature from gravitational lensing and pulsar timing. The three lines with different colors used different constraints on the UCMH fraction. The regions above the lines are allowed. The orange region is disfavored by the BBN and CMB [9].

Non-thermal WIMP Baryogenesis
When the reheating temperature is smaller than the electro-weak transition temperature, then questions about the baryogenesis problem often arise, since it is not easy to accommodate the model of baryogenesis with such a low-reheating temperature.

Baryogenesis is a mechanism to explain the asymmetry between the matter and anti-matter in the Universe. In the present Universe, generally speaking, only matter exists; anti-matters exist, albeit rarely, in cosmic rays or in laboratories. The asymmetry between matter and antimatter is give by

Here nB is the baryon number density and s is the entropy density.

To generate asymmetry from an initially symmetric world, the following three Sakharov conditions must be satisfied [10]: 1. Baryon number violation; 2. C-symmetry and CP-symmetry violation; and 3. Out-of-thermal equilibrium.

One popular baryogenesis model uses heavy particle decay: baryogenesis in the grand-unified theories or leptogenesis using the heavy right-handed neutrinos. However this model needs high temperature in the early Universe such as a Grand-Unified Theory (GUT) scale or 1012 GeV, which is not applicable with low-reheating temperatures.

A new method was suggested recently for baryogenesis with low-reheating temperature, called non-thermal WIMP baryogenesis [11]. In this scenario, the WIMPs produced from the decay of heavy particles can reannihilate into light particles after the thermal freeze-out of WIMP dark matter. The non-thermally produced WIMPs are out-of-thermal equilibrium and therefore have the possibility to produce baryon asymmetry, if some annihilation modes violate the baryon symmetry, C- and CP-symmetry.

When the WIMPs are produced from the decay, their energy is around half of the mass of the decaying particle. Their interactions with thermal particles distribute the kinetic energy and soon the WIMPs are kinetically thermalized. However the number of WIMPs is still large enough to make reannihilation, when they satisfy

Here σAν is the thermal averaged annihilation cross-section of WIMPs and H is the Hubble expansion rate. After the reannihilations, the WIMPs freeze-out and the relic density is fixed as


At the same time, if CP and B-violating annihilation mode exists, then baryon asymmetry can be generated too [11]. The evolution of baryon asymmetry can be described by the Boltzmann equation,

Here epsilon is the CP asymmetry generated via the B-violating annihilation and the second term in the Right-Hand-Side (RHS) is the washout effect. The washout must be suppressed to preserve the baryon asymmetry produced.

There are two ways to suppress the washout effect. One is to suppress the cross section of washout, and the other is to suppress the number density of the relevant final states in the thermal equilibrium. The first one is difficult to obtain since the washout is usually the same magnitude as the B-violating annihilation. The second way can be realized by changing the mass of the final particle. For example, if psi particle mass mψ is large, then the washout can be suppressed exponentially. Here we used the second way to suppress washout effect.

Fig. 5: The evolution of the abundance of dark matter (blue) and the baryon asymmetry (red) with different B-violating annihilation cross section [11].

In Fig. 5, we show the evolution of the abundance of dark matter (blue) and baryon asymmetry (red) with a different b-violating annihilation cross section [11]. The horizontal axis is dark matter mass divided by temperature and the vertical axis is the abundance. Initially, dark matter is in thermal equilibrium until it becomes quasi-stable due to the decay from heavy particles. After that, the annihilation rearranges the abundance of dark matter to the final value consistent with dark matter relic density. Baryon asymmetry is generated during the annihilation of WIMP dark matter and becomes quasi-stable during EMD and finally frozen. Here we assumed that the washout effect is small. As can be seen in the figure, we can find that the correct abundance for dark matter and for baryon asymmetry can be obtained.

In Fig.6, we show the effect of washout by changing the mass of psi when the reheating temperature is 20 GeV and WIMP mass is 2TeV. We can see that the washout effect is negligible when the mass of psi is bigger than 500 GeV, which is roughly 25 times greater than the reheating temperature. For lower mass, the washout effect is significant and the baryon asymmetry is reduced.

Fig. 6: The effect of washout. The abundance of baryon asymmetry vs mass of psi. The green line is the value for the correct baryon asymmetry. The three lines are for different values of couplings of baryon number violation. The shaded region is disfavored due to the collider search for the psi particle [11].


The reheating temperature of the Universe can be low down to a few MeV. In this case, there are many problematic issues about dark matter and baryogenesis. In this article, we showed that these problems might be solved; the correct amount of dark matter can be produced and the baryon asymmetry can be explained. Furthermore, WIMPs with low-reheating temperature can have observational signals in the direct and indirect detection of dark matter. They can produce more UCMHs and affect gravitational lensing and pulsar timing. We are interested in investigating, ever further, the effects of dark matter in low-reheating temperature.

Acknowledgements: K.-Y.C. was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (NRF-2016R1A2B4012302). K.-Y.C. acknowledge the support from APCTP during the program of TRP, The origin and evolution of Universe and also by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science and ICT.


[1] R.Brout, F.Englert, E.Gunzig, Annals of Physics 115, 78-106 (1978); A.A.Starobinsky, JETP Lett. 30, 682-685 (1979); Physics Letters B 91, 99-102 (1980); K.Sato, Mon.Not.Roy.Astron.Soc. 195, 467-479 (1981); A.H.Guth, Physical Review D 23, 347-356 (1981).
[2] M.Kawasaki, K.Kohri, N.Sugiyama, PRL82, 4168 (1999); PRD62, 023506 (2000).
[3] H.Baer, K.-Y.Choi, J.Kim.E, L.Roszkowski, Phys. Report, 555 (2015).
[4] B.W.Lee, S.Weinberg, PRL 39, 165 (1977).
[5] K.-Y.Choi, J.Kim.E, H.M.Lee, O.Seto, PRD77, 123501 (2008).
[6] K.-Y.Choi, J.Kim.E, L.Roszkowski, JKPS63 (2013).
[7] S. Hofmann, D. J. Schwarz, and H. Stöcker, Phys. Rev. D 64, 083507 (2001); A. M. Green, S. Hofmann, and D. J. Schwarz, J. Cosmol. Astropart. Phys. 08 (2005) 003.
[8] K.-Y.Choi, J.-O.Gong, C.S.Shin, PRL115, 211302 (2015).
[9] K.-Y.Choi, T.Takahashi, PRD96, 041301 (2017).
[10] A.D.Sakharov, PIsma Zh.Eksp.Teor.Fiz.5,32 (1967).
[11] K.-Y.Choi, S.K.Kang, J.Kim, PLB (2018).


Ki-Young Choi is an assistant professor in the physics department of Sungkyunkwan University, Korea. After receiving a PhD from Seoul National University, he worked at Sheffield University, Madrid Autonoma University, Pusan National University, APCTP (Asia Pacific Center for Theoretical Physics), KASI (Korea Astronomy and Space Science Institute), and Chonnam National University before joining Sungkyunkwan University in 2017. His research field is theoretical particle physics and cosmology.