You are an expert at summarizing long articles. Proceed to summarize the following text: 
it is an exciting possibility that dark matter has a supersymmetric origin . various species can have the properties of dark matter depending on the supersymmetry breaking mechanism and further particulars of the model , with the neutralino and gravitino being the most prominent candidates .    in classes of models like anomaly @xcite and mirage @xcite mediation , the gravitino is heavier than the other sparticles and thus can not constitute dark matter . on the other hand , in gauge @xcite and gaugino @xcite mediation , the gravitino is light and represents a good candidate for dark matter @xcite,@xcite . in gravity mediation @xcite , the situation is more model - dependent and both relatively heavy and light gravitinos are possible . in this work , we study the circumstances under which the gravitino is the lsp in gravity mediation . if we further require r- or matter parity @xcite , which can descend from string theory @xcite , the gravitino is stable and can constitute dark matter . phenomenology of the gravitino lsp has been an active research subject @xcite@xcite , while in this paper we focus on its supergravity side and identify relevant constraints on fundamental supergravity quantities . let us review relevant features of the supergravity formalism , following @xcite ( and the original work @xcite ) . the supergravity scalar potential is given ( in planck units ) by @xmath7 here the subscript @xmath8 ( @xmath9 ) denotes differentiation with respect to the @xmath10-th ( @xmath10-th complex conjugate ) scalar field . @xmath11 is a function of the khler potential @xmath0 and the superpotential @xmath12 , @xmath13 , and the susy breaking @xmath14-terms are @xmath15 with @xmath16 being the inverse of @xmath17 . the gravitino mass is given by @xmath18 another quantity we need is the khler metric @xmath19 for the observable fields @xmath20 . it is found by expanding the khler potential around @xmath21 : @xmath22 then the soft susy breaking terms are given by @xcite @xmath23\;,\nonumber\end{aligned}\ ] ] where @xmath24 are the gauge kinetic functions , @xmath25 @xmath26 , and @xmath27 are the superpotential yukawa couplings . vanishing of the vacuum energy requires @xmath28 at the minimum of the scalar potential . thus , the magnitude of the @xmath14-terms depends on the khler metric of the susy breaking fields @xmath17 . the @xmath14-terms and , consequently , the soft masses can be much larger than the gravitino mass provided the khler metric is sufficiently small . let us consider the case of a single dominant susy breaking field @xmath29 . omitting for simplicity complex phases , we have @xmath30 where @xmath31 . let us further assume universal gauge kinetic functions and khler metrics for the matter fields . then the soft terms simplify to @xmath32~ m_{3/2}^2 ~ , \nonumber\\ a_0 & = & \sqrt{3\over   k''}~ \biggl [ k ' -3 { \tilde k ' \over \tilde k }    \biggr]~m_{3/2}~ , \label{softmassessinglefield}\end{aligned}\ ] ] where a prime denotes differentiation with respect to @xmath29 and a double prime differentiation with respect to @xmath29 and @xmath33 . we have assumed that the yukawa couplings are independent of @xmath29 , which allows us to avoid strong constraints from electric dipole moments @xcite . this case corresponds to the cmssm . we see that the scalar and gaugino masses can be made arbitrarily large by decreasing @xmath34 . this requires a non - negligible @xmath35 and @xmath36 . if this quantity vanishes at the gut scale , large scalar masses are induced by the renormalization group evolution down to the electroweak ( ew ) scale . since the gravitino mass does not run , we have @xmath37 and the gravitino is the lsp . the @xmath38-terms usually do not play any significant role unless they are much larger than the other soft parameters . let us quantify this effect . in the cmssm , the lightest superparticle is either a neutralino ( mostly bino ) or a stau . unless @xmath39 is large , their masses can be approximated by @xcite,@xcite @xmath40 where we have neglected the ew contributions . for moderate @xmath41 , the lightest neutralino is lighter than the staus . then the gravitino is the lsp for @xmath42 for small @xmath41 , the stau is lighter than the neutralino , so that a larger @xmath43 is required for a gravitino lsp . however , eq .  ( [ masses ] ) shows that the change in the lower bound will be rather small , so that eq . ( [ 2.5 ] ) is still a good approximation . thus , the key parameter is the gaugino mass @xmath43 and as long as the scalar masses squared are non - negative , we obtain the gravitino lsp for @xmath44 where we have used @xmath45 . this bound does not involve the superpotential nor the khler metric for the observable fields and is therefore largely model - independent .    in figs . [ fig1 ] and [ fig2 ] we illustrate these results with a numerical analysis in the cmssm . we have used softsusy @xcite to determine the low - energy superpartner spectrum . the figures display parameter space regions with the gravitino , neutralino and stau lsp . we have chosen @xmath46  gev to fix the overall mass scale for definiteness , while the qualitative features of the plots are independent of this .    at large @xmath39 , eq . ( [ masses ] ) receives corrections mainly from the @xmath47 yukawa coupling so that the @xmath48 becomes the lsp at small @xmath41 . this is displayed in the right panel of fig . [ fig1 ] . also , large @xmath38-terms further decrease the stau mass and can lead to tachyons , so that the @xmath48 lsp and the excluded regions are enlarged , cf.fig . [ fig2 ] . gev and @xmath49.,title="fig : " ]  gev and @xmath49.,title="fig : " ]    , but with a large @xmath38-term . ] let us note that our parameter space is subject to further ( model - dependent ) phenomenological constraints . these depend on the overall mass scale , assumptions on the cosmological history , whether r - symmetry is exact or approximate and whether the gravitino constitutes all or just part of the observed dark matter . for instance , as the lep bound on the higgs mass requires @xmath50  gev , eq . ( [ softmassessinglefield ] ) implies @xmath51  gev for @xmath52 and @xmath53 . for detailed studies , we refer an interested reader to refs . @xcite@xcite .    from eq . ( [ bound ] ) , we see that @xmath34 is not required to be very small . in fact , it is of the order of magnitude of typical @xmath34 expected in string theory . the usual moduli / dilaton khler potential is @xmath54 with @xmath55 so that @xmath56 just to have an idea of the numerics , take @xmath29 to be the dilaton of the heterotic string . then @xmath57 , @xmath58 and @xmath59 at the minimum of the potential , as required by the observed values of the gauge couplings . we get @xmath60 , which falls just short of the bound ( [ bound ] ) . one should keep in mind , however , that the dilaton - dominated susy breaking is not possible with the above khler potential and in realistic cases one has to include either non - perturbative corrections to the khler potential @xcite,@xcite or additional fields . in the former case , one typically has @xmath61 at the minimum of the potential @xcite,@xcite , although the zero vacuum energy is not enforced . when @xmath29 is the modulus associated with the radius of the compact dimensions , one can trust the supergravity approximation for @xmath62 in which case @xmath63 can be arbitrarily small . in realistic cases , however , one has to include more than one field to have the correct gauge coupling , e.g. @xmath64 . otherwise , the gauge coupling becomes too small . one can also entertain the possibility that @xmath29 is a hidden matter - like field with the khler potential @xmath65 , which dominates susy breaking @xcite . in this case , @xmath66 can be very small due to large moduli , @xmath67 . however , the gauge kinetic function is then given predominantly by some other field , e.g.  the dilaton , so that @xmath68 . consequently , @xmath69 can be sufficiently small for the gravitino to be the lsp , yet @xmath70 would require careful engineering .    the above formulae can be generalized to the case of multiple susy breaking fields in a straightforward manner . let us illustrate with an example how the gravitino lsp can arise in string - motivated setups . consider two modulus - type fields @xmath71 and @xmath72 with @xmath73 and @xmath74 . here @xmath75 is the matter `` modular weight '' , which can be negative , positive or zero @xcite . for @xmath76 , locally stable vacua with zero ( or small ) vacuum energy are possible @xcite for instance , this is the case when @xmath77 are the overall modulus and the dilaton . finally , one can choose an appropriate superpotential such that the fields stabilize at @xmath78 in order to have the correct gauge couplings at the gut scale . `` mixed '' gauge kinetic functions of this type appear in string models with fluxes @xcite,@xcite .    requiring zero vacuum energy at the minimum of the scalar potential and neglecting complex phases , we can parametrize supersymmetry breaking by the goldstino angle @xmath79 : @xmath80 then the soft terms read @xmath81    ~m_{3/2 } ~ , \nonumber\\ m_0 ^ 2 & = & \biggl [ 1 +   { 3n \over a     } ~\cos^2\theta   \biggr]~ m_{3/2}^2 ~ , \nonumber\\ a_0 & = & -\sqrt{3}~ \biggl [ \sqrt{a } \left(1 + { 3n \over a     } \right ) ~\cos\theta + \sqrt{b } ~ \sin\theta     \biggr]~m_{3/2}~.\end{aligned}\ ] ] for a sufficiently large @xmath71 and @xmath82 , the gauginos are heavy so that @xmath83 and the gravitino is the lsp . note that the @xmath84 dependence cancels out in @xmath85 and @xmath86 . taking as an example @xmath77 to be the overall modulus and the dilaton , @xmath87 and @xmath88 . then for @xmath89 , the gravitino lsp imposes the bound @xmath90 . note that the scalar masses are non - tachyonic at the gut scale for @xmath91 . let us finally note that the superpotential does not play a role in this discussion as long as it stabilizes the fields at the desired values with vanishing vacuum energy . this question can be analyzed locally , in terms of @xmath92 and @xmath93 , along the lines of ref . @xcite . as a result , the superpotential expansion coefficients @xmath94 , @xmath95 , have to satisfy certain ( model - dependent ) constraints . we have studied the conditions for the gravitino to be the lsp in models of gravity mediated susy breaking . this requirement constrains mainly the gaugino mass parameter at the gut scale while the other parameters play a minor role , as long as the scalar masses are non - tachyonic . for cmssm - type models at moderate @xmath39 , the resulting constraint on the khler potential and the gauge kinetic function is approximately @xmath2 , where the derivatives are taken with respect to the dominant susy breaking field . for large @xmath39 and @xmath38-terms , the above constraint gets modified at small values of the universal scalar mass @xmath41 . the results are illustrated in figs . [ fig1 ] and [ fig2 ] . the condition @xmath2 can easily be satisfied in string - motivated set - ups and thus the gravitino lsp is a reasonable alternative to the neutralino lsp in gravity mediation . as it is hard to obtain an extremely small value of @xmath34 without finetuning , the gravitino mass is still expected to be of the same order of magnitude as the other soft masses . k.  choi , a.  falkowski , h.  p.  nilles and m.  olechowski , nucl . b * 718 * , 113 ( 2005 ) ; m.  endo , m.  yamaguchi and k.  yoshioka , phys . d * 72 * , 015004 ( 2005 ) ; k.  choi , k.  s.  jeong and k .- okumura , jhep * 0509 * , 039 ( 2005 ) ; a.  falkowski , o.  lebedev and y.  mambrini , jhep * 0511 * , 034 ( 2005 ) . m.  dine , w.  fischler and m.  srednicki , nucl . b * 189 * , 575 ( 1981 ) ; m.  dine and w.  fischler , phys . b * 110 * , 227 ( 1982 ) ; m.  dine and a.  e.  nelson , phys . d * 48 * , 1277 ( 1993 ) ; m.  dine , a.  e.  nelson and y.  shirman , phys . d * 51 * , 1362 ( 1995 ) . d.  e.  kaplan , g.  d.  kribs and m.  schmaltz , phys .  rev . d * 62 * , 035010 ( 2000 ) ; z.  chacko , m.  a.  luty , a.  e.  nelson and e.  ponton , jhep * 0001 * , 003 ( 2000 ) ;    w.  buchmller , k.  hamaguchi and j.  kersten , phys . b * 632 * , 366 ( 2006 ) ; w.  buchmller , l.  covi , j.  kersten and k.  schmidt - hoberg , jcap * 0611 * , 007 ( 2006 ) ; j.  l.  evans , d.  e.  morrissey and j.  d.  wells , phys . d * 75 * , 055017 ( 2007 ) .                        s.  k.  soni and h.  a.  weldon , phys . b * 126 * , 215 ( 1983 ) ; v.  s.  kaplunovsky and j.  louis , phys . b * 306 * , 269 ( 1993 ) . s.  abel , s.  khalil and o.  lebedev , phys . lett .   * 89 * , 121601 ( 2002 ) . d.  g.  cerdeo , k.  y.  choi , k.  jedamzik , l.  roszkowski and r.  ruiz de austri , jcap * 0606 * , 005 ( 2006 ) . s.  p.  martin and p.  ramond , phys . d * 48 * , 5365 ( 1993 ) . a.  riotto , e.  roulet and i.  vilja , phys . b * 390 * , 73 ( 1997 ) . j.  r.  ellis , j.  giedt , o.  lebedev , k.  olive and m.  srednicki , phys . d * 78 * , 075006 ( 2008 ) . b.  c.  allanach , comput . commun .   * 143 * , 305 ( 2002 ) p.  binetruy , m.  k.  gaillard and y.  y.  wu , nucl . b * 481 * , 109 ( 1996 ) .
we study general conditions for the gravitino to be the lightest supersymmetric particle ( lsp ) in models with gravity mediated supersymmetry breaking . 
 we find that the decisive quantities are the khler potential @xmath0 and the gauge kinetic function @xmath1 . in constrained mssm ( cmssm ) 
 type models , the gravitino lsp occurs if the gaugino mass at the gut scale is greater than approximately 2.5 gravitino masses . 
 this translates into @xmath2 , where the derivatives are taken with respect to the dominant susy breaking field . 
 this requirement can easily be satisfied in string - motivated setups . 
 = 20pt    * jrn kersten@xmath3 and oleg lebedev@xmath4 * +    @xmath5__university of hamburg , ii . 
 institute for theoretical physics + luruper chaussee 149 , 22761 hamburg , germany _ 
 _ + @xmath6__desy theory group + notkestrae 85 , 22603 hamburg , germany _ _