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at the end of the last century , the astronomical observations of high redshift type ia supernovae ( snia ) indicated that our universe is not only expanding , but also accelerating , which conflicts with our deepest intuition of gravity . with some other observations , such as cosmic microwave background radiation ( cmbr ) , baryon acoustic oscillations ( bao ) and large - scale structure ( lss ) , physicists proposed a new standard cosmology model , @xmath0cdm , which introduces the cosmological constant back again . although this unknown energy component accounts for 73% of the energy density of the universe , the measured value is too small to be explained by any current fundamental theories.@xcite-@xcite if one tries to solve this trouble phenomenologically by setting the cosmological constant to a particular value , the so - called fine - tuning problem would be brought up , which is considered as a basic problem almost any cosmological model would encounter . a good model should restrict the fine - tuning as much as possible . in order to alleviate this problem , various alternative theories have been proposed and developed these years , such as dynamical dark energy , modified gravity theories and even inhomogeneous universes . recently , a new attempt , called torsion cosmology , has attracted researchers attention , which introduces dynamical torsion to mimic the contribution of the cosmological constant . it seems more natural to use a pure geometric quantity to account for the cosmic acceleration than to introduce an exotic energy component . torsion cosmology could be traced back to the 1970s , and the early work mainly focused on issues of early universe , such as avoiding singularity and the origin of inflation . in some recent work , researchers attempted to extend the investigation to the current evolution and found it might account for the cosmic acceleration . among these models , poincar gauge theory ( pgt ) cosmology is the one that has been investigated most widely . this model is based on pgt , which is inspired by the einstein special relativity and the localization of global poincar symmetry@xcite . et al_. made a comprehensive survey of torsion cosmology and developed the equations for all the pgt cases.@xcite based on goenner s work , nester and his collaborators@xcite found that the dynamical scalar torsion could be a possible reason for the accelerating expansion . et al_.@xcite extended the investigation to the late time evolution , which shows us the fate of our universe . besides pgt cosmology , there is another torsion cosmology , de sitter gauge theory ( dsgt ) cosmology , which can also be a possible explanation to the accelerating expansion . this cosmological model is based on the de sitter gauge theory , in which gravity is introduced as a gauge field from de sitter invariant special relativity ( dssr ) , via the localization of de sitter symmetry.@xcite dssr is a special relativity theory of the de sitter space rather than the conventional minkowski spacetime , which is another maximally symmetric spacetime with an uniform scalar curvature @xmath1 . and the full symmetry group of this space is de sitter group , which unifies the lorentz group and the translation group , putting the spacetime symmetry in an alternatively interesting way . but in the limit of @xmath2 , the de sitter group could also degenerate to the poincar group . to localize such a global symmetry , de sitter symmetry , requires us to introduce certain gauge potentials which are found to represent the gravitational interaction . the gauge potential for de sitter gauge theory is the de sitter connecion , which combines lorentz connection and orthonormal tetrad , valued in @xmath3(1,4 ) algebra . the gravitational action of dsgt takes the form of yang - mills gauge theory . via variation of the action with repect to the the lorentz connection and orthonormal tetrad , one could attain the einstein - like equations and gauge - like equations , respectively . these equations comprise a set of complicated non - linear equations , which are difficult to tackle . nevertheless , if we apply them to the homogeneous and isotropic universe , these equations would be much more simpler and tractable . based on these equations , one could construct an alternative cosmological model with torsion . analogous to pgt , dsgt has also been applied to the cosmology recently to explain the accelerating expansion.@xcite    our main motivation of this paper is to investigate ( i)whether the cosmological model based on de sitter gauge theory could explain the cosmic acceleration ; ( ii)where we are going , i.e. , what is the fate of our universe ; ( iii ) the constraints of the parameters of model imposed by means of the comparison of observational data . by some analytical and numerical calculations , we found that , with a wide range of initial values , this model could account for the current status of the universe , an accelerating expanding , and the universe would enter an exponential expansion phase in the end .    this paper is organized as follows : first , we summarize the de sitter gauge theory briefly in sec .  [ sec : de - sitter - gauge ] , and then show the cosmological model based on de sitter gauge theory in sec .  [ sec : cosm - evol - equat ] . second , we rewrite these dynamical equations as an autonomous system and do some dynamical analysis and numerical discussions on this system in the sec .  [ sec : autonomous - system ] and  [ sec : numer - demonstr ] . next in the [ sec : supern - data - fitt]th section , we compare the cosmological solutions to the snia data and constrain the parameters . last of all , we discuss and summarize the implications of our findings in section [ sec : summary - conclusion ] . [ supernovae data fitting]in dsgt , the de sitter connection is introduced as the gauge potential , which takes the form as @xmath4 -r^{-1}e^b_\mu & 0 \end{array } \right ) \in \mathfrak{so}(1,4),\ ] ] where @xmath5 , @xmath6 and @xmath7 , which combines the lorentz connection and the orthonormal tetrad are 4d coordinate indices , whereas the capital latin indices @xmath8 and the lowercase latin indices , @xmath9 denote 5d and 4d orthonormal tetrad indices , respectively . ] . the associated field strength is the curvature of this connection , which is defined as @xmath10          -r^{-1}t^b_{~\mu\nu } & 0      \end{array }    \right ) \in \mathfrak{so}(1,4),\end{aligned}\ ] ] where @xmath11 , @xmath12 is the de sitter radius , and @xmath13 and @xmath14 are the curvature and torsion of lorentz - connection , @xmath15 which also satisfy the respective bianchi identities .    the gauge - like action of gravitational fields in dsgt takes the form , @xcite @xmath16.\label{gym}\end{aligned}\ ] ] here , @xmath17 , @xmath18 is a dimensionless constant describing the self - interaction of the gauge field , @xmath19 is a dimensional coupling constant related to @xmath18 and @xmath12 , and @xmath20 is the scalar curvature of the cartan connection . in order to be consistent with einstein - cartan theory , we take @xmath21 and @xmath22 , where @xmath23 .    assuming that the matter is minimally coupled to gravitational fields , the total action of dsgt could be written as : @xmath24 where @xmath25 denotes the action of matter , namely the gravitational source . now we can obtain the field equations via variational principle with respect to @xmath26 , @xmath27 \label{feq2}% & & \nabla_{\nu}f_{ab}^{~~\mu\nu}-r^{-2}\left(y^\mu_{~\,\lambda\nu } e_{ab}^{~~\lambda\nu}+y ^\nu_{~\ , \lambda\nu } e_{ab}^{~~\mu\lambda } + 2t_{[a}^{~\mu\lambda } e_{b]\lambda}\right ) = 16\pi gr^{-2}s^{\quad \mu}_{{\rm m}ab},%\end{aligned}\ ] ] where@xmath28 represent the effective energy - momentum density and spin density of the source , respectively , and @xmath29 is the contorsion . it is worth noticing that the nabla operator in eq . ( [ feq1 ] ) and ( [ feq2 ] ) is the covariant derivative compatible with christoffel symbols \{@xmath30 } for coordinate indices , and lorentz connection @xmath31 for orthonormal tetrad indices . readers can be referred to ref.@xcite for more details on dsgt . since current observations favor a homogeneous , isotropic universe , we here work on a robertson - walker ( rw ) cosmological metric @xmath32.\ ] ] for robertson - walker metric , the nonvanishing torsion tensor components are of the form , @xmath33 where @xmath34 denotes the vector piece of torsion , namely , in components , the trace of the torsion , and @xmath35 indicates the axial - vector piece of torsion , which corresponds in components to the totally antisymmetric part of torsion . @xmath34 and @xmath35 are both functions of time @xmath36 , and their subscripts , + and - , denote the even and odd parities , respectively .    the nonvanishing torsion 2-forms in this case are @xmath37 where @xmath38 .    according to the rw metric eq . and the torsion eq . , the field equations could be reduced to @xmath39   \label{el-11}% & & \frac{\ddot a^2 } { a^2 } + \left(\dot t_+ + 2\frac{\dot a } a   t_+ - 2\frac{\ddot a } a + \frac{6}{r^2}\right)\dot t_+ -\frac 1 4 \left(\dot t_- + 2 \frac { \dot a } a t_-\right)\dot t_- - t_+^4 + \frac 3 2 t_+^2 t_-^2 - \frac1 { 16 } t_-^4 \nonumber\\ & & \quad+ \frac { \dot a } a(4   t_+^2 - 3 t_-^2)t_+   - \left(5\frac{\dot a^2 } { a^2 } + 2 \frac k { a^2 }   + \frac3 { r^2}\right ) t_+^2 + \frac 1 2 \left(\frac 5 2\frac{\dot a^2 } { a^2 } + \frac k { a^2 } +   \frac 3 { r^2}\right ) t_-^2- 2\frac{\dot a } a \left(\frac{\ddot a } { a}- 2\frac{\dot a^2 } { a^2 } \right.\nonumber \\[0.2 cm ] & & \quad \left . - 2   \frac k { a^2}- \frac6 { r^2}\right)t_+   - \frac 4 { r^2 } \frac{\ddot a } a -\frac{\dot a^2 } { a^2 } \left(\frac{\dot a^2}{a^2 } + 2\frac k { a^2}\right ) +   \frac2 { r^2 } -\frac{k^2}{a^4 }   - \frac2 { r^2}\frac k { a^2 } + \frac6 { r^4 } = -\frac{16\pi g p}{r^2 } , \\[0.3 cm ] \label{yang1 } % & & \ddot t_-   + 3 \frac{\dot a } a \dot t_- + \left ( \frac 1 2 t_-^2 - 6 t_+^2 + 12 \frac { \dot a } a t_+   + \frac{\ddot a } a - 5\frac{\dot a^2}{a^2 } -   2\frac k { a^2}+   \frac 6 { r^2}\right )   t_-=0 , \\[0.3 cm ] \label{yang2}% & &   \ddot t_+ + 3 \frac{\dot a } a \dot t_+ -\left ( 2   t_+^2   -\frac 3 2 t_-^2 - 6\frac{\dot a } a t_+ -\frac { \ddot a } a   + 5 \frac { \dot a^2 }   { a^2 } + 2 \frac k { a^2}- \frac 3 { r^2}\right ) t_+ - \frac 3 2 \frac{\dot a } a t_-^2-\frac{\dddot a } a - \frac{\dot a\ddot a}{a^2 } \nonumber\\ & & \quad+ 2\frac { \dot a^3 } { a^3 } + 2\frac{\dot a } a \frac k { a^2 } = 0 , % \end{aligned}\ ] ] where eqs . and are the @xmath40 and @xmath41 component of einstein - like equations , respectively ; and eqs . and are 2 independent yang - like equations , which is derived from the @xmath42 and @xmath43 components of lorentz connection . the spin density of present time is generally thought be very small which could be neglected . therefore , we here assumed the spin density is zero .    the bianchi identities ensure that the energy momentum tensor is conserved , which leads to the continuity equation : @xmath44 equation can also be derived from eqs .  -  , which means only four of eqs . -   are independent . with the equation of state ( eos ) of matter content , these four equations comprise a complete system of equations for five variables , @xmath45 . by some algebra and differential calculations , we could simplify these 5 equations as : @xmath46t_+,\\ \ddot{t}_- & = & -3h\dot{t}_- -\left[-\frac{15}{2}t_{+}^{2}+\frac{33h t_{+}}{2}-6h^{2}-\frac{3k}{a^2}+\frac{8}{r^{2}}+\frac{5}{4}t^{2}_{-}+\frac{3}{2}\dot{t}_+ \right.\nonumber\\ & & \left . + \frac{4\pi g}{3}(\rho+3p)\right]t_{-},\\ \dot{\rho}&=&-3h(\rho+p),\\ \label{eq : eos } w&=&\frac{p}{\rho } ,   \end{aligned}\ ] ] where @xmath47 is the hubble parameter . if we rescale the variables and parameters as @xmath48 where @xmath49 is the hubble radius in natural units , these variables and parameters would be dimensionless . under this transformation , - remain unchanged expect for the terms including @xmath50 and @xmath51 , which change into @xmath52 and @xmath53 respectively . the contribution of radiation and spatial curvature in current universe are so small that it could be neglected , so we here just consider the dust universe with spatial flatness , whose eos is equal to zero . by some further calculations , these equations could be transformed to a set of six one - order ordinary derivative equations , which forms a six - dimensional autonomous system , as follows , @xmath54t_+ + 6h\rho , \\[0.2 cm ] \dot{t_{+}}&=&p,\\ \dot q&=&-3h q -\left(-\frac{15}{2}t_{+}^{2}+\frac{33h      t_{+}}{2}-6h^{2}+\frac{8}{r^{2}}+\frac{5}{4}t^{2}_{-}+\frac{3}{2}p + \rho \right)t_{-},\\ \dot{t_{-}}&=&q,\\ \dot{\rho}&=&-3h\rho . \label{rho}\end{aligned}\ ] ] for such an autonomous system , we can use the dynamics analysis to investigate its qualitative properties . critical points are some exact constant solutions in the autonomous system , which indicate the asymptotic behavior of evolution . for example , some solutions , such as heteroclinic orbits , connect two different critical points , and some others , such as homoclinic orbits , are a closed loop starting from and coming back to the same critical point . in the dynamics analysis of cosmology , the heteroclinic orbit is more interesting.@xcite thus , critical points could be treated as the basic tool in dynamics analysis , form which one could know the qualitative properties of the autonomous system . by some algebra calculation , we find all the 9 critical points ( @xmath55 ) of this system , as shown in table 1 .    . [ tab : critical - points]the critical points and their corresponding eigenvalues . the point 9 is not physically acceptable , for its negative energy density . [ cols="<,<,<",options="header " , ]     based on the current observations , the present density of torsion in our universe is very small , so it is reasonable to assume that the initial values of all torsions and their first order derivative are zero at @xmath56 . but their second order derivatives does not vanish yet , which would have a significant impact on the history and future of the evolution of our universe . in this case , the number of parameter and initial value is reduced , and the rest parameters and initial values are just @xmath12 and @xmath57 . it is easy to find the best - fit of these 2 parameters , which are shown in table [ tab : best - fit ] . and the minimal @xmath58 is @xmath59 , whereas the value for @xmath0cdm is @xmath60 , with @xmath61 . in fig . [ fig : chi2-distribution ] we show the @xmath58 distribution with respect to @xmath12 and @xmath52 compared to @xmath0cdm model , where the plane @xmath62 corresponds to the value of @xmath0cdm . furthermore , we plot the contours of some particular confidence levels , as shown in fig .  [ fig : contour ] . from these figures , we could find that the evolution of our universe is insensitive to the initial value , which alleviate the fine - tuning problem .    the @xmath58 distribution with respect to @xmath12 and @xmath52 , compared to the @xmath0cdm , the plane @xmath63 . here we assume that all the torsions and their first order derivatives vanish at present time.,width=642,height=340 ]    the 68.3% , 95.4% and 99.7% @xmath58 confidence contours of dsgt with respect to @xmath12 and @xmath52 , using the union 2 dataset . here we also assume that the current - time values for all the torsions and their first order derivatives are zero . the yellow point is the best - fit point . , height=264 ] the astronomical observations imply that our universe is accelerating to a de sitter spacetime . this gives us a strong motive to consider the cosmic evolution based on the de sitter gauge theory instead of other gravity theories . the localization of de sitter symmetry requires us to introduce curvature and torsion . so in de sitter gauge theory , the torsion is an indispensable quantity , by which people tried to include the effect of spin density in gravity theory at first . but now this essential quantity might account for the acceleration of our universe , if we apply dsgt to cosmology . we found the cosmological equations for dust universe in dsgt could form an autonomous system by some transformations , where the evolution of the universe is described in terms of the orbits in phase space . therefore , by dynamics analysis to the dsgt cosmology , one could study the qualitative properties of this phase space . we found all 9 critical points , as shown in table  [ tab : critical - points ] . we also analyzed the stabilities of these critical points , and found among these critical points there is only one positive attractor , which is stable . the positive attractor alleviates the fine - tuning problem and implies that the universe will expand exponentially in the end , whereas all other physical quantities will turn out to vanish . in this sense , dsgt cosmology looks more like the @xmath0cdm , than pgt cosmology . and we conducted some concrete numerical calculations of this the destiny of our model of the universe , which confirms conclusions from dynamics analysis . finally , in order to find the best - fit values and constraints of model parameters and initial conditions , we fitted them to the union 2 snia dataset . the maximum likelihood estimator here we used is the @xmath58 estimate . by minimizing the @xmath58 , we found the best - fit parameters @xmath64 and the corresponding @xmath65 , while the value for @xmath0cdm is @xmath60 , with @xmath66 . note that we here set all the initial values of torsions and their first - order derivatives to zero at @xmath67 , since the contribution of torsion to the current universe is almost negligible . we also plotted the confidence contour fig . 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a new cosmological model based on the de sitter gauge theory ( dsgt ) is studied in this paper . by some transformations , 
 we find , in the dust universe , the cosmological equations of dsgt could form an autonomous system . 
 we conduct dynamics analysis to this system , and find 9 critical points , among which there exist one positive attractor and one negative attractor . 
 the positive attractor shows us that our universe will enter a exponential expansion phase in the end , which is similar to the conclusion of @xmath0cdm . 
 we also carry out some numerical calculations , which confirms the conclusion of dynamics analysis . 
 finally , we fit the model parameter and initial values to the union 2 snia dataset , present the confidence contour of parameters and obtain the best - fit values of parameters of dsgt .