DFAQ-TH/2000-03

INFNFE-04-00

hep-ph/0008105

July 2000

The Early Mirror Universe: Inflation,

Baryogenesis, Nucleosynthesis and Dark Matter

Zurab Berezhiani,^{1}^{1}1E-mail:
,
Denis Comelli^{2}^{2}2E-mail:
and
Francesco L. Villante ^{3}^{3}3E-mail:

Dipartimento di Fisica, Università di L’Aquila, 67010 Coppito
AQ, and

INFN, Laboratori Nazionali del Gran Sasso, 67010 Assergi AQ, Italy

Andronikashvili Institute of Physics, Georgian Academy of Sciences,

380077 Tbilisi, Georgia

INFN, sezione di Ferrara, 44100 Ferrara, Italy

Dipartimento di Fisica, Università di Ferrara, 41000 Ferrara, Italy

There can exist a parallel ‘mirror’ world which has the same particle physics as the observable world and couples the latter only gravitationally. The nucleosynthesis bounds demand that the mirror sector should have a smaller temperature than the ordinary one. By this reason its evolution should be substantially deviated from the standard cosmology as far as the crucial epochs like baryogenesis, nucleosynthesis etc. are concerned. Starting from an inflationary scenario which could explain the different initial temperatures of the two sectors, we study the time history of the early mirror universe. In particular, we show that in the context of the GUT or electroweak baryogenesis scenarios, the baryon asymmetry in the mirror world should be larger than in the observable one and in fact the mirror baryons could provide the dominant dark matter component of the universe. In addition, analyzing the nucleosynthesis epoch, we show that the mirror helium abundance should be much larger than that of ordinary helium. The implications of the mirror baryons representing a kind of self-interacting dark matter for the large scale structure formation, the CMB anysotropy, the galactic halo structures, microlensing, etc. are briefly discussed.

## 1 Introduction

The old idea
that there can exist a hidden mirror sector of
particles and interactions which is the exact duplicate
of our visible world [1]
has attracted a significant interest over last years,
in particular being motivated by the problems of
neutrino physics [2, 3], gravitational microlensing
[4, 5], gamma ray bursts [6],
ultra-high energy cosmic rays [7],
flavour and CP violation [8], etc.
The basic concept is to have a theory given by the
product of two identical gauge factors with
the identical particle contents, which could naturally emerge
e.g. in the context of superstring.
Two sectors communicate through gravity and
perhaps also via some other messengers.
A discrete symmetry interchanging
corresponding fields of and , so called mirror parity,
implies that both particle sectors are described by the
same Lagrangians.^{1}^{1}1In the brane world picture,
the M-sector can be the same O-world realized on a
parallel brane, [9].

In particular, one can consider
a minimal symmetry
where stands for the
standard model of observable particles: three families of
quarks and leptons ) and the Higgs doublet ,
while is its mirror
gauge counterpart with analogous particle content:
fermions .
(From now on all fields and quantities of the
mirror (M) sector will have an apex
to distinguish from the ones belonging to the
observable or ordinary (O) world.)
The mirror parity
implies that all coupling constants (gauge, Yukawa, Higgs)
have the same pattern in both sectors and thus
their microphysics is the same.^{2}^{2}2 The mirror parity
could be spontaneously broken and the weak interaction scales
and
could be different, which leads to somewhat different particle
physics in the mirror sector [3, 4, 7]. and
the Higgs
(

One could naively think that due to mirror parity the O- and M- particles should have the same cosmological densities, which would be in the immediate conflict with the Big Bang nucleosynthesis (BBN) bounds on the effective number of extra light neutrinos, [11]: the mirror photons, electrons and neutrinos would give a contribution to the Hubble expansion rate equivalent to . Therefore, the M-particle density in the early universe should be appropriately reduced. This situation is plausible if two following conditions are satisfied:

A. At the initial moment two systems are born with different densities. In particular, the inflationary reheating temperature in the M-sector should be lower than in the visible one, , which can be achieved in certain models [4, 7, 10].

B. The M- and O-particles interact very weakly, so that two systems do not come into the thermal equilibrium with each other in the early universe. This condition is automatically fulfilled if two worlds communicate only via the gravity. More generally, there could be other messengers like superheavy gauge singlet fields or light singlets of the moduli type. In either case, they should mediate the effective couplings between the O- and M- particles suppressed by a large mass factor or so.

If two sectors have different reheating temperatures, and if they do not come into the thermal contact at later stages, then during the universe expansion they evolve independently and approach the BBN epoch with different temperatures. Namely, the BBN bound implies that .

In this paper we study the comparative time history of two sectors in the early universe. We show that due to the temperature difference, in the mirror sector all key epochs as are the baryogenesis, nucleosynthesis, etc. proceed at somewhat different conditions than in the observable universe. The paper is organized as follows. In sect. 2 we describe an inflationary model which could provide different reheating temperatures between two sectors. The sect. 3 we show that the baryon asymmetry in the M-world generically should be larger than that in the O-sector either in the GUT or electroweak baryogenesis scenarios. Moreover, it is pretty plausible that M-baryons provide a significant fraction of the dark matter of the universe, i.e. . In sect. 4 we study the chemical composition of the M-sector and find that it should be dominantly a helium world – the primordial abundance of the mirror He should be times larger than of the ordinary one. In sect. 5 we briefly address the problem of the cosmological structure formation in the presence of M-baryons as a dominant dark matter component. Namely, M-baryons being a sort of self-interacting dark matter could provide interesting signatures on the CMB anisotropy, the large scale structure of the universe, the form of the galactic halos, microlensing, etc. Finally, in sect. 6 we summarize our findings.

## 2 Inflation and post-inflation

An attractive realization of the inflationary paradigm is provided by supersymmetric models of hybrid inflation. The symplest model is based on the superpotential containing the inflaton field and the additional ‘orthogonal’ field , where is order 1 coupling constant and is a dimensional parameter of the order of the GUT scale [13]. The supersymmetric vacuum is located at , , while for the field values , the tree level potential has a flat valley with an energy density . Since the supersymmetry is broken by the non-vanishing -term, , the flat direction is lifted by radiative corrections and the potential of gets a slope which is appropriate for the slow roll conditions. The COBE results on the CMB anisotropy imply that GeV, where is a slow-roll parameter.

The genetic problem of the hybrid inflation models concerns the choice of the initial conditions [14, 15]. Namely, at the end of the Planck era the scalar should have an initial value while must be zero with the high accuracy over a region much larger than the initial horizon size . In other words, the initial field configuration should be located just on the bottom of the valley, and so the energy density to start with should be , at least eight orders of magnitude smaller than the natural energy density at the Planck era. If the field would have initial amplitude , then its oscillation should be damped within typical time , otherwise it induces too a big curvature for the inflaton and violate the slow-roll conditions, thus preventing the onset of the inflation.

Such a Fine Tuning can be avoided by a possible preheating before the onset of the inflation: the oscillating field could decay into some light particles [15]. In this view, one can consider a model based on superpotential [15]:

(1) |

Now all fields can have initial values order , and thus the initial energy density can be . At first instants, due to oscillation of , the system behaves as matter dominated universe. Fast damping of is a pretext of inflationary stage which allows the inflaton energy density to dominate and then can slowly roll to the origin. This function is carried by the second term in (1) – the oscillating orthogonal field fastly decays into and particles which have practically no contact to inflaton . In addition, with vanishing , also effective mass terms of ’s disappear and the latter fields start to behave as massless – they stop oscillating and freeze. In general, oscillations and freeze at different amplitudes, typically , at which they are catched by the moment when their mass drops below the Hubble parameter (see Fig. 3 of ref. [15]). When slow roll ends up, all fields start to oscillate around their vacuum values, , , , and reheat the universe.

Let us assume now that reheating occurs due to superpotential terms:

(2) |

where and are the Higgs
doublet superfields respectively for the O- and M-sectors.
Then different magnitudes of and
at the end of slow-roll phase should reflect into
difference of reheating temperatures and
in two systems, simply because of the energy difference
stored into and oscillations which decay
respectively into O- and M-Higgses.
More detailed analysis of this mechanism will be presented
elsewhere.^{3}^{3}3For other scenarios of
the asymmetric reheating, see [4, 7, 10].

We have also to make sure that after reheating two sectors do not come into the thermal equilibrium to each other, or in other words, that interactions between O- and M-particles are properly suppressed. In a supersymmetric theory this condition is fulfilled in a rather natural manner. In particular, the mixed terms of the lowest dimension in the superpotential are:

(3) |

which are suppressed by a large mass factor or so, and thus are safe. The same holds true for soft supersymmetry breaking - and -terms like , etc., where is the supersymmetry breaking spurion with TeV. As for the the kynetic mixing term between the field-strength tensors of the gauge factors and , it can be forbidden by embedding in the grand unified group like .

Once the O- and M-systems are decoupled already after reheating, at later times they will have different temperatures and , and so different energy and entropy densities:

(4) |

(5) |

The factors , and ,
accounting for the effective number of the degrees of freedom
in two systems can in general be different from each other.
During the universe expansion, the two sectors evolve
with separately conserved entropies. Therefore,
the ratio is time
independent,^{4}^{4}4 We assume
that expansion goes adiabatically in both sectors and
neglect the additional entropy production due to the possible
weakly first order electroweak or QCD phase transitions.
while the ratio of the temperatures
in two sectors is simply given by:

(6) |

The Hubble expansion rate is determined by the total energy density , . Therefore, at a given time in a radiation dominated epoch we have

(7) |

in terms of O- and M-temperatures and , where

(8) |

Here the factor
takes into account that for the relativistic
particle contents of the two worlds can be different.
However, except for very small values of ,
we have . So hereafter we always take
and
.
In particular,
in the modern universe we have ,
, and ,
where are the present
temperatures of the O- and M- relic photons.^{5}^{5}5
The frozen ratio of the neutrino and photon temperatures
in the M-sector
depends on the decoupling temperature from the
mirror plasma which scales approximatively as
, where MeV is
the decoupling temperature of the usual neutrinos.
Therefore, unless ,
has a standard value
.
For , becomes larger than
the QCD scale MeV,
so that due to the mirror gluons and light quarks
contribution we would obtain ,
and so .
However, in the following such small values of
are not of our interest.
In fact, is the only free parameter in our model
and it is constrained by the BBN bounds.

The observed abundances of light elements are in good agreement with the standard nucleosynthesis predictions, when at MeV we have as it is saturated by photons , electrons and three neutrino species . The contribution of mirror particles (, and ) would change it to . Deviations from are usually parametrized in terms of the effective number of extra neutrino species, . Thus we have:

(9) |

In view of the present observational situation, a reliable bound is [11], which translates as . This limit very weakly depends on . E.g. implies .

As far as , in a relativistic epoch the Hubble expansion rate (7) is dominated by the O-matter density and the presence of M-sector practically does not affect the standard cosmology of the early ordinary universe. However, even if the two sectors have the same microphysics, the cosmology of the early mirror world can be very different from the standard one as far as the crucial epochs like baryogenesis, nuclesosynthesis, etc. are concerned. Any of these epochs is related to an instant when the rate of the relevant particle process , which is generically a function of the temperature, becomes equal to the Hubble expansion rate . Obviously, in the M-sector these events take place earlier than in the O-sector, and as a rule, the relevant processes in the former freeze out at larger temperatures than in the latter.

In the matter domination epoch the situation becomes different. In particular, we know that ordinary baryons can provide only a minor fraction of the present cosmological density, , whereas the observational data indicate the presence of dark matter which can amount for . It is interesting to question whether the missing matter density of the universe could be due to mirror baryons? In the next section we show that this situation can emerge in a pretty natural manner.

## 3 Baryogenesis and mirror baryon density

It is well known that a non-zero baryon asymmetry (BA) can be produced in the initially baryon symmetric universe if three following conditions are fulfilled: B-violation, CP violation and departure from the thermal equilibrium. Generally speaking, the baryogenesis scenarios can be divided in two categories in which the out of equilibrium conditions are provided (a) by the universe expansion itself, or (b) by fast phase transition and bubble nucleation. In particular, the latter concerns the electroweak baryogenesis schemes, while the former is typical for a GUT type baryogenesis or leptogenesis.

At present it is not possible to say which of the known mechanisms is responsible for the observed BA. We only know that the baryon to photon number density ratio is restricted by the BBN constraints to the range . It is most likely that the BA in the M-world is produced by same mechanism and moreover, the rates of the and CP violation processes are parametrically the same in both cases. However, the out of equilibrium conditions should be different since at relevant temperatures the universe expansion is faster for the M-sector. Below we show that by this reason typically emerges larger than for either type (a) or (b) scenarios.

The M-baryons can be of the cosmological relevance if exceeds , whereas would overclose the universe. So we are interested in a situation when the ratio falls in the range from 1 to about 100. Since , we obtain . Therefore, does not apriori mean that , and in fact there is a lower limit or so for the relevant parameter space. Indeed, it arises from by recalling that , while can be taken at most , the biggest value which can be principally realized in any baryogenesis scheme under the realistic assumptions.

### 3.1 GUT Baryogenesis

The GUT baryogenesis mechanism typically based on a superheavy boson undergoing the B- and CP-violating decays into quarks and leptons. The following reaction rates are of relevance:

Decay: for or for , where is the coupling strength of to fermions and is its mass;

Inverse decay: for or for ;

The boson mediated processes: , where the factor amounts for the possible reaction channels.

The final BA depends on a temperature at which bosons go out from equilibrium. One can introduce a parameter which measures the effectiveness of the decay at the epoch [16]: . The larger is the longer equilibrium is maintained and the freeze-out abundance of boson becomes smaller. Hence, the resulting baryon number to entropy ratio, is a decreasing function of . It is approximately given as , where is the CP violating factor and

(10) |

Here is a critical value defined by equation . It distinguishes between the regimes , in which inverse decay is relevant and , in which instead processes are the dominant reason for baryon damping.

In a general context, without referring to a particular model, it is difficult to decide which range of parameters and can be relevant for baryogenesis. One can impose only the most reasonable constraints and , and thus or so. For a given mechanism responsible for the observed baryon asymmetry , this translates into a lower bound .

The presence of the mirror sector practically does not alter the ordinary baryogenesis. The effective particle number is and thus the contribution of M-particles to the Hubble constant at is suppressed by a factor .

In the mirror sector everything should occur in a similar way, apart from the fact that now at the Hubble constant is not dominated by the mirror species but by ordinary ones: . As a consequence, we have . Since the value of is the same in the two sectors, the mirror baryon asymmetry can be simply obtained by replacing in eq.10, i.e. . Since is a decreasing function of , then for we have and thus we conclude that the mirror world always gets a larger BA than the visible one, .

However, this does not apriori mean that is always larger than . Since the entropy densities are related as , for the ratio we have:

(11) |

The behaviour of the factor as a function of for different values of the parameter is given in the Fig. 1A. Clearly, in order to have the function have to decrease faster than between and . Closer inspection of the function 10 reveals that the M-baryons can be overproduced only if is order or larger. In other words, the relevant interactions in the observable sector maintain equilibrium longer than in the mirror one, and thus ordinary BA can be suppressed by an exponential Boltzmann factor while the mirror BA could be produced still in non-exponential regime .

In Fig. 1B we show the parameter region in which falls in the range , in confront to the parameter area excluded by condition . We see that for there is an allowed parameter space in which can reach values up to 10, but is excluded. For a limiting case , as it was expected, the parameter space for becomes incompatible with . For intermediate values of , say , also the values can be compatible.

The above considerations can be applied also in the context of leptogenesis. One should remark, however, that potentially both the GUT baryogenesis or leptogenesis scenarios are in conflict with the supersymmetric inflation scenarios, because of the upper limit on the reheating temperatures about GeV from the thermal production of gravitinos [17]. Moreover, it was shown recently that the non-thermal gravitino production can impose much stronger limits, GeV or so [18]. This problem can be fully avoided in the electroweak baryogenesis scenario, which instead is definitely favoured by the supersymmetry.

### 3.2 Electroweak Baryogenesis

The electroweak (EW) baryogenesis mechanism is based on the anomalous B-violating processes induced by the sphalerons which are quit rapid at high temperatures, but become much slower when temperature drops below 100 GeV. A succesfull scenario needs the first order EW phase transition and sufficient amount of CP violation, which conditions can be satisfied in the frames of the supersymmetric standard model, for certain parameter ranges [19].

The characteristic temperature scales of the electroweak phase transition are fixed entirely by the form of the finite temperature effective potential:

(12) |

where all parameters can be expressed in terms of the fundamental couplings in the Lagrangian. For large temperatures, GeV, the electroweak symmetry is restored and has a minimum at . With the universe expansion the temperature drops, approaching the specific values which define the sequence of the phase transition. These are all in the 100 GeV range and ordered as . Namely, below the potential gets a second local minimum . At the critical temperature the latter becomes degenerate with the false vacuum . At temperatures to the true vacuum state becomes energetically favoured, and transition to this state can occur via thermal quantum tunneling, through the nucleation of the bubbles which then expand fastly, percolate and finally fill the whole space within a horizon by the true vacuum.

The bubble production starts when the free energy barrier separating the two minima becomes small enough. The bubble nucleation temperature is defined as a temperature at which the probability for a single bubble to be nucleated within a horizon volume becomes order one:

(13) |

where is the free energy and is an order one coefficient [19]. In particular, in the limit of thin wall approximation we have:

(14) |

The condition (13) results into large values of , typically order .

Once the bubble nucleation and expansion rate is larger than the Hubble parameter, the out of equilibrium condition for anomalous B-violating processes is provided by the fast phase transition itself. The BA can be produced inside the bubbles due to the CP violation since the quarks and antiquarks have different reflection coefficients on the bubble wall. The baryogenesis rate is completely independent from the universe expansion and it occurs practically in one instant as compared to the cosmological time scale of this epoch.

As for the mirror sector, it is described by the same Lagrangian as the ordinary one and so the effective thermal potential of the mirror Higgs has the same form as (12). Then the temperature scales which are defined entirely by the form of the effective potential should be exactly the same for O- and M-sectors. Namely, and .

The equation (13) is the same for the M-sector apart of the fact that the corresponding Hubble constant is different: . Therefore, we obtain:

(15) |

which in turn tells that the bubble nucleation temperatures in two sectors are practically equal: . (Clearly, the phase transition in M-sector occurs at earlier time than in O-sector: .) The reason is that between the temperature scales and the free energy is a rapidly changing function but the change in temperature itself is insignificant. Hence, we expect that the initial BA’s produced right at the phase transition to be the same in O- and M-sectors: .

However, the instantly produced baryon number can be still washed out by the sphaleron interactions. The anomalous B-violation rate , where is the sphaleron free energy at finite , may be large enough inside the bubble as far as the temperature is large. But it quickly falls as the temperature decreases, and baryon number freezes out as soon as drops below (7). The wash-out equation can be rewritten as

(16) |

and integrated. Then the final BA in the O- and M-sectors can be expressed respectively as

(17) |

where is the baryon number depletion factor:

(18) |

and in the supersymmetric standard model. Thus we always have , while the M-baryon mass density relative to O-baryons reads:

(19) |

Lacking a precise theory for non-perturbative sphaleron transitions in the broken phase, the exact value of one cannot be calculated even in the context of concrete models. If , the wash-out is ineffective and practically all BA produced right at the bubble nucleation is conserved. In this case should smaller than . However, if is enough small, one can achieve sufficiently large . The contourplot for the parameters and for which falls in the range is given in Fig. 2. For small we have essentially and thus requires a depletion factor in the interval . Once again, for one needs the marginal values below which the observable BA cannot be produced at all.

## 4 Primordial Nucleosynthesis and mirror helium abundance

The time scales relevant for standard BBN are defined by the “freeze-out” temperature of weak interactions MeV ( s) and by the “deuterium bottleneck” temperature MeV ( s) [16]. When , weak interactions transform neutrons into protons and viceversa and keep them in chemical equilibrium. The neutron abundance , defined as the ratio of neutron to baryon densities, is given by , where MeV is the neutron-proton mass difference. For the weak reaction rate drops below the Hubble expansion rate , the neutron abundance freezes out at the equilibrium value and it then evolves only due to the neutron decay: , where s is the neutron lifetime.

At temperatures , the process is faster than the universe expansion, and free nucleons and deuterium are in chemical equilibrium. The light element nucleosynthesis essentially begins when the system cools down to the temperature

(20) |

where MeV is the deuterium binding energy, and is the nucleon mass. Below this temperature the deuterium abundance starts to grow which in turn allows to produce also the heavier nuclei. Nearly all neutrons present at this time are finally captured in He nuclei, due to the large binding energy of the latter. Thus, the primordial He mass fraction is:

(21) |

As we have already discussed, the presence of the mirror sector with a temperature has practically no impact the standard BBN. In fact, the limit has been set by uncertainties of the present observational situation. In the mirror sector nucleosynthesis proceeds along the same lines. However, the impact of the O-world for the mirror BBN is dramatic.

For any given temperature , now we have for the Hubble expansion rate. Therefore, the freeze-out temperature is larger than , whereas the time scales as . In addition, is different from . However, since depends on baryon density only logarithmically (see (20)), the temperature remains essentially the same as , while the time scales as . Thus, for the mirror He mass fraction we obtain:

(22) |

We see that is an increasing function of . In particular, for one has .

In reality, eq. (22) is not valid for small , since in this case deuterium production through reaction can become ineffective. By a simple calculation one can make sure that for , the rate at which neutrons are captured to form the deuterium nuclei, , where is the M-photons density and cm s is the thermal averaged cross section, becomes smaller than the Hubble rate for temperatures . In this case M-nucleosynthesis is inhibited, because the neutron capture processes becomes ineffective before deuterium abundance grows enough to initiate the synthesis of the heavier elements. Therefore, for any given , first increases with increasing , reaches a maximum and then starts to decrease. The true dependence of on the computed for different values of by standard BBN code [20], is presented in Fig. 3. The Hubble expansion rate of the mirror world was implemented, for each value of , by taking an effective number of extra neutrinos as .

We have to remark, however, that in the most interesting situation when , the condition is never fulfilled and the behaviour of is well described by the approximate formula (22). Hence, in this case is always bigger than . In other words, if dark matter of the universe is represented by the baryons of the mirror sector, it should contain considerably bigger fraction of primordial He than the ordinary world.

## 5 Mirror baryons as dark matter

We have shown that mirror baryons could provide a significant contribution to the energy density of the universe and thus they could constitute a relevant component of dark matter. Immediate question arises: how the mirror baryon dark matter (MBDM) behaves and what are the differences from the more familiar dark matter candidates as the cold dark matter (CDM), the hot dark matter (HDM) etc. In this section we briefly address the possible observational consequences of such a cosmological scenario.

In the most general context, the present energy density contains relativistic (radiation) component , non-relativistic (matter) component and the vacuum energy density (cosmological term). According the inflationary paradigm the universe should be almost flat, , which well agrees with the recent results on the CMB anisotropy [21]. The Hubble parameter is known to be km s Mpc with , and for redshifts of the cosmological relevance, , it becomes

(23) |

In the context of our model, the relativistic fraction
is represented by the ordinary and mirror
photons and neutrinos,
, and
contribution of the mirror species is negligible
in view of the BBN constraint .
As for the non-relativistic component,
it contains the O-baryon fraction and
the M-baryon fraction ,
while the other types of dark matter, e.g. the CDM,
could also present and so
.^{6}^{6}6
In the context of supersymmetry,
the CDM component could exist in the form of
the lightest supersymmetric particle (LSP).
It is interesting to remark that the mass fractions
of the ordinary and mirror LSP are related as
.
In addition, a significant HDM component
could be due to neutrinos with order eV mass.
The contribution of the mirror neutrinos
scales as and thus
it is irrelevant.
At present it is not completely clear what is the matter
fraction in the universe. Many observational data favour
while the rest
of the energy density is due to the cosmological term,
, but also
cannot be excluded.

The important moments for the structure formation are related to the matter-radiation equality (MRE) epoch which occurs at the redshift (we denote ):

(24) |

and to the plasma recombination and matter-radiation decoupling (MRD) epochs. The latter takes place only after the most of electrons and protons recombine into neutral hydrogen and the free electron number density diminishes, so that the photon scattering rate drops below the Hubble expansion rate , where cm is the Thomson cross section. In condition of chemical equilibrium, the fractional ionization is given by the Saha equation, which for reads:

(25) |

where eV is the hydrogen binding energy. Thus we obtain the familiar result that in our universe the MRD takes place in the matter domination period, at the temperature eV which corresponds to redshift .

The MRD temperature in the M-sector can be calculated following the same lines as in the ordinary one. Due to the fact that in either case the photon decoupling occurs when the exponential factor in eq. (25) becomes very small, we have , up to small logarithmic corrections related to , different from , . Hence

(26) |

so that the MRD in the M-sector occurs earlier than in the ordinary one. Moreover, for less than , the mirror photons would decouple yet during the radiation dominated period (see Fig. 4).

Let us discuss now cosmological evolution of the MBDM. The relevant length scale for the gravitational instabilities is characterized by the mirror Jeans scale , where is the matter density at a given redshift and is the sound speed in the M-plasma. The latter contains more baryons and less photons than the ordinary one, and . Let us consider for simplicity the case when dark matter of the universe is entirely due to M-baryons, . Then we have:

(27) |

Hence, for the redshifts of the cosmological relevance, , we have , quite in contrast with the ordinary world, where practically till the photon decoupling, .

The M-baryon Jeans mass reaches the maximal value at , . Notice, however, that becomes smaller than the Hubble horizon mass starting from a redshift , which is about for , but it sharply increases for smaller values of (see Fig. 4). So, the density perturbation scales which enter horizon at have mass larger than and thus undergo uninterrupted linear growth immediately after . The smaller scales for which instead would first oscillate. Therefore, the large scale structure formation is not delayed even if the mirror MRD epoch did not occur yet, i.e. even if . The density fluctuations start to grow in the M-matter and the visible baryons are involved later, after being recombined, when they rewritte the spectrum of already developed mirror structures.

The main feature of the MBDM scenario is that the M-baryon density fluctuations should undergo the strong collisional damping around the time of M-recombination. The photon diffusion from the overdense to underdense regions induce a dragging of charged particles and wash out the perturbations at scales smaller than the mirror Silk scale Mpc, where for , and for .

Thus, the density perturbation scales which can run
the linear growth after the MRE epoch are limited by the
length .
This could help in avoiding the excess of small scales
(of few Mpc) in the large scale power spectrum without
tilting the spectral index.^{7}^{7}7One should keep
in mind also delaying of the MRE moment,
e.g. by taking .
This would correspond to the case when M-baryons provide
only a fraction of the present energy density, say
, while the rest is due to the
cosmological term, .
The smallest perturbations that survive the
Silk damping will have the mass
,
which should be less than
in view of the BBN bound .
Interestingly, for we have
,
a typical galaxy mass.

To some extend, the cutoff effect is analogous to the free streaming damping in the case of warm dark matter (WDM), but there are important differences. The point is that alike usual baryons, the MBDM should show acoustic oscillations whith an impact on the large scale power spectrum. In particular, it is tempting to imagine that the M-baryon oscillation effects are related to the anomalous features observed at Mpc clustering [22].

In addition, the MBDM oscillations transmitted via gravity to the ordinary baryons, could cause observable anomalies in the CMB angular power spectrum for ’s larger than 200. This effect can be observed only if the M-baryon Jeans scale is larger than the Silk scale of ordinary baryons, Mpc, which sets a principal cutoff for CMB oscillations around . As we have seen above, this would require enough large values of , near the upper bound set by the BBN constraints: or so. The detailed analysis of this effect will be given elsewhere. In our opinion, together with the possible effects on the large scale power spectrum, it can provide a most direct test for the MBDM and can be verified by the next CMB experiments with higher sensitivity.

Clearly, for small the M-matter recombines before the MRE moment, and thus it should rather manifest as the CDM as far as the large scale structure is concerned. However, there still can be crucial difference at smaller scales which already went non-linear, like galaxies. In our scenario, dark matter in galaxies and clusters can contain the mixed CDM and MBDM components, and can be even constituted entirely by the mirror baryons. Then one can question whether the MBDM distribution in halos can be different from that of the CDM? Namely, simulations show that the CDM forms triaxial halos with a density profile too clumped towards the center, and overproduce the small substructures within the halo. As for the MBDM, it constitutes a sort of collisional dark matter and thus potentially could avoide these problems, at least clearly the one related with the excess of small substructures.

The halo distribution in galaxies depends on the mass
and on the self-scattering cross section
of dark matter.
In our case it mainly consists of the mirror hydrogen atoms,
and so GeV and cm.
At the first glance, this is in strong discrepancy
with the range cm/GeV
preferred by the analysis of ref. [24].^{8}^{8}8
In the case of asymmetric M-world with
, the mirror electron mass should
scale as while the nucleon mass
remains GeV. Therefore, the elastic
scattering cross-section of the M-hydrogen atoms
scales as and so
for one could obtain a
reasonably small cross section.

However, one has to take into account the possibility
that during the galaxy evolution
the bulk of the M-baryons could fastly fragment
into the stars.
A difficult question to address here
is related to the star formation in the M-sector,
also taking into account that its temperature/density
conditions and chemical contents
are much different from the ordinary ones.
In any case, the fast star formation would
extint the mirror gas and thus
could avoide the M-baryons to form disk galaxies
as ordinary baryons do. The M-protogalaxy,
which at certain moment before disk formation
essentially becomes the collisionless system of the
mirror stars,
could maintain a typical elliptical structure.^{9}^{9}9
In other words, we speculate on the possibility
that the M-baryons form mainly the elliptical galaxies.
For a comparison, in the ordinary world
the observed bright galaxies are mainly spiral while
the elliptical galaxies account about of them.
Remarkably, the latter contain old stars, very little dust
and show no sign of active star formation.
Certainly, in this consideration also the galaxy merging
process should be taken into account.
As for the O-matter, within the dark M-matter halo it should
typically show up as an observable elliptic or spiral galaxy,
but some anomalous cases can be also possible,
like certain types of irregular galaxies or even
dark galaxies dominantly made out of M-baryons.

The central part of halo can nevertheless contain a
large amount of the ionized mirror gas and it is not
excluded that it can have a quasi-spherical form.
Even if the stellar formation is very efficient,
the massive mirror stars in the dense central region
fastly evolve^{10}^{10}10
Since mirror matter contains more
helium, the mirror stars should evolve much
faster than the ordinary ones.
and explode as supernovae, leaving behind the compact
objects like neutron stars or black holes,^{11}^{11}11
Another tempting issue is whether the M-matter itself
could help in producing big central black holes,
with masses , which are thought
to be main engines of the active galactic nuclei.
and reproducing the mirror gas and dust.
Although the cross section is large,
it does not necessarily implies that the galaxy core
will collapse within a dynamical time, since the inner
halo should be opaque for M-particles.
They undergo many scatterings and escape from the
system via diffusion, so the energy drain can be
small enough and the instability time can substantially
exceed the age of the universe [25].

In the galactic halo
(provided that it is the elliptical mirror galaxy)
the mirror stars should be observed as
Machos in gravitational microlensing [4, 5].
Leaving aside the difficult question of the initial
stellar mass function, one can remark that once
the mirror stars could be very old
and evolve faster than the ordinary ones,
it is suggestive to think that most
of massive ones, with mass above the
Chandrasekhar limit
have already ended up as supernovae, so that only the
lighter ones
remain as the microlensing objects.^{12}^{12}12The
M-supernovae explosion in our galaxy cannot be directly
seen by ordinary observer, however it
could be observed in terms of gravitational waves.
In addition, if the M- and O-neutrinos are mixed [2, 3],
it can lead the observable neutrino signal, which could
be also accompanied by the weak gamma ray burst [6].
The recent data indicate the average mass of
Machos around , which is difficult
to explain in terms of the brown dwarves with masses
below the hydrogen ignition limit
or other baryonic objects [23].
Perhaps, this is the first observational evidence
of the mirror matter?

It is also plausible that in the galactic halo some fraction of mirror stars exists in the form of compact substructures like globular or open clusters. In this case, for a significant statistics, one could observe interesting time and angular correlations between the microlensing events.

## 6 Conclusions

We have discussed cosmological implications of the parallel mirror world with the same microphysics as the ord