document: modified theories of gravity have attained much attention after the discovery of expanding accelerated universe . 
   the basic ingredient responsible for this tremendous change in cosmic history is some mysterious type force having repulsive nature dubbed as dark energy . 
   the enigmatic nature of this energy has motivated many researchers to unveil its hidden characteristics which are still not known . 
   modified gravity approach is considered as the promising and optimistic scenario among several other proposals that have been presented to explore the salient features of dark energy . 
   these modified theories are established by adding or replacing curvature invariants and their corresponding generic functions in the einstein - hilbert action . 
   lovelock theory of gravity is the direct generalization of general relativity ( gr ) in @xmath3-dimensions which coincides with gr in @xmath4-dimensions @xcite . 
   the ricci scalar @xmath5 is known as first lovelock scalar while gauss - bonnet ( gb ) invariant is the second lovelock scalar yielding einstein - gauss - bonnet gravity in @xmath6-dimensions @xcite . 
   the gb invariant is a linear combination with an interesting feature that it is free from spin-2 ghost instabilities defined as @xcite @xmath7 where @xmath8 and @xmath9 are the ricci and riemann tensors , respectively . 
   this quadratic curvature invariant is a topological term in 4-dimensions which possesses trivial contribution in the field equations . to discuss the dynamics of gb invariant in 4-dimensions , 
   there are two interesting scenarios either to couple @xmath1 with scalar field or to add generic function @xmath10 in the einstein - hilbert action . 
   the first scheme naturally appears in the effective action in string theory which investigates singularity - free cosmological solutions @xcite . 
   the second approach known as @xmath10 gravity is introduced as an alternative for dark energy which successfully discusses the late - time cosmological evolution @xcite . 
   this modified theory of gravity is endowed with a quite rich cosmological structure as well as consistent with solar system constraints @xcite . 
   the current cosmic accelerated expansion has also been discussed in modified theories of gravity involving the curvature - matter coupling . 
   harko et al . 
   @xcite established @xmath11 gravity to study the curvature - matter coupling . 
   recently , we introduced the curvature - matter coupling in @xmath10 gravity named as @xmath0 theory of gravity @xcite . 
   this coupling yields non - zero covariant divergence of the energy - momentum tensor and an extra force appears due to which massive test particles follow non - geodesic trajectories while geodesic lines of geometry are followed by the dust particles . 
   shamir and ahmad @xcite constructed some cosmologically viable models in @xmath0 gravity using noether symmetry approach . 
   it is mentioned here that cosmic expansion can be obtained from geometric as well as matter components in such coupling . 
   the reconstruction as well as stability of cosmic evolutionary models in modified theories of gravity are the captivating issues in cosmology . in reconstruction technique , 
   any known cosmic solution is used in the modified field equations to find the corresponding function which reproduces the given evolutionary cosmic history . in stability analysis , the isotropic and homogeneous perturbations are usually considered in which hubble parameter as well as energy density are perturbed to examine the background stability as time evolves @xcite . 
   nojiri et al . 
   @xcite formulated the reconstruction scheme to reproduce some cosmological models in @xmath12 gravity . 
   elizalde et al . 
   @xcite applied the same scenario for @xmath13cdm cosmology ( @xmath13 denotes cosmological constant while cdm stands for cold dark matter ) in @xmath14 gravity as well as in modified gb theories of gravity . 
   the stability of power - law solutions are also discussed in modified gravity theories @xcite . 
   sez - gmez @xcite explored the cosmological solutions in @xmath12 horava - lifshitz gravity and analyzed their stability against first order perturbations around frw universe . 
   myrzakulov and his collaborators @xcite discussed the cosmological models and found that @xmath10 gravity could successfully explain the cosmic evolutionary history . 
   jamil et al . 
   @xcite reconstructed the cosmological models in @xmath11 gravity and found that numerical analysis for hubble parameter is in good agreement with observational data for redshift parameter @xmath15 . 
   the stability of de sitter , power - law solutions as well as @xmath13cdm are analyzed in the context of @xmath14 gravity @xcite . 
   salako et al . 
   @xcite studied the cosmological reconstruction , stability as well as thermodynamics including first and second laws for @xmath13cdm model in generalized teleparallel theory of gravity . 
   sharif and zubair @xcite demonstrated that @xmath11 gravity can reproduce @xmath13cdm model , phantom or non - phantom eras , de sitter universe and power - law cosmic history . 
   they also analyzed the stability of reconstructed de sitter as well as power - law solutions .    in this paper , we reconstruct various cosmological models including de sitter universe , power - law solutions , phantom or non - phantom eras and @xmath13cdm model in @xmath0 theory . 
   we also analyze the stability against linear homogeneous perturbations for de sitter as well as power - law solutions . 
   the paper has the following format . in section 
   * 2 * , we formulate the modified field equations while section * 3 * is devoted to reconstruct some known cosmological solutions in this gravity . 
   section * 4 * analyzes the stability of specific solutions against linear perturbations around frw universe model . 
   the results are summarized in the last section . 
   the action for @xmath0 gravity is defined as @xcite @xmath16 where @xmath17 and @xmath18 represent coupling constant , determinant of the metric tensor ( @xmath19 ) and lagrangian associated with matter distribution , respectively . 
   varying eq.([1 ] ) with respect to @xmath19 , we obtain the field equations @xmath20f_{\mathcal{g}}(\mathcal{g},t ) \\\nonumber&-&[2rg_{\alpha\beta } \box-4r_{\alpha\beta}\box-2r\nabla_{\alpha}\nabla_{\beta } + 4r^{\mu}_{\beta}\nabla_{\alpha}\nabla_{\mu } + 4r^{\mu}_{\alpha}\nabla_{\beta}\nabla_{\mu}\\\label{2}&- & 4g_{\alpha\beta}r^{\mu\nu } \nabla_{\mu}\nabla_{\nu}+4r_{\alpha\mu\beta\nu } \nabla^{\mu}\nabla^{\nu}]f_{\mathcal{g}}(\mathcal{g},t)=0,\end{aligned}\ ] ] where @xmath21 ( @xmath22 denotes a covariant derivative ) and @xmath23 is the energy - momentum tensor . 
   the expressions for @xmath23 and @xmath24 are @xcite @xmath25 where we have assumed that @xmath18 depends only on @xmath19 rather than its derivatives . the non - zero divergence of @xmath23 is given by @xmath26.\end{aligned}\ ] ] the above equations indicate that the complete dynamics of @xmath0 gravity is based on the suitable choice of @xmath18 . 
   the energy - momentum tensor for perfect fluid is @xmath27 where @xmath28 and @xmath29 represent the four velocity , energy density and pressure of matter distribution , respectively . in this case , the expression for @xmath24 becomes @xmath30 where @xmath31 . 
   the line element for frw universe model is given by @xmath32 where @xmath33 is the scale factor . 
   using eqs.([5])-([7 ] ) in ( [ 2 ] ) , we obtain the corresponding field equation as follows @xmath34 where @xmath35 and dot represents derivative with respect to time . 
   the non - zero continuity equation ( [ 4 ] ) takes the form @xmath36.\ ] ] the standard conservation law holds if right hand side of this equation vanishes . for equation of state @xmath37 ( 
   @xmath38 is the equation of state parameter ) , eq.([9 ] ) yields @xmath39 with additional constraint @xmath40    we rewrite the above equations in terms of new variable @xmath41 known as e - folding instead of @xmath42 which is also related with redshift parameter @xmath43 as @xcite @xmath44 using the above definition of @xmath41 , eqs.([8 ] ) and ( [ 9 ] ) become @xmath45,\end{aligned}\ ] ] where @xmath46 and prime denotes derivative with respect to @xmath41 . 
   the simplest choice of @xmath0 model is @xmath47 which possesses no direct non - minimally coupling between curvature and matter . for this particular model , the field equation ( [ 13 ] ) 
   splits into a set of two ordinary differential equations as @xmath48 @xmath49 where @xmath50 and @xmath51 . 
   the field equations for perfect fluid matter distribution in @xmath10 gravity is recovered if @xmath52 vanishes while gr is achieved for @xmath53 . 
   in this section , we reproduce different cosmological scenarios including de sitter universe , power - law solutions , phantom / non - phantom eras and @xmath13cdm model in @xmath0 gravity .      the de sitter cosmic evolution is interesting and well - known as it elegantly describes current expansion of the universe . 
   the scale factor of this evolutionary model grows exponentially with constant hubble parameter @xmath54 , defined as @xcite @xmath55 where @xmath56 is an integration constant . 
   equation ( [ 10 ] ) gives energy density of the form @xmath57 where @xmath58 and @xmath59 is a constant . 
   using eqs.([1d ] ) and ( [ 2d ] ) in ( [ 8 ] ) , we obtain @xmath60 where @xmath61 is the gb invariant at @xmath54 . 
   the solution of the above differential equation is @xmath62 where @xmath63 s @xmath64 are integration constants . since we have used the continuity equation ( [ 10 ] ) in eq.([3d ] ) , so we must constrain its solution . using the above equation with eq.([11 ] ) , we obtain the following functions @xmath65 where @xmath66 s @xmath67 are constants in terms of @xmath38 and @xmath68 given in appendix * a*. for the model ( [ 15 ] ) , we have @xmath69 where the first equation corresponds to de sitter universe in the absence of matter contents in @xmath10 gravity @xcite . using the constraint ( [ 11 ] ) 
   , the second equation becomes @xmath70 the solution of eqs.([7d ] ) and ( [ 8d ] ) leads to @xmath71 where @xmath72 s are constants of integration . equations ( [ 4d ] ) and ( [ 9d ] ) indicate that de sitter expansion can also be described in @xmath0 gravity . 
   power - law solutions have significant importance to discuss different evolutionary phases of the universe in modified theory . 
   these solutions describe the decelerated as well as accelerated cosmic eras which are characterized by the scale factor as @xcite @xmath73 the cosmic decelerated phase is observed for @xmath74 including the radiation @xmath75 as well as dust @xmath76 dominated eras while @xmath77 covers the accelerated phase of the universe . 
   for this scale factor , the gb invariant takes the form @xmath78 using eqs.([10 ] ) , ( [ 1p ] ) and ( [ 2p ] ) , the field equation becomes @xmath79 whose solution is given by @xmath80 where @xmath81 s are integration constants and @xmath82,\\\nonumber\gamma_{2}&=&\left[\frac{3}{4}\lambda \tilde{c}_{2}(1+\omega)\{2\tilde{c}_{2}\lambda(1+\omega)+2(\lambda-1 ) -8\}+\frac{1}{4}(\lambda-1)(\lambda-7)+4\right.\\\nonumber&+&\left . 
   8\tilde{c}_{2}(\lambda-1)\left(\frac{1+\omega}{1 - 3\omega}\right ) \right]^{\frac{1}{2}},\quad\gamma_{3}=-\frac{1}{2}\left(\frac{1 - 3\omega } { 1+\omega}\right),\quad\gamma_{4}=\frac{2\kappa^2}{\omega-3},\\\nonumber \gamma_{5}&=&\left(\frac{18\lambda^{3}(1 - 3\omega)^{\frac{3\lambda ( 1+\omega)-2}{3\lambda(1+\omega)}}}{3\lambda(1 - 3\omega)+4}\right ) \rho_{0}^{\frac{-2}{3\lambda(1+\omega)}},\quad\gamma_{6}=\frac{2 } { 3\lambda(1+\omega)}.\end{aligned}\ ] ] inserting eq.([4p ] ) in ( [ 11 ] ) , we obtain @xmath83 where @xmath84 s and @xmath85 s @xmath86 are given in appendix * a*.    now we find the expression of @xmath0 for the choice of model ( [ 15 ] ) . the differential equation ( [ 3p ] ) yields two ordinary differential equations in variables @xmath1 and @xmath2 . 
   the first is the second order cauchy - euler s equation related to curvature given by @xmath87 whose solution is given by @xmath88 where @xmath89 s are constants of integration which is consistent with power - law solutions in @xmath10 gravity @xcite . 
   the second equation is obtained using the additional constraint ( [ 11 ] ) as @xmath90 the solution of this equation corresponds to matter distribution given by @xmath91}\left(\frac{t}{\rho_{0}(1 - 3\omega)}\right ) ^{\frac{2}{3\lambda(1+\omega)}},\end{aligned}\ ] ] where @xmath92 s @xmath93 are integration constants . 
   consequently , @xmath0 model becomes @xmath94}\\\label{7p}&\times & \left(\frac{t}{\rho_{0}(1 - 3\omega)}\right)^{\frac{2}{3\lambda(1+\omega)}}.\end{aligned}\ ] ] thus , the power - law solutions are reconstructed which may be helpful to explore the expansion history of the universe in this modified theory of gravity . 
   here , we reconstruct @xmath0 model which can explain the system including both phantom and non - phantom eras . in the einstein gravity , 
   the hubble parameter describing the phantom as well as non - phantom matter distribution is given by @xcite @xmath95 where @xmath96 and @xmath97 represent the model parameter , energy densities of phantom and non - phantom matter fluids , respectively . 
   when the scale factor is large , the first term on right hand side dominates which corresponds to the phantom era of the universe with @xmath98 . 
   the non - phantom era in the early universe is observed for @xmath99 when the scale factor is small and the second term dominates . 
   we rewrite @xmath100 in terms of a new function @xmath101 as @xmath102 so that eq.([1q ] ) becomes @xmath103 where @xmath104 and @xmath105 . 
   the gb invariant takes the form @xmath106 inserting eq.([2q ] ) in ( [ 3q ] ) , we obtain a quadratic equation in @xmath107 whose solution is given by @xmath108 for the sake of simplicity , we consider @xmath109 so that it reduces to @xmath110 using eqs.([2q ] ) and ( [ 4q ] ) in ( [ 8 ] ) , we have @xmath111 which is a complicated partial differential equation whose analytical solution can not be found .    to find the reconstructed @xmath0 model , we consider its particular form ( [ 15 ] ) which provides the following set of differential equations @xmath112 where we have used the additional constraint in the second equation . solving these equations 
   , it follows that @xmath113-\frac{2\kappa^{2}t}{1 - 3\omega}.\end{aligned}\ ] ] where @xmath114 s are constants of integration . 
   thus , phantom and non - phantom cosmic history can be discussed in @xmath0 gravity . 
   now we apply the usual reconstruction technique to reproduce the @xmath13cdm cosmology in this gravity . in gr , 
   the @xmath13cdm cosmological evolution is discussed by adding @xmath13 in the einstein - hilbert action whereas we reconstruct such evolution in the absence of @xmath13 in the action ( [ 1 ] ) . 
   the hubble parameter for @xmath13cdm model is given by @xcite @xmath115 the first term indicates the contribution of cdm while the second term corresponds to @xmath13 . 
   the hubble parameter in terms of gb invariant takes the form @xmath116 equation ( [ 1h ] ) gives @xmath117 using eqs.([2h ] ) and ( [ 3h ] ) in ( [ 13 ] ) , we obtain @xmath118    this equation can not be solved analytically hence we solve it for a specific @xmath0 model ( [ 15 ] ) with dust fluid . 
   the corresponding equations become @xmath119 using constraint ( [ 11 ] ) , the solution of eq.([4h ] ) is given by @xmath120 where @xmath121 s are constants of integration while solution of eq.([5h ] ) can not be found . 
   let us consider the case when @xmath122 with the assumption @xmath123 which reduces eq.([5h ] ) to @xmath124 whose solution yields @xmath125 where @xmath126 s are integration constants . 
   consequently , @xmath0 takes the form @xmath127 provided that @xmath128 . here 
   @xmath0 gravity can not explain @xmath13cdm cosmological evolution rather it corresponds to cdm evolution . 
   in this section , we analyze stability of some cosmological evolutionary solutions about linear homogeneous perturbations in this modified gravity . 
   we construct the perturbed field as well as continuity equations using isotropic and homogeneous universe model for both general and particular cases including de sitter and power - law solutions . 
   we assume a general solution @xmath129 which satisfies the basic field equations for frw universe model in @xmath0 gravity . in terms of the above solution , 
   the expressions for @xmath130 and @xmath131 are @xmath132 for any particular @xmath0 model that can regenerate the above solution ( [ 1 t ] ) , the following equation of motion as well as non - zero divergence of the energy - momentum tensor must be satisfied @xmath133,\end{aligned}\ ] ] where superscript @xmath134 denotes that the function and its corresponding derivatives are calculated at @xmath135 and @xmath136 . if the conservation law holds , we get energy density in terms of @xmath137 as @xmath138 the first order perturbations in hubble parameter and energy density are defined as @xmath139 where @xmath140 and @xmath141 are the perturbation parameters .    in order to analyze first order perturbations about the solution ( [ 1 t ] ) , 
   we apply the series expansion on the function @xmath0 as @xmath142 where @xmath143 involves the terms proportional to quadratic or higher powers of @xmath1 and @xmath2 while only the linear terms are considered . using eqs.([6 t ] ) and ( [ 7 t ] ) in ( [ 8 ] ) , we obtain the following perturbed field equation @xmath144 where @xmath145 s @xmath146 are given in appendix * a*. inserting these perturbations in eq.([9 ] ) , the perturbed continuity equation is @xmath147 where @xmath148 s are provided in appendix * a*. if the conversation law holds in this modified gravity , eq.([9 t ] ) reduces to @xmath149 the perturbed equations ( [ 8 t ] ) and ( [ 9 t ] ) are helpful to analyze the stability of any specific frw cosmological evolutionary model in @xmath0 gravity . for the particular model ( [ 15 ] ) , these perturbed equations reduce to @xmath150 where the coefficients of @xmath151 and their derivatives are expressed in appendix * a*. in the following subsections , we investigate the stability of de sitter and power - law solutions .      consider the de sitter solution @xmath152 , the perturbed equation ( [ 8 t ] ) takes the form @xmath153 f_{\mathcal{g}t}^{0}-3456\rho_{*}h_{0}^{8}(1 - 3\omega)(1+\omega ) f_{\mathcal{gg}t}^{0}\right)\delta+12\rho_{*}h_{0}^{3}\\\nonumber & \times&(1 - 3\omega)f_{\mathcal{g}t}^{0}\dot{\delta}_{m}+\left(\kappa^{2 } \rho_{*}+\frac{1}{2}\rho_{*}(3-\omega)f_{t}^{0}+\rho_{*}^{2}(1 - 3\omega ) ( 1+\omega)f_{tt}^{0}\right.\\\nonumber&-&\left.12\rho _ { * } h_{0}^{2}(1 - 3\omega)[h_{0}^{2}+3(1+\omega)h_{0}^{2}]f_{\mathcal{g}t}^{0 } -36\rho_{*}^{2}h_{0}^{4}(1 - 3\omega)^{2}(1+\omega ) \right.\\\label{13t}&\times&\left.f_{\mathcal{g}tt}^{0}\right)\delta_{m}=0,\end{aligned}\ ] ] where the superscript @xmath154 represents that the function and its corresponding derivatives are evaluated at @xmath155 and @xmath156 . 
   we consider the conserved perturbed equation for stability analysis since the de sitter solutions are constructed using the constraint ( [ 11 ] ) in the previous section . 
   the numerical technique is used to solve eqs.([10 t ] ) and ( [ 13 t ] ) for the model ( [ 5d ] ) . 
   the evolution of @xmath140 and @xmath141 are shown in figure * 1*. we consider @xmath157 and @xmath158 throughout the stability analysis of de sitter universe models whereas integration constants are @xmath159 and @xmath160 . 
   figure * 1 * shows smooth behavior of @xmath140 ( left ) and @xmath141 ( right ) which do not decay in late times indicating that de sitter model ( [ 5d ] ) is unstable . 
   the stability analysis of model ( [ 6d ] ) with same integration constants is shown in figure * 2*. in the left panel , it is observed that small oscillations are produced about @xmath161 while it decays in late times , thus the model ( [ 6d ] ) shows stable behavior against perturbations . for model ( [ 9d ] ) , eq.([13 t ] ) becomes @xmath162 figure * 3 * represents the behavior of @xmath140 and @xmath141 for model ( [ 9d ] ) with integration constants @xmath163 and @xmath164 . 
   it is shown that oscillations in perturbation parameters are produced initially as shown in figure * 3*. this oscillating behavior is clearly observed in figure * 4 * which decays in future for both @xmath140 as well as @xmath141 and hence the solution becomes stable .      here 
   we investigate the stability of power - law solutions . 
   these solutions describe the accelerated as well as decelerated cosmological evolutionary phases in the background of frw universe . 
   we first consider the reconstructed power - law solution ( [ 5p ] ) and numerically solve eqs.([8 t ] ) and ( [ 10 t ] ) . 
   for this model , we choose integration constants @xmath165 and @xmath166 figure * 5 * shows the oscillating behavior of perturbed parameters @xmath167 for the cosmic accelerated era with @xmath168 and @xmath169 . 
   the perturbations around the power - law solutions decay in future leading to stable results . 
   the radiation ( @xmath170 and @xmath171 ) as well as matter ( @xmath172 and @xmath173 ) dominated eras can not be discussed for the model ( [ 5p ] ) because singular as well as complex terms appear which lead to non - physical case . 
   secondly , we consider the model ( [ 6p ] ) and analyze its behavior against linear perturbations . 
   figure * 6 * shows the fluctuating behavior of considered perturbations in the cosmic accelerated phase with @xmath168 and @xmath169 . here 
   , we choose @xmath174 and @xmath166 it is observed that the oscillating behavior disappears in future while both perturbation parameters will not decay in late times leading to unstable cosmological solutions . 
   the considered model can not explain the cosmological evolution corresponding to matter and radiation dominated eras like previous model ( [ 5p ] ) . 
   lastly , we explore the stability of model ( [ 7p ] ) with integration constants @xmath175 and @xmath176 . figure * 7 * represents the evolution of ( @xmath177 ) versus time for @xmath178 with @xmath168 . 
   the left panel shows that the oscillations of @xmath140 decay in late times while fluctuations of @xmath141 remain present in future . since a complete perturbation against any cosmological solution includes the matter perturbations therefore , 
   the solutions are unstable . 
   in this paper , we have employed the reconstruction scheme to @xmath0 gravity in the background of isotropic and homogeneous universe model to reproduce some important cosmological models . 
   the basic aspect of this modified gravity is the coupling between curvature and matter components which yields non - zero divergence of the energy - momentum tensor . 
   we have imposed additional constraint to obtain the standard conservation equation which has been used to explain the cosmic evolution in this gravity . 
   the de sitter and power - law solutions have been reconstructed for general as well as particular cases which are of great interest and have significant importance in cosmology . 
   we have also reconstructed the @xmath0 model which can explain cosmic history of the phantom as well as non - phantom phases of the universe . 
   similar reconstruction technique is carried out for @xmath13cdm model . in this case 
   , we have found that the considered gravity fails to reproduce @xmath13cdm cosmology for both cases . 
   for the specific form of function , this result is consistent with @xmath10 gravity in the absence of matter @xcite . 
   on physical grounds , the stability analysis of different forms of generic function leads to classify the modified theories of gravity . 
   we have applied the first order perturbations to hubble parameter and energy density to analyze the stability of models which reproduce de sitter and power - law cosmic history . 
   we have perturbed the field equation as well as conservation law whose numerical solutions provide the stable / unstable results . 
   * for the de sitter universe , the evolution of perturbation has been plotted against time as shown in figures * 1 * -*4*. these indicate that models ( [ 6d ] ) and ( [ 9d ] ) are stable against linear perturbations . * for the power - law universe , the stability analysis is given in figures * 5 * -*7*. it is found that @xmath0 gravity fails to reproduce matter and radiation dominated eras while stable results are obtained for accelerated phase of the universe for model ( [ 5p ] ) . 
   we conclude that the cosmological reconstruction and stability analysis might restrict @xmath0 gravity in the background of frw universe . 
   the expressions for @xmath179 s in eqs.([5d ] ) and ( [ 6d ] ) are @xmath180\\\nonumber & \times&[1+\omega-36c_{1}h_{0}^{4}(1 - 3\omega)]^{-2},\\\nonumber \xi_{2}&=&18c_{1}h_{0}^{4}[(1 - 11\omega)(1-\omega^{2})-8c_{1 } h_{0}^{4}\{2(2 + 59\omega^{2})-11\omega(5 - 3\omega^{2})\}]\\\nonumber & \times&[(1+\omega)(1 - 24c_{1}h_{0}^{4})\{1+\omega-6c_{1}h_{0}^{4 } ( 5 - 4\omega-33\omega^{2})\}]^{-1},\\\nonumber\xi_{3}&=&-[18c_{1 } h_{0}^{4}(1 - 32c_{1}h_{0}^{4})-3\omega\{1 - 6c_{1}h_{0}^{4}(3 - 352c_{1 } h_{0}^{4})\}\\\nonumber&-&2\omega^{2}\{1 - 9c_{1}h_{0}^{4 } ( 7 - 1248c_{1}h_{0}^{4})\}+\omega^{3}\{1 - 54c_{1}h_{0}^{4}(7 - 480c_{1 } h_{0}^{4})\}]\\\nonumber&\times&[(1 - 3\omega)(1 - 24c_{1}h_{0}^{4 } ) \{1+\omega-6c_{1}h_{0}^{4}(5 - 4\omega-33\omega^{2})\}]^{-1}.\end{aligned}\ ] ] the expressions for @xmath84 s and @xmath85 s in eqs.([5p ] ) and ( [ 6p ] ) are @xmath181 where @xmath182,\\\nonumber\gamma_{8}&=&\frac{\tilde{c}_{2 } } { 6\lambda}\left[6\tilde{c}_{2}\lambda(1+\omega)^{2}-3\lambda ( 1 + 5\omega+2\omega^2)+2(\gamma_{1}-\gamma_{2})\right].\end{aligned}\ ] ] the values of @xmath145 s in eq.([8 t ] ) are given as follows @xmath183f_{\mathcal{g}t}^{*}-864(1+\omega)(1 - 3\omega)\rho _ { * } h_{*}^{6}(4h_{*}^{2}\\\nonumber&+&\dot{h}_{*})f_{\mathcal{gg}t}^ { * } , \\\nonumber\chi_{4}&=&12(1 - 3\omega)\rho_{*}h_{*}^{3}f_{\mathcal{g}t}^ { * } , \\\nonumber\chi_{5}&=&\kappa^{2}\rho_{*}-\frac{1}{2}(\omega-3 ) \rho_{*}f_{t}^{*}+(1 - 3\omega)(1+\omega)\rho_{*}^{2}f_{tt}^{*}-12 ( 1 - 3\omega)\rho_{*}h_{*}^{2}\\\nonumber&\times&[(4 + 3\omega)h_{*}^{2 } + \dot{h}_{*}]f_{\mathcal{g}t}^{*}+288(1 - 3\omega)\rho_{*}h_{*}^{4 } ( 4h_{*}^{2}\dot{h}_{*}+2\dot{h}_{*}^{2}+h_{*}\ddot{h } _ { * } ) \\\nonumber&\times&f_{\mathcal{gg}t}^{*}-36(1+\omega ) ( 1 - 3\omega)^{2}\rho_{*}^{2}h_{*}^{4}f_{\mathcal{g}tt}^{*}.\end{aligned}\ ] ] the expressions for @xmath148 s are @xmath184f_{\mathcal{g}t}^ { * } -72\rho_{*}^{2}h_{*}^{2}(1 - 3\omega)(1+\omega)^{2}(4h_{*}^{2 } \\\nonumber&+&\dot{h}_{*})f_{\mathcal{g}tt}^{*}+576\rho_{*}h_{*}^{3 } ( 1+\omega)(4h_{*}^{2}+\dot{h}_{*})(4h_{*}^{2}\dot{h}_{*}+2 \dot{h}_{*}^{2}\\\nonumber&+&4h_{*}\ddot{h}_{*})f_{\mathcal{gg}t}^ { * } , \\\nonumber\upsilon_{2}&=&-12\rho_{*}h_{*}^{2}(1+\omega)\left[3h_{*}^{2 } ( 1-\omega)-4(2h_{*}^{2}+3\dot{h}_{*})\right]f_{\mathcal{g}t}^ { * } + 576\rho_{*}h_{*}^{2}\\\nonumber&\times&(1+\omega)(4h_{*}^{2 } \dot{h}_{*}+2\dot{h}_{*}^{2}+h_{*}\dot{h}_{*})f_{\mathcal{gg}t}^ { * } -72\rho_{*}^{2}h_{*}^{4}(1 - 3\omega)\\\nonumber&\times&(1+\omega^{2 } ) f_{\mathcal{g}tt}^{*},\\\nonumber\upsilon_{3}&=&24\rho_{*}h_{*}^{3 } ( 1+\omega)f_{\mathcal{g}t}^{*},\\\nonumber\upsilon_{4}&=&-\frac{3}{2 } \rho_{*}h_{*}(1+\omega)\left[(1-\omega)f_{t}^{*}+2\rho_{*}^{2 } ( 1+\omega)(1 - 3\omega)^{2}f_{ttt}^{*}\right]-\frac{15}{2 } \rho_{*}^{2}h_{*}\\\nonumber&\times&(1 - 3\omega)(1+\omega)^{2}f_{tt}^ { * } + 24\rho_{*}h_{*}(1+\omega)(4h_{*}^{2}\dot{h}_{*}+2\dot{h}_{*}^{2}+h _ { * } \ddot{h}_{*})\\\nonumber&\times&\left[f_{\mathcal{g}t}^{*}+\rho _ { * } ( 1 - 3\omega)f_{tt\mathcal{g}}^{*}\right],\\\nonumber\upsilon_{5 } & = & \rho_{*}\left(\kappa^2+\frac{1}{2}(3-\omega)f_{t}^{*}\right ) + ( 1+\omega)(1 - 3\omega)\rho_{*}^{2}f_{tt}^{*}.\end{aligned}\ ] ] for model ( [ 15 ] ) , the coefficients of @xmath151 have the following expressions @xmath185-\frac{15}{2 } \rho_{*}^{2}h_{*}\\\nonumber&\times&(1 - 3\omega)(1+\omega)^{2 } \mathcal{f}_{tt}^{*},\\\nonumber\hat{\upsilon}_{5}&=&\rho _ { * } \left(\kappa^2+\frac{1}{2}(3-\omega)\mathcal{f}_{t}^{*}\right ) + ( 1+\omega)(1 - 3\omega)\rho_{*}^{2}\mathcal{f}_{tt}^{*}.\end{aligned}\ ] ]
summary: the aim of this paper is to reconstruct and analyze the stability of some cosmological models against linear perturbations in @xmath0 gravity ( @xmath1 and @xmath2 represent the gauss - bonnet invariant and trace of the energy - momentum tensor , respectively ) . 
   we formulate the field equations for both general as well as particular cases in the context of isotropic and homogeneous universe model . 
   we reproduce the cosmic evolution corresponding to de sitter universe , power - law solutions and phantom / non - phantom eras in this theory using reconstruction technique . finally , we study stability analysis of de sitter as well as power - law solutions through linear perturbations . 
   * keywords : * reconstruction ; stability analysis ; modified gravity . + * pacs : * 04.50.kd ; 98.80.-k .