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finding clues for the nature of dark matter in the universe is one of the most pressing issues in the interface between particle physics and cosmology . in this talk
we briefly review some work we have done [ @xcite ] in the direction of finding a suitable , particle physics motivated , candidate that could solve some of the recent problems with the usual cold dark matter scenario .    the cold dark matter model ( cdm ) supplemented by a cosmological constant sucessfully explains , in the context of inflationary models , the observed structure of the universe on large scales , the cosmic microwave background anisotropies and type ia supernovae observations [ @xcite ] for a given set of density parameters , _
e.g. _ , @xmath0 , @xmath1 and @xmath2 .
according to this scenario , initial gaussian density fluctuations , mostly in non - relativistic collisionless particles , the so - called cold dark matter , are generated in an inflationary period of the universe .
these fluctuations grow gravitationally forming dark halos into which luminous matter is eventually condensed and cooled .
however , despite its successes , there is a growing wealth of recent observational data that raise problems in the cdm scenarios .
n - body simulations predict a number of halos which is a factor @xmath3 10 larger than the observed number at the level of local group [ @xcite ] .
furthermore , cdm models yield dispersion velocities in the hubble flow within a sphere of @xmath4mpc between @xmath5kms@xmath6 for @xmath7 and between @xmath8kms@xmath6 for @xmath0 .
the observed value is about @xmath9kms@xmath6 .
neither model can produce a single local group candidate with the observed velocity dispersion in a simulation box of comoving volume @xmath10 [ @xcite ] .
a related issue is that astrophysical systems which are dm dominated like dwarf galaxies [ @xcite ] , low surface brightness galaxies [ @xcite ] and galaxy clusters without a central cd galaxy [ @xcite ] show shallow matter
 density profiles which can be modeled by isothermal spheres with finite central densities .
this is in contrast with galactic and galaxy cluster halos in high resolution n - body simulations [ @xcite ] which have singular cores , with @xmath11 and @xmath12 in the range between 1 and 2 . indeed
, cold collisionless dm particles do not have any associated length scale leading , due to hierarchical gravitational collapse , to dense dark matter halos with negligible core radius [ @xcite ] .    a possible solution , coming from particle physics
, would be to allow dm particles to self - interact so that they have a large scattering cross section and negligible annihilation or dissipation .
self - interaction induces a characteristic length scale via the mean free path of the particle in the halo .
this idea has been originally proposed to suppress small scale power in the standard cdm model [ @xcite ] and has been recently revived in order to address the issues discussed above [ @xcite ] .
the main feature of self - interacting dark matter ( sidm ) is that large self - interacting cross sections lead to a short mean free path , so that dark matter particles with mean free path of the order of the scale length of halos allows for the transfer of conductive heat to the halo cores , a quite desirable feature [ @xcite ] .
recently performed numerical simulations indicate that strongly self - interacting dark matter does indeed lead to better predictions concerning satellite galaxies [ @xcite ] . however , only in presence of weak self - interaction [ @xcite ] the core problem might be solved .
the two - body cross section is estimated to be in the range of @xmath13 @xmath14/gev , from a variety of arguments , such as the requirement of a mean free path between 1 and 1000 kpc [ @xcite ] , the core expansion time scale to be smaller than the halo age [ @xcite ] and analysis of cluster ellipticity [ @xcite ] .
larger value of @xmath15 @xmath14/gev corresponds to the best fit to the rotation curve of a low surface brightness in simulations [ @xcite ] . in our work , we assume for definiteness that the the cross section is fixed via the requirement that the mean free path of the particle in the halo is in the range @xmath16 kpc .
many models of physics beyond the standard model suggest the existence of new scalar gauge singlets , _
e.g. _ , in the so - called next - to - minimal supersymmetric standard model [ @xcite ] . in this section ,
we provide a simple example for the realization of the idea proposed in [ @xcite ] of a self - interacting , non - dissipative cold dark matter candidate that is based on an extra gauge singlet , @xmath17 , coupled to the standard model higgs boson , @xmath18 , with a lagrangian density given by :    @xmath19    where @xmath20 is the field @xmath17 self - coupling constant , @xmath21 is its mass , @xmath22 gev is the higgs vacuum expectation value and @xmath23 is the coupling between the singlet @xmath17 and @xmath18 .
we assume that the @xmath17 mass does not arise from spontaneous symmetry breaking since tight constraints from non - newtonian forces eliminates this possibility due to the fact that , in this case , there is a relation among coupling constant , mass and vacuum expectation value that leads to a tiny scalar self - coupling constant . in its essential
features our self - interacting dark matter model can be regarded as a concrete realization of the generic massive scalar field with quartic potential discussed in [ @xcite ] .
we mention that a model with features similar to ours has been discussed long ago in [ @xcite ] .
we shall assume that @xmath17 interacts only with @xmath18 and with itself .
it is completely decoupled for @xmath24 . for reasonable values of @xmath23 , this new scalar would introduce a new , invisible decay mode for the higgs boson .
this could be an important loophole in the current attemps to find the higgs boson at accelerators [ @xcite ] . this coupling could , in principle , be relevant for @xmath25 scattering but we shall be conservative and assume that it is small and neglect its contribution .
these particles are non - relativistic , with typical velocities of @xmath26 km @xmath27 .
therefore , there is no dissipation of energy by , for instance , creating more particles in reactions like @xmath28 .
only the elastic channel is kinetically accessible and the scattering matrix element near threshold ( @xmath29 ) is given by : @xmath30 near threshold the cross section is given roughly by : @xmath31    we shall derive limits on @xmath21 and @xmath20 by demanding that the mean free path of the particle @xmath17 , @xmath32 , should be in the interval @xmath33mpc .
this comes about because , if the mean free path were much greater than about @xmath34mpc , dark matter particles would not experience any interaction as they fly through a halo . on the other hand ,
if the dark matter mean free path were much smaller than @xmath34kpc , dark matter particles would behave as a collisional gas altering substantially the halo structure and evolution .
hence , we have : @xmath35 where @xmath36 and @xmath37 are the number and mass density in the halo of the @xmath17 particle , respectively . using @xmath38 gev/@xmath39 ,
corresponding to the halo density , one finds : @xmath40 equating eqs .
( [ cross1 ] ) and ( [ cross2 ] ) we obtain : @xmath41    demanding the mean free path of the @xmath17 particle to be of order of 1 mpc implies in the _ model independent _ result : @xmath42    recently , it has been argued , on the basis of gravitational lensing analysis , that the shape of the ms2137 - 23 system is elliptical while self - interacting non - dissipative cdm implies that halos are spherical [ @xcite ] . furthermore , the limit    @xmath43    arises from that analysis , which is about an order of magnitude smaller than ( [ sstein ] ) .
indeed , gravitational lensing arguments are acknowledged to be crucial in validating sidm ; however , estimates made in [ @xcite ] were criticized as they rely on a single system and because their intrinsic uncertainties actually allow for consistency with sidm [ @xcite ] .    in order to estimate the amount of @xmath17 particles that were produced in the early universe and survived until present , we assume that @xmath17 particles were mainly produced during reheating after the end of inflation . a natural setting to consider this issue is within the framework of @xmath44 supergravity inspired inflationary models , where the inflaton sector couples with the gauge sector only through the gravitational interaction . hence , the number of @xmath17 particles expressed in terms of the ratio @xmath45 , where @xmath46 is the photonic entropy density , is related with the inflaton ( @xmath47 ) abundance after its decay by    @xmath48    where @xmath49 is the number of degrees of freedom . notice that @xmath50 is a conserved quantity since @xmath17 does not couple to fermions . in the context of @xmath44 supergravity inflationary models , the upper bound on the reheating temperature in order to avoid the gravitino problem ( see [ @xcite ] and references therein ) , @xmath51 is given by the ratio of the reheating temperature and the inflaton mass and , for typical models    @xmath52    where @xmath53 is an order one constant .
this estimate allows us to compute the energy density contribution of @xmath17 particles in terms of the baryonic density parameter :    @xmath54    where @xmath55 is the baryon asymmetry of the universe .    using eq .
( [ mass ] ) and taking @xmath56 , we obtain :    @xmath57    which allows identifying @xmath17 as the cosmological dark matter candidate , i.e. @xmath58 [ @xcite ] , for @xmath59 , @xmath20 of order one and @xmath60 of about @xmath34mpc .
we have also found that the @xmath17 particle do not generate dangerous non - newtonian forces [ @xcite ] .
in this work [ @xcite ] , we suggest that a scalar gauge singlet coupled with the higgs field in such a way as to give origin to an invisible higgs is a suitable candidate for self - interacting dark matter .
this proposal has some quite distinct features .
firstly , since gauge invariance prevents the scalar singlet to couple to fermions , hence strategies for directly searching this dark matter candidate must necessarily concentrate on the hunt of the higgs field itself in accelerators .
furthermore , in what concerns its astrophysical and cosmological implications , the main aspects of our proposal are quite unambiguously expressed by eqs .
( [ cross2 ] ) , ( [ mass ] ) and ( [ finaldensity ] ) .
confronting the result of simulations with our candidate for different values of the relevant parameters with observations may turn out to be crucial for validating our proposal .
we would like to add that a recent detailed study of our simple model [ @xcite ] has shown that our abundance computation is valid only if the higgs field is very weakly coupled to the scalar gauge singlet ( @xmath61 ) , since otherwise the scalar field will reach thermal equilibrium [ @xcite ] .
the study of phion annihilation processes via exchange of virtual higgs particles indicates that in order to achieve @xmath62 requires @xmath63 [ @xcite ] which leads to a higgs decay width that is distinctly different than the standard model one .
r.r . would like to thank pronex ( cnpq ) for providing travel funds and grupo de detectores avanados of centro de fsica nuclear da universidade de lisboa under project praxis / p / fis/10033/98 for support during his stay in portugal .
l.t . would like to acknowledge the financial support from fundao para a cincia e a tecnologia ( portugal ) under the grant praxis xxi /bpd/16354/98 and the project praxis / c / fis/13196/98 .
self - interacting dark matter has been suggested in order to overcome the difficulties of the cold dark matter model on galactic scales . 
 we argue that a scalar gauge singlet coupled to the higgs boson , leading to an invisibly decaying higgs , is an interesting candidate for this self - interacting dark matter particle .    
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