Mirror matter is a self-collisional dark matter candidate. If exact mirror
parity is a conserved symmetry of the nature, there could exist a parallel
hidden (mirror) sector of the Universe which has the same kind of particles and
the same physical laws of our (visible) sector. The two sectors interact each
other only via gravity, therefore mirror matter is naturally "dark". The most
promising way to test this dark matter candidate is to look at its
astrophysical signatures, as Big Bang nucleosynthesis, primordial structure
formation and evolution, cosmic microwave background and large scale structure
power spectra.Comment: 9 pages, 2 figure

Joseph Cugnon

Lansberg Jean-Philippe

Nicolas Matagne

P. Ciarcelluti

English

arXiv

Crossref

Astrophysical tests of mirror dark matter

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E-mail: paolo.ciarcelluti@ulg.ac.be
Astrophysical tests of
mirror dark matter
P. Ciarcelluti
Université de Liège, Département de Physique B5, Sart Tilman,B-4000 LIEGE 1, Belgium
Abstract.
Mirror matter is a self-collisional dark matter candidate. If exact mirror parity is a
conserved symmetry of the nature, there could exist a parallel hidden (mirror) sector of the
Universe which has the same kind of particles and the same physical laws of our (visible)
sector. The two sectors interact each other only via gravity, therefore mirror matter is
naturally “dark”. The most promising way to test this dark matter candidate is to look
at its astrophysical signatures, as Big Bang nucleosynthesis, primordial structure formation
and evolution, cosmic microwave background and large scale structure power spectra.
Keywords: dark matter, structure formation, Big Bang nucleosynthesis, cosmic microwave
background, large scale structure
PACS: 26.35.+c, 95.35.+d, 98.65.Dx, 98.70.Vc, 98.80.-k
1. INTRODUCTION
The idea that there may exist a hidden mirror sector of particles and interactions
with exactly the same properties as our visible world was suggested long time ago
by Lee and Yang [1], and the model with exact parity symmetry interchanging
corresponding fields of two sectors was proposed many years later by Foot at
al. [1]. The two sectors communicate with each other only via gravity1. A discrete
symmetry G↔G′ interchanging corresponding fields of G and G′, so called mirror
parity, guarantees that two particle sectors are described by identical Lagrangians,
with all coupling constants (gauge, Yukawa, Higgs) having the same pattern. As a
consequence the two sectors should have the same microphysics. Once the visible
matter is built up by ordinary baryons, then the mirror baryons would constitute
dark matter in a natural way, since they interact with mirror photons, but not
interact with ordinary photons.
The phenomenology of mirror matter was studied in several papers (for an
extended list see the bibliografy of ref. [2]), in particular the implications for Big
Bang nucleosynthesis [3, 4], primordial structure formation and cosmic microwave
background [5, 6], large scale structure of the Universe [7, 8], microlensing events
(MACHOs) [9, 10].
If the mirror (M) sector exists, then the Universe along with the ordinary (O)
1 There could be other interactions, as for example the kinetic mixing between O and M photons,
but they are negligible for the present study.
particles should contain their mirror partners, but their densities are not the same
in both sectors. In fact, the BBN bound on the effective number of extra light
neutrinos implies that the M sector has a temperature lower than the O one, that
can be naturally achieved in certain inflationary models [11]. Then, two sectors
have different initial conditions, they do not come into thermal equilibrium at
later epoch and they evolve independently, separately conserving their entropies,
and maintaining approximately constant the ratio among their temperatures.
All the differences with respect to the ordinary world can be described in terms
of only two free parameters in the model,
x≡
(
s′
s
)1/3
≈
T ′
T
; β ≡ Ω′b/Ωb , (1)
where T (T ′), Ωb (Ω
′
b), and s (s
′) are respectively the ordinary (mirror) photon
temperature, cosmological baryon density, and entropy density. The bounds on the
mirror parameters are x < 0.7 and β > 1, the first one coming from the BBN limit
and the second one from the hypothesis that a relevant fraction of dark matter is
made of mirror baryons.
As far as the mirror world is cooler than the ordinary one, x < 1, in the mirror
world all key epochs (as are baryogenesis, nucleosynthesis, recombination, etc.)
proceed in somewhat different conditions than in ordinary world. Namely, in the
mirror world the relevant processes go out of equilibrium earlier than in ordinary
world, which has many far going implications.
2. THERMODYNAMICS OF THE EARLY UNIVERSE
Since ordinary and mirror sectors have the same microphysics, it is obvious that
the neutrino decoupling temperature TDν is the same in both of them, that
is TDν = T
′
Dν . We use this fact together with the entropy conservation to find
equations which will give the mirror photon temperature T ′ and the ordinary and
mirror thermodynamical quantities corresponding to any values of the ordinary
photon temperature T . From them it is possible to work out the total effective
number of degrees of freedom (DOF) in both sectors, which can be, as common
in the literature, expressed in terms of total effective neutrino number Nν . The
presence of the other sector indeed, leads in both sectors to the same effects of
having more particles.
At temperatures we are interested (below ∼ 10 MeV) we can in general use the
following equations derived from the conservations of separated entropies:
22
21
=
7
8
qe(T
′)+ qγ
7
8
qν
(
T ′
T ′ν
)3
;
22
21
=
7
8
qe(T )+ qγ
7
8
qν
(
T
Tν
)3
, (2)
and neglecting the entropy exchanges between the sectors (imposing x constant):
x3 =
s′ ·a3
s ·a3
=
[
7
8
qe(T
′)+ qγ
]
T ′3+ 7
8
qνT
′
ν
3
[
7
8
qe(T )+ qγ
]
T 3+ 7
8
qνT 3ν
, (3)
TABLE 1. Effective Nν in the ordinary sector.
T(MeV) standard x= 0.1 x= 0.3 x= 0.5 x= 0.7
5 3.00000 3.00063 3.04989 3.38430 4.47563
0.005 3.00000 3.00074 3.05997 3.46270 4.77751
where s is the entropy density, a the scale factor, qi the entropic DOF of species i.
At T ≃ TDν (T
′
Dν) ordinary (mirror) neutrinos decouple and soon after ordinary
(mirror) electrons and positrons annihilate.
The mirror world must be colder than the ordinary one and therefore the neutrino
decoupling takes place before in the mirror sector. We can split the early Universe
evolution in three phases.
1) T > TDν′ : photons and neutrinos are in thermal equilibrium in both worlds, that
is Tν = T , T
′
ν = T
′.
2) TDν < T ≤ TDν′: at T ≃ TDν′ M neutrinos decouple and soon after M electrons
and positrons annihilate, raising the M photon temperature (T ′ 6=T ′ν). Nevertheless,
O photons and neutrinos still have the same temperature (T = Tν).
3) T ≤ TDν : at T ≃ TDν O neutrinos decouple and soon after O electrons and
positrons annihilate, raising the O photon temperature (T 6= Tν).
We solved numerically equations (2) and (3) in order to work out the total, ordi-
nary and mirror numbers of entropic (q) and energetic (g) DOF at any temperature
T . The corresponding number of neutrinos Nν is found assuming that all particles
contributing to the Universe energy density, to the exclusion of electrons, positrons
and photons, are neutrinos; in formula that means
Nν =
ḡ−ge±(T )−gγ
7
8
·2
·
(
T
Tν
)4
. (4)
In table 1 we report the asymptotic numerical results before (T = 5 MeV) and
after (T = 0.005 MeV) BBN for different values of x. We stress that the standard
value Nν = 3 is the same at any temperatures, while a distinctive feature of the
mirror scenario is that the number of neutrinos raises with the temperature and
with x. Anyway, this effect is not a problem; on the contrary it may be useful since
recent data fits give indications for a number of neutrinos at recent times higher
than at BBN.
It is possible to approximate the difference between the effective numbers of
neutrinos before and after the BBN process with the the follwing expression:
Nν(T ≪ Tanne±)−Nν(T ≫ TDν) = x
4 ·
1
7
8
·2

10.75−3.36
(
11
4
)
4
3

≃ 1.25 ·x4 . (5)
The effective number of neutrinos in the mirror sector can be worked out in a
similar way, and the values (much higher than the ordinary ones) are reported in
table 2.
TABLE 2. Effective Nν in the mirror sector.
T(MeV) x= 0.1 x= 0.3 x= 0.5 x= 0.7
5 61432 761.4 101.3 28.59
0.005 74011 917.0 121.4 33.83
TABLE 3. Light elements produced in the ordinary sector.
standard x= 0.1 x= 0.3 x= 0.5 x= 0.7
4He 0.2483 0.2483 0.2491 0.2538 0.2675
D/H (10−5) 2.554 2.555 2.575 2.709 3.144
3He/H (10−5) 1.038 1.038 1.041 1.058 1.113
7Li/H (10−10) 4.549 4.548 4.523 4.356 3.871
3. BIG BANG NUCLEOSYNTHESIS
As we have seen, the presence of the mirror sector can be parametrized in terms of
extra DOF number or extra neutrino families; therefore, since the physical processes
involved in BBN are not affected by the mirror sector, we can use and modify a
pre-existing numerical code to work out the light elements production.
The number of DOF enters the program in terms of neutrino species number;
this quantity is a free parameter, but instead of using the same number during
the whole BBN process, we use the variable Nν(T,x) numerically computed in the
previous section. The only parameter of the mirror sector which affects ordinary
BBN is x; the baryon ratio β does not induce any changes on the production of
ordinary nuclides, but it plays a crucial role for the mirror nuclides production.
In table 3 we report the final abundances (mass fractions) of the light elements
4He, D, 3He and 7Li produced in the ordinary sector at the end of BBN process
(at T ∼ 8 · 10−4 MeV) for several x values and compared with the standard. We
can easily infer that for x < 0.3 the light element abundances do not change more
than a few percent, and the difference between the standard and x= 0.1 is of order
10−4 or less.
Even mirror baryons undergo nucleosynthesis via the same physical processes
than the ordinary ones, thus we can use the same numerical code also for the M
nucleosynthesis. Mirror BBN is affected also by the second mirror parameter, that
is the M baryon density (introduced in terms of the ratio β =Ω′b/Ωb ∼ 1÷5), which
raises the baryon to photon ratio η′ = βx−3η.
The results are reported in table 4, which is the analogous of table 3 but for a
mirror sector with β = 5. We can see that BBN in the mirror sector is much more
different from the standard than the ordinary sector one. This is a consequence
of the high ordinary contribution to the number of total mirror DOF, which
scales as ∼ x−4 (while in the ordinary sector the mirror contribution is almost
insignificant, since it scales as ∼ x4). Hence, in this case the M helium abundance
should be much larger than that of the O helium, and for x < 0.5 the M helium
gives a dominant mass fraction of the dark matter of the Universe. This is a very
TABLE 4. Light elements produced in the mirror sector (β = 5).
x= 0.1 x= 0.3 x= 0.5 x= 0.7
4He 0.8051 0.6351 0.5035 0.4077
D/H (10−5) 1.003 ·10−7 4.838 ·10−4 6.587 ·10−3 3.279 ·10−2
3He/H (10−5) 0.3282 0.3740 0.4172 0.4691
7Li/H (10−10) 1.996 ·103 3.720 ·102 1.535 ·102 0.7962 ·102
interesting feature, because it means that mirror sector can be a helium dominated
world, with important consequences on star formation and evolution [9], and other
related astrophysical aspects.
4. STRUCTURE FORMATION
The important moments for the structure formation are related to the matter-
radiation equality (MRE) and to the matter-radiation decoupling (MRD) epochs.
The MRE occurs at the redshift
1+ zeq =
Ωm
Ωr
≈ 2.4 ·104
Ωmh
2
1+x4
. (6)
Therefore, for x≪ 1 it is not altered by the additional relativistic component of
the M sector. The mirror MRD temperature T ′dec can be calculated following the
same lines as in the O one, obtaining T ′dec ≈ Tdec, and hence
1+ z′dec ≃ x
−1(1+ zdec)≃ 1100 x
−1 , (7)
so that the MRD in the M sector occurs earlier than in the O one.
Moreover, for values x < xeq ≃ 0.046 (Ωmh
2)
−1
, the mirror photons would de-
couple yet during the radiation dominated period. This critical value plays an
important role in our further considerations, where we distinguish between two
cases: x > xeq and x < xeq. For typical values of Ωmh
2 we obtain xeq ≃ 0.3.
The relevant scale for gravitational instabilities is the mirror Jeans mass, defined
as the minimum scale at which, in the matter dominated epoch, sub-horizon sized
perturbations start to grow. In the case x > xeq (where the mirror decoupling
happens after the matter-radiation equality) its maximum value is reached just
before the M decoupling, and is expressed in terms of the O one as
M ′J,max ≈ β
−1/2
(
x4
1+x4
)3/2
·MJ,max , (8)
which, for β ≥ 1 and x < 1, means that the Jeans mass for the M baryons is lower
than for the O ones, with implications for the structure formation. If, e.g., x= 0.6
and β = 2, then M ′J ∼ 0.03MJ. We can also express the same quantity in terms of
Ωb, x and β, in the case that all the dark matter is in the form of M baryons, as
M ′J(a
′
dec)≈ 3.2 ·10
14M⊙ β
−1/2(1+β)−3/2
(
x4
1+x4
)3/2
(Ωbh
2)−2 . (9)
For the case x < xeq, the mirror decoupling happens before the matter-radiation
equality. In this case we obtain for the highest value of the Jeans mass just before
decoupling the expression
M ′J(a
′
dec)≈ 3.2 ·10
14M⊙ β
−1/2(1+β)−3/2
(
x
xeq
)3/2(
x4
1+x4
)3/2
(Ωbh
2)−2 . (10)
In case x = xeq, the expressions (9) and (10), respectively valid for x ≥ xeq and
x ≤ xeq, are coincident, as we expect. If we consider the differences between the
highest mirror Jeans mass for the particular values x= xeq/2, x= xeq and x= 2xeq,
we obtain the following relations:
M ′J,max(xeq/2)≈ 0.005M
′
J,max(xeq) ; M
′
J,max(2xeq)≈ 64M
′
J,max(xeq) . (11)
Density perturbations in M baryons on scales M ≥M ′J,max, which enter the horizon
at z ∼ zeq, undergo uninterrupted linear growth. Perturbations on scales M ≤
M ′J,max start instead to oscillate after they enter the horizon, thus delaying their
growth till the epoch of M photon decoupling.
As occurs for perturbations in the O baryonic sector, also the M baryon density
fluctuations should undergo the strong collisional Silk damping around the time of
M recombination, so that the smallest perturbations that survive the dissipation
will have the mass
M ′S ∼ [f(x)/2]
3(βΩbh
2)−5/41012 M⊙ , (12)
where f(x) = x5/4 for x ≥ xeq, and f(x) = (x/xeq)
3/2x5/4eq for x ≤ xeq. For x ∼ xeq
we obtain M ′S ≈ 10
7(Ωbh
2)−5M⊙ ∼ 10
10M⊙, a typical galaxy mass.
5. COSMIC MICROWAVE BACKGROUND AND
LARGE SCALE STRUCTURE
In order to obtain quantitative predictions we computed numerically the evolution
of scalar adiabatic perturbations in a flat Universe in which is present a significant
fraction of mirror dark matter at the expenses of diminishing the cold dark matter
(CDM) contribution and maintaining constant Ωm.
We have chosen a “reference cosmological model” with the following set of
parameters: ωb = Ωbh
2 = 0.023, Ωm = 0.25, ΩΛ = 0.75, ns = 0.97, h = 0.73. The
dependence of the CMB and LSS power spectra on the parameters x and β is
shown in fig. 1. The predicted CMB spectrum is quite strongly dependent on the
value of x, and it becomes practically indistinguishable from the CDM case for
FIGURE 1. CMB (left) and LSS (right) power spectra for different values of x and ω′
b
, as
compared with a reference standard model (solid line) and with observations. Models where dark
matter is entirely due to M baryons (no CDM) are plotted in top panels for x= 0.3,0.5,0.7, while
models with mixed CDM + M baryons (β = 1,2,3,4 ; x= 0.7) in bottom panels.
x < xeq ≈ 0.3. However, the effects on the CMB spectrum rather weakly depend
on the fraction of mirror baryons. As a result of the oscillations in M baryons
perturbation evolution, one observes oscillations in the LSS power spectrum; their
position clearly depends on x, while their depth depends on the mirror baryonic
density. Superimposed to oscillations one can see the cut-off in the power spectrum
due to the aforementioned Silk damping.
In the same figure our predictions can be compared with the observational data
in order to obtain some general bound on the mirror parameters space.
• The present LSS data are compatible with a scenario where all the dark
matter is made of mirror baryons only if we consider enough small values
of x: x≤ 0.3≈ xeq.
• High values of x, x > 0.6, can be excluded even for a relatively small amount
of mirror baryons. In fact, we observe relevant effects on LSS and CMB power
spectra down to values of M baryon density of the order Ω′b ∼ Ωb.
• Intermediate values of x, 0.3< x < 0.6, can be allowed if the M baryons are a
subdominant component of dark matter, Ωb ≤ Ω
′
b ≤ ΩCDM .
• For small values of x, x < 0.3, the M baryons and the CDM scenarios are
FIGURE 2. Current status of the astrophysical research with mirror dark matter: solid lines
mark what is already done, while dashed ones mark what is still to do.
indistinguishable as concerns the CMB and the linear LSS power spectra. In
this case, in fact, the mirror Jeans and Silk lengths, which mark region of the
spectrum where the effects of mirror baryons are visible, decrease to very low
values, which undergo non linear growth from relatively large redshift.
Thus, with the current experimental accuracy, we can exclude only models with
high x and high Ω′b.
6. SUMMARY
Figure 2 shows the current situation of the astrophysical research in presence of
mirror dark matter. We have already investigated the early Universe (thermody-
namics and Big Bang nucleosynthesis), and the process of structure formation in
linear regime, that permit to obtain predictions, respectively, on the primordial el-
ements abundances, and on the observed cosmic microwave background and large
scale structure power spectra. In addition, we have studied the evolution of mirror
dark stars, which, together with the mirror star formation, are necessary ingredients
for the study and the numerical simulations of non linear structure formation, and
of the formation and evolution of galaxies; furthermore, in future studies they will
provide predictions on the observed abundances of MACHOs and on the gravita-
tional waves background. Ultimately we will be able to obtain theoretical estimates
to be compared with observations of gravitational lensing, galactic dark matter dis-
tribution, and strange astrophysical events still unexplained (as for example dark
galaxies, bullet galaxy, ...).
Concluding, the astrophysical tests so far used show that mirror matter can be
a viable candidate for dark matter, but we still need to complete the entire picture
of the Mirror Universe.
ACKNOWLEDGMENTS
This work was supported by the Belgian Science Policy Office Inter University
Attraction Pole VI/11 “Fundamental Interactions”.
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