You are an expert at summarizing long articles. Proceed to summarize the following text: 
in recent years , experimental cosmology has provided strong evidence that the universe is currently undergoing a phase of accelerated expansion . the physical phenomena responsible for this expansion has proved elusive , and there are numerous theories that attempt to explain the current epoch of the universe . typically , the observed acceleration is attributed to a new energy component , dark energy , which dominates at late times . numerous models exist of this form , the simplest of which include introducing a cosmological constant @xmath1 , or alternatively a scalar field slowly rolling down a potential .    although dark energy is undoubtedly the most popular explanation of the current epoch of the universe , it is not the only way to obtain late time acceleration . in this paper we consider a class of models where gravity is modified at large scales , in such a way that the late - time expansion of the universe could arise naturally from the new gravitational field equations . these modified gravity models have been considered by numerous authors , see for example @xcite .    modifying gravity in a manner consistent with experimental data has proved difficult . general relativity ( gr ) is a very robust and well tested theory , and it has been found that even slight modifications often lead to instabilities , such as the propagation of ghosts @xcite , or in otherwise stable matter sources @xcite,@xcite . when introducing additional terms into the gravitational action , we must be careful to respect the success of gr in both the low and high curvature regimes , to ensure that any potentially new model agrees with known observational tests of gravity .    in the literature , there are numerous simple conditions that exist which restrict the form that a modified gravity model may take . in this paper , we combine all of these conditions , and in doing so find that the modified gravity function @xmath0 is well constrained , even before considering stringent experimental tests . the philosophy adopted throughout is that before attempting to reconcile any potential modified gravity model with experimental data , that modified gravity model must first satisfy these consistency requirements . we will take a trial @xmath0 model which satisfies all of the existing constraints . we find that our model exhibits a late - time accelerating solution , in the absence of a cosmological constant . we then consider the cosmology of our model , and obtain a modified friedmann equation . we show that to satisfy all constraints , and to obtain an acceptable newtonian limit for small @xmath2 , our model must act like gr with highly suppressed corrections throughout its cosmological history . in addition , we find that although our model has no true cosmological constant , we must still fine tune a particular combination of the free parameters in @xmath0 to obtain an acceptably small curvature in the current accelerating epoch . we conjecture that our results are generic features of models which satisfy the consistency requirements . before we consider a specific @xmath0 model , we first briefly review the field equations in modified gravity theories . throughout this paper , we will study the action    @xmath3    where @xmath0 is some function of the ricci scalar @xmath2 , @xmath4 is the mass scale of our model , and @xmath5 the matter action . the field equations obtained by varying the action ( @xmath6 ) with respect to the metric are    @xmath7    where @xmath8 is the energy momentum tensor of any matter present . taking the trace of ( @xmath9 ) gives the more useful equation    @xmath10    where the function @xmath11 is given by @xmath12 . vacuum solutions to the field equations satisfy @xmath13 when @xmath14 , and hence @xmath15 . in addition to the above field equations in the jordan frame , we will also want to consider the potential of the scalar field in the einstein frame . to transform to the einstein frame , we first write ( @xmath6 ) as    @xmath16 + \int \sqrt{-g } d^{4}x{\cal l}_{\rm m } , \ ] ]    where @xmath17 is the matter lagrange density . the actions ( @xmath18 ) and ( @xmath6 ) are equivalent if @xmath19 . we then use the conformal transform @xmath20 , which gives    @xmath21    where @xmath2 and @xmath22 are the ricci scalars associated with the metrics @xmath23 and @xmath24 respectively . using this in ( @xmath18 ) gives the following einstein frame action    @xmath25 + \int \sqrt{-\tilde{g } }   d^{4}x   { 1 \over ( f')^{2}}{\cal l}_{\rm m } , \ ] ]    where the einstein frame potential is given by    @xmath26    finally , by making the field redefinition @xmath27 , we obtain    @xmath28,\ ] ]    with potential    @xmath29e^{-2 \sigma\sqrt{2 } / \sqrt{3m^{2}}}.\ ] ]    in many instances , it is preferable to study modified gravity in the einstein frame , since the field equations are much simpler . additionally , the potential ( @xmath30 ) is useful since its critical points correspond to the vacuum solutions @xmath31 in the jordan frame . we stress that the two frames are globally equivalent only if @xmath19 . here we briefly review the constraints in the literature imposed on the form of the function @xmath0 . we begin by demanding @xmath32 and @xmath33 for all @xmath2 . the first of these is to ensure stability ; it has been shown @xcite that if @xmath34 for any @xmath2 then the model will possess ghost instabilities in this region . the second condition @xmath19 is imposed since it has been found that models which have @xmath35 will generically possess instabilities , when we consider the metric variational approach of our model @xcite . we note that the possibility of @xmath36 being zero for some @xmath2 has not been completely discounted in the literature . nevertheless , we will impose @xmath33 for all @xmath2 . the next constraint that we impose on @xmath0 is that in the limit @xmath37 , we have @xmath38 . writing @xmath39 , this implies that @xmath40 as @xmath41 . this in turn implies that @xmath42 as @xmath43 , from which we can deduce that @xmath44 as @xmath45 . this condition is imposed to ensure that the modified gravity model acts suitably like @xmath46 in the large @xmath2 regime , where gravity is well constrained by ppn constraints and the cmb . with this bound , we have @xmath42 as @xmath43 . however , in ref . @xcite it was found that for a given @xmath0 theory to be stable to perturbations in the large @xmath2 regime , we must have @xmath47 as @xmath43 . this means that @xmath48 must asymptote to unity from below , since @xmath49 implies that it must be an increasing function . next , we can use the fact that we have imposed @xmath19 for all @xmath2 . this means that there can be no turning points in @xmath48 , implying that if @xmath48 asymptotes to unity from below , then it must remain less than unity for all @xmath2 . however , we have also imposed @xmath50 . from this we conclude that @xmath48 must be an increasing function of @xmath2 , and must satisfy @xmath51 . another set of constraints on @xmath0 are discussed in ref . @xcite , where the cosmology of @xmath0 models was considered . in order for a theory to be a viable alternative to gr , it must exhibit an acceptable cosmological history , that is it must have suitable radiation , matter and late time accelerating eras . it was found that in order for a particular @xmath0 to have a valid matter era , @xmath0 must satisfy @xmath52 and @xmath53 at @xmath54 , where @xmath55 and @xmath56 are given by @xmath57 and @xmath58 . in addition , to obtain a late time accelerating era such as we are currently in , the function @xmath59 must satisfy either ; @xmath60 @xmath61 , @xmath62 and @xmath63 or @xmath64 @xmath65 at @xmath66 . if these are not satisfied for any @xmath2 , then the model will not have an acceptable cosmological history . in this section , we give an example @xmath0 function which satisfies all of the conditions in the previous section . given that @xmath48 must be an increasing function , and lie in the range @xmath67 , an obvious choice is    @xmath68,\ ] ]    where @xmath69 and @xmath70 are free parameters . this function has the appropriate behaviour @xmath42 as @xmath43 and @xmath71 as @xmath72 . integrating this @xmath48 gives us    @xmath73 + a , \ ] ]    where @xmath74 is an integration constant . we are looking for @xmath0 models that exhibit late time accelerating solutions in the absence of a cosmological constant . therefore to specify @xmath74 , we impose that @xmath75 . hence we find @xmath76 and    @xmath77.\ ] ]    it is this @xmath0 that will be studied for the remainder of this paper . we will begin by considering some of the general properties of our model . first , we look for vacuum solutions to the field equations , that is solutions to @xmath15 . the behaviour of @xmath11 is exhibited in fig . we have found that @xmath11 for our @xmath0 generically possesses three zeros , for any @xmath79 and @xmath80 . this means that our @xmath0 model can have three vacuum states , which are minkowski space ( @xmath81 ) , and two de - sitter vacua , one of which is stable .    to see these vacuum states more explicitly , we move to the einstein frame . a plot of the potential @xmath82 for our @xmath0 is given in figs . @xmath83 , @xmath84 . we can clearly see that the potential has two minima , one at @xmath85 ( which corresponds to the minkowski vacuum ) and the other at some @xmath86 . this second minima corresponds to a stable de sitter vacuum solution in the jordan frame , and hence our model has a stable accelerating solution , in the absence of a cosmological constant . this is exactly the behaviour we seek . finally , the third vacuum in the jordan frame corresponds to the maxima in the potential @xmath83 , and is unstable . following @xcite , we also briefly consider the functions @xmath55 , @xmath56 and @xmath87 for our model , as given in section @xmath88 . we plot these functions parametrically as functions of @xmath2 in fig . we see that there is a region in which @xmath90 and @xmath91 for @xmath92 , which corresponds to a matter era . as @xmath43 , we have @xmath93 and @xmath94 , suggesting that the condition for a matter epoch is satisfied asymptotically . further , as @xmath2 decreases , there is a region where @xmath95 , at which @xmath96 . this region corresponds to the late - time de - sitter phase . hence our model connects the points @xmath97 and @xmath98 in the @xmath99 plane , as is required @xcite for it to have an acceptable cosmic history . we now consider the newtonian limit of our model . in doing so , we will be able to constrain the free parameters @xmath79 and @xmath70 . the constant @xmath79 will be fixed by the following two conditions ; we require the de - sitter vacuum solution to be @xmath100 , and as we will see shortly , we require @xmath101 . using these conditions , the constant @xmath70 will not be fixed , but we will find that it must be large .    to see how @xmath79 and @xmath70 are determined , we consider the newtonian limit of modified gravity theories . the full field equations for the action ( @xmath6 ) are    @xmath102    we would like to perform a weak - field expansion of these equations around the de - sitter minima of our model . in doing so , we hope to obtain an acceptable newtonian limit . an analysis has been performed previously in ref . @xcite , and expanding the field equations about a symmetric de - sitter vacuum gives    @xmath103    where    @xmath104    in order to obtain an acceptable newtonian limit from these perturbative equations , we require that @xmath105 , @xmath106 and @xmath107 , where @xmath108 is a macroscopic distance . if this is the case , then the perturbative equations ( @xmath9 ) will be approximately given by    @xmath109    equation ( @xmath110 ) is simply the weak field expansion of general relativity , from which the standard newtonian limit is recovered . the only difference is the coefficient of the first term in ( @xmath110 ) , which is @xmath105 as opposed to unity . note that to obtain the correct limit we must have @xmath111 ; if this were not the case then fourth order derivative terms such as @xmath112 would be present in ( @xmath110 ) , and it has been shown that these terms would lead to strong curvature at all lengthscales @xcite .    for our model ( and generically in @xmath0 theories ) , we have @xmath113 for @xmath114 , which is the first condition to obtain an acceptable newtonian limit . however , the second condition , @xmath115 , is not generically satisfied , and we must choose our free parameters to obtain the correct behaviour . from ( @xmath116 ) , we find @xmath36 to be    @xmath117    and hence to ensure that @xmath118 is very small , we require @xmath119 . we can use this condition to fix @xmath79 in terms of @xmath120 and @xmath70 . to do so , we note that in the vicinity of the de - sitter minima , @xmath121 , we can expand @xmath0 and @xmath48 for large @xmath122 ,    @xmath123    and hence from the vacuum field equations @xmath15 , we can use our approximations ( @xmath124 ) to give    @xmath125    from which we find @xmath126 . this fixes the free parameter @xmath79 in terms of @xmath120 and the remaining free parameter @xmath70 . next , we can constrain @xmath70 from the condition @xmath127 . using this , and expanding @xmath36 in powers of @xmath128 , we find that @xmath70 must satisfy    @xmath129    which is satisfied for large @xmath70 , such that @xmath130 . to review our conditions ; we are working with a model with two free parameters , @xmath79 and @xmath70 , and we have imposed two constraints on this model , which are that @xmath131 and @xmath132 . these constraints force us to choose @xmath79 and @xmath70 such that @xmath133 and @xmath134 . together , they imply that @xmath135 , and hence @xmath136 . we note that we have not been forced to specify the constant @xmath70 , other than imposing the condition @xmath135 . this parameter controls how closely our model mimics gr ; the larger we set @xmath70 the more suppressed our corrections @xmath137 become .    before moving onto the cosmology of our model , we remark that the above weak - field expansion was performed around the de - sitter vacuum @xmath138 . it has been noted @xcite that for local tests of gravity , the expansion should instead be around the local energy density of the solar system , which is much larger than @xmath120 . in a subsequent paper we will perform a detailed analysis of the local tests of gravity for our model , but for now we simply expand around @xmath139 . performing a weak - field expansion around a solar system background will not significantly modify our conclusion ; we are simply stating that in order to obtain an acceptable weak - field limit for small @xmath2 , we must choose the constants @xmath79 and @xmath70 such that @xmath140 is satisfied . having considered the newtonian limit of our models , we now evaluate the friedmann equation , and attempt to reconstruct the cosmic history of our models . we will find that this model mimics general relativity very closely throughout its cosmic history . to show this , we first write down the equivalent friedmann equation for a general @xmath0 model , obtained from the @xmath141 component of the field equations ( @xmath9 ) ,    @xmath142 = { \rho \over m^{2 } } .\ ] ]    with our highly non - trivial @xmath0 , this equation corresponds to a complex , non linear , third - order differential equation in the scale factor @xmath79 . however , we can use our approximations ( @xmath124 ) to write ( @xmath143 ) in a much simplified form . we first note that the approximations ( @xmath124 ) are valid for the entire cosmic history of this model , because they are applicable for large @xmath144 . since @xmath145 throughout the cosmic history , and since @xmath146 is at its smallest value at @xmath138 , then given that we have constrained @xmath146 to be large at @xmath138 then it must be large for all @xmath145 .    using the approximations ( @xmath124 ) in ( @xmath143 ) , we find the following modified friedmann equation ,    @xmath147    where we have used the condition that @xmath70 must be large , and hence @xmath148 . the first two terms are what we would expect from standard general relativity with a fine tuned cosmological constant @xmath149 . the remaining terms on the left hand side are corrections to the friedmann equation , but they are highly suppressed by a factor of @xmath150 for all @xmath151 . it follows that our model will not significantly differ from standard gr . the exponentially suppressed corrections to general relativity that we have found are small in the current epoch , and decrease in significance as we track our model back through its cosmic history . additionally , we note that we still have a fine tuning problem , in that we have two free parameters , and we have chosen them specifically such that the combination @xmath152 satisfies @xmath153 . we stress however that the combination @xmath154 in ( @xmath155 ) is not a true cosmological constant ; rather our model mimics standard general relativity with a small vacuum energy . the fine - tuning found in our model is a generic feature of modified gravity theories . since we demand that @xmath156 for small @xmath2 to obtain an acceptable weak field limit , it follows that in the vicinity of the vacuum @xmath157 , we must have @xmath158 , and hence @xmath159 , where @xmath160 and @xmath161 are constants . this means that for vacuum @xmath121 , we can expand @xmath0 in the form @xmath162 , where @xmath160 and @xmath161 will be some combination of constants in the model . this is exactly what we have done for our @xmath0 model above ; we have expanded @xmath0 as @xmath163 for @xmath121 . it follows that to obtain an acceptable vacuum solution @xmath164 , we must fine - tune the parameters in the model . the fact that our model must necessarily mimic gr with suppressed corrections is a consequence of the constraints that we have imposed . specifically , we have used the fact that to obtain an acceptable weak field expansion , we require @xmath156 for small @xmath2 . in addition , we have also assumed that in the large @xmath2 regime @xmath165 , which suggests that @xmath156 as @xmath41 . since we are considering models which have @xmath19 for all @xmath2 , then it follows that @xmath36 must be small throughout the cosmic history . we expect that any @xmath0 function that satisfies the consistency conditions that we have considered will possess a friedmann equation of the form ( @xmath155 ) , that is standard gr plus @xmath1 with small correction terms . these correction terms will not necessarily be exponentially suppressed as they are for the @xmath0 considered in this paper , but they must be suppressed throughout the expansion history of the universe regardless of the particular form of @xmath0 . however , although these models will mimic gr , this does not imply that they are observationally identical to gr if we consider all aspects of gravity . for example , it might be possible to observe small corrections to gr by considering solar system tests of gravity or the binary pulsar . in a subsequent paper we hope to find distinct observational signatures of our model by analyzing local gravity constraints .    finally , we observe that the conclusions that we have reached do not apply if we were to relax any of the constraints on @xmath0 , for example by allowing @xmath166 for some @xmath2 in the past . hence it might be possible to construct an acceptable model that does not obey all of the constraints at all times , and hence will not mimic gr throughout the entire cosmic history . in addition , it is not strictly necessary for an acceptable modified gravity model to obey the consistency conditions for all @xmath2 , since they can only be probed for @xmath167 . we could have an acceptable model which has @xmath168 for some @xmath169 in the future . however , there is a possibility of such models evolving to a final state containing instabilities . we have taken the consistency constraints that exist in the literature for modified gravity models , and used them to construct a particular modified gravity function @xmath0 . a study of the model has shown that in order to satisfy all constraints , it must act like gr with highly suppressed corrections throughout cosmic history . in addition , we find that even though we do not have a true cosmological constant in our setup , we must still fine - tune the parameters in our @xmath0 function to obtain an acceptable late time accelerating epoch . although we have come to this conclusion for our specific model , we expect our results to hold true for a large class of @xmath0 models which satisfy all of the constraints that we have considered .    while we were completing this work we became aware of refs . @xcite , which come to similar conclusions . in ref . @xcite , it was found that in order to satisfy local gravity constraints , the function @xmath55 as defined in section @xmath88 must satisfy @xmath170 for @xmath171 . this places a severe constraint upon @xmath36 , which must be very small in the current epoch of the universe . the model considered in this paper can satisfy the constraint @xmath170 by making the free parameter @xmath70 sufficiently large . however , such a stringent constraint is likely to yield a model that is virtually indistinguishable to gr . was considered , where @xmath59 , @xmath173 , @xmath174 and @xmath175 are free parameters . the model considered in this paper shares many similarities with ( @xmath176 ) ; the condition @xmath177 was imposed in ref . @xcite both at @xmath178 and as @xmath43 . this implies that the function @xmath179 can be expanded as      for small @xmath181 , which is valid throughout the cosmic history of the model . we have arrived at a very similar expansion for the @xmath0 function considered in this paper , ( @xmath124 ) . the difference between the two models is that ( @xmath182 ) contains power law corrections to gr , whereas ( @xmath124 ) contains exponentially suppressed corrections .
modified gravity models are subject to a number of consistency requirements which restrict the form that the function @xmath0 can take . 
 we study a particular class of @xmath0 functions which satisfy various constraints that have been found in the literature . 
 these models have a late time accelerating epoch , and an acceptable matter era . 
 we calculate the friedmann equation for our models , and show that in order to satisfy the constraints we impose , they must mimic general relativity plus @xmath1 throughout the cosmic history , with exponentially suppressed corrections . 
 we also find that the free parameters in our model must be fine tuned to obtain an acceptable late time accelerating phase . 
 we discuss the generality of this conclusion .