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it is generally believed today that we live in an expanding universe . after the discovery of cmbr @xcite the big - bang cosmology has become the standard model for cosmology which accommodates a beginning of the universe at some finite past . however , on its own big - bang cosmology does face some problems both in early and late universe . a number of problems cripped up when one describes the early universe , namely , the horizon problem , flatness problem etc .
the above problems can be resolved evoking a phase of inflation @xcite at a very early epoch . on the other hand recent observations
predict that our universe is passing through a phase of acceleration @xcite .
this phase of acceleration is believed to be a late time phase of the universe and may be accommodated in the standard model with a positive cosmological constant . despite its overwhelming success , modern big - bang cosmology still has some unresolved issues .
the physics of the inflation and introduction of a small cosmological constant for late acceleration , is not clearly understood @xcite .
this is why there is enough motivation to search for alternative cosmology .
emergent universe ( eu ) models are employed to find a model which would accommodate the early inflationary phase and avoid the messy situation of the initial singularity @xcite .
eu scenario can be realized in the framework of general relativity @xcite , gauss - bonnet gravity @xcite , brane world gravity @xcite , brans - dicke theory @xcite etc .
emergent universe are late time de - sitter and thus naturally incorporate the late time accelerating phase as well .
one such model was proposed by @xcite in which a polytropic equation of state ( eos)in the form : @xmath0 where @xmath1 and @xmath2 are constants is used .
this is a special case of a more general equation @xmath3 with @xmath4 . for such eos
a phenomenological construction can be found in string theories where most of the time models interpolate between two phases of universe @xcite .
universe in this model can stay large enough to avoid quantum gravitational effects even in the very early universe .
recently @xcite studied the viability of this type of model in the light of recent observational data and established bounds on model parameters @xmath1 and @xmath2 .
it is shown that the best fit value for @xmath1 may be very small but negative although a small positive value is allowed with 95@xmath5 confidence . for a viable cosmology
the bounds on @xmath1 and @xmath2 are determined for some fixed value of @xmath6 .
the parameter @xmath6 , however , appears in the theory as an integration constant and may be fixed to some other value for different initial configuration .
@xcite recently worked with a more specific model for a small value of @xmath1 ( @xmath7 ) . in the original work of @xcite
it was shown that the choice of @xmath1 drastically changes the matter energy composition of the universe that eq .
( [ eos1 ] ) can mimic .
in the present paper we obtain observational bounds on the model parameters @xmath2 and @xmath6 for different choices of @xmath1 as was considered in @xcite .
these choices correspond to very different compositions of cosmic fluid and it would be interesting to see whether realistic cosmologies are permitted for each case since the theory itself puts some constraints over @xmath2 and @xmath6 @xcite ] .
the paper is presented as follows : in the next section we describe the relevant field equations . in section three
we discuss the methods applied to constrain the parameters from ( i ) observed hubble data ( ohd)@xcite and ( ii ) sdss data measuring a model independent bao peak parameter @xcite . in section four
we study the density parameters ( dp ) of the model ( at the present epoch ) and finally we discuss the results in section 5 .
+   +   +    friedmann equation in a flat universe reads as : @xmath8 where @xmath9 is the hubble parameter and @xmath10 is the scale factor of the universe.the usual conservation equation holds : @xmath11 using the eos given by eq .
( [ eos1 ] ) in eq.([fr1 ] ) and eq .
( [ csv ] ) one obtains : @xmath12 where @xmath13 represents the cosmological redshift . the first term in the right hand side of eq.([rho1 ] ) is a constant which can be interpreted as cosmological constant and describing dark energy .
( [ rho1 ] ) can be written as : @xmath14 where @xmath15 , @xmath16 and @xmath17 represents densities at the present epoch .
the friedmann equation ( eq . [ fr1 ] ) can now be written in terms of redshift and density parameter as follows : @xmath18 where we define density parameter : @xmath19 .
for a given @xmath20 ( say ) we note that the nature of evolution for the variable parts of the matter energy density may now be established . hence , choice of a suitable value for @xmath1 leads to a known composition of fluids .
for example , @xcite considered the case @xmath21 with dark energy , dark matter and dust in the universe .
fixing @xmath1 one can re - write eq .
( [ fr2 ] ) as : @xmath22 where , @xmath23 here we have replaced the constant part of the dp ( @xmath24 ) by a new notation @xmath25 .
using observed value of hubble parameter at different redshifts ( twelve data points listed in observed hubble data by @xcite ) we analyse the model in this section . for the analysis
we first define a chi square function as follows : @xmath26 where @xmath27 and @xmath28 are theoretical and observational values of hubble parameter at different redshifts respectively and @xmath29 is the corresponding error . here , @xmath30 is a nuisance parameter and can be safely marginalized .
we consider @xmath31 and a fixed prior distribution .
a reduced chi square function can be defined as follows : @xmath32dh_{0}\ ] ] where @xmath33 is the prior distribution .
the graph is plotted with @xmath34 ( solid ) , @xmath35 ( dashed ) and @xmath36 ( dotted ) confidence level .
the corresponding contours are shown in fig .
( [ ohd ] ) for different @xmath1 values .
the best fit values are tabulated in table ( [ thub ] ) .
.findings : ohd [ cols="<,^,^,^",options="header " , ]     in this work we obtained observational constraints on the model parameters for a class of eu solutions . here
we consider different values of @xmath1 belonging to a class of eu given by @xcite .
the model parameters of the eu are constrained using the observed hubble data ( ohd ) as well as using a joint analysis with the measurement of a bao peak parameter .
we use bao peak parameter as suggested by @xcite which is independent of dark energy model .
the present day value for the density parameters are determined . for the case
@xmath37 we have found that the present values of the dp are unrealistic .
however , in the original work @xcite showed that for the case @xmath37 , evolution of the cosmic fluid mimics a composition of dark energy ( cosmomological constant ) , domain walls and cosmic strings .
as the evaluated value of the present day density parameter in the model with @xmath37 is not realistic the model with @xmath37 may be ruled out .
however , in the other two cases , namely for @xmath38 and @xmath39 , we obtain cosmological models with physically realistic density parameter .
the best fit values for the model parameters @xmath2 and @xmath6 are determined .
it is found that the model admits dark energy density close to that predicted by observations in @xmath40cdm cosmology .
the analysis we adopted here involves kinematics only and it would be interesting to analyze and determine the model constraints using the dynamical aspects like structure formation etc . also it is worthwhile to note that the parameter @xmath6 should in principle be fixed from the initial conditions itself .
a more stringent constraint on the eu may be obtained for a viable candidate for cosmology .
all these issues will be considered elsewhere .
sg would like to thank csir for awarding senior research fellowship .
bcp and pt would like to thank iucaa resource centre , nbu for providing research facilities .
bcp would like to thank ugc , new delhi for financial support ( grant no .
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a class of emergent universe ( eu ) model is studied in the light of recent observational data . 
 significant constraints on model parameters are obtained from the observational data . 
 density parameter for a class of model is evaluated . 
 some of the models are in favour of the recent observations . 
 some models have been found which are not interesting yielding unrealistic present day value of the density parameter .    
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