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precision measurements of the cmb and the lss have opened a window to the physics of the early universe ( ( * ? ? ?
* wmap 2012 ) , ( * ? ? ?
* planck 2013 ) ) .
in particular it has become possible to measure the exact statistics of the primordial curvature perturbations on uniform density hypersurfaces , @xmath0 , which turned out to be almost gaussian ( ( * ? ? ?
* planck 2013(2 ) ) ) .
these small deviations from gaussianity are commonly represented by the parameters @xmath1 and @xmath2 and allow to write @xmath3 where @xmath4 denotes the gaussian curvature perturbations .    on the other side ,
the exact statistics of @xmath0 are predicted by inflation models .
this suggests to relate current observations directly to inflation models , parametrized by inflationary parameters , @xmath5 , by higher order statistics of the curvature perturbations ( see fig .
[ cosmo ] ) . how to set up such an inference approach in the framework of information field theory ( ( * ? ? ?
* enlin et al . 2011 ) ) was originally developed in ( ( * ? ? ?
* dorn et al . 2013 ) , ( * ? ? ?
* dorn et al .  2014 ) ) and is addressed in the work at hand .    to do inference of inflationary parameter we consider the observation ( cmb , lss ) to be a discrete data set , @xmath6 , given by @xmath7 where @xmath8 denotes some gaussian noise , @xmath9 , and @xmath10 the so - called response operator .
if we consider the cmb , the latter is a linear operator that transfers the curvature perturbations into temperature anisotropies , i.e. the radiation transfer function , and contains all measurement and instrumental effects .    ]
since the non - gaussianity parameters depend on a particular inflation model , the calculation of their posterior , @xmath11,\ ] ] is done first ( ( * ? ? ?
* dorn et al .  2014 ) ) .
@xmath12 denotes the information hamiltonian , @xmath13 .
a straightforward calculation of this hamiltonian shows that it contains terms up to @xmath14 .
therefore the integral of eq .
( [ inte ] ) can not be performed analytically . however , this obstacle can be circumvented by conducting a saddle - point approximation in @xmath4 around @xmath15 $ ] up to the second order in @xmath4 to be still able to perform the path - integration analytically .
this means , we replace @xmath16 by the gaussian @xmath17 , with @xmath18 including the saddle - point approximation and performing the path integral in eq .
( [ inte ] ) yields the final expression of the posterior ( ( * ? ? ?
* dorn et al .  2014 ) ) , @xmath19\mathcal{p}(f_\text{nl},g_\text{nl}).\ ] ] eq .  ( [ end ] ) enables to calculate the posterior of @xmath20 fully analytic without expensive monte carlo sampling techniques .
this analyticity has been conserved by conducting a saddle - point approximation , whose sufficiency has been validated by the dip test ( ( * ? ? ?
* dorn et al . 2013(2 ) ) ) .
note that @xmath21 as well as @xmath22 denpends on the two point correlation function of @xmath4 and thus requires some a priori knowledge on the primordial power spectrum .
one might use the currently measured and therefore well motivated primordial power spectrum ( pure power law ) with best fit parameters from _ planck _ ( ( * ? ? ?
* planck 2013(3 ) ) ) .    to obtain the posterior of inflationary parameters we replace @xmath23 by
their parameter dependent expressions , predicted by inflation models , e.g. , for the simplest curvaton model with potential @xmath24  ( ( * ? ? ?
* bartolo et al .
2002 ) , ( * ? ? ?
* sasaki et al .
2006 ) ) one obtains @xmath25 the posterior for the curvaton parameter @xmath26 for a toy example in two dimensions as well as possible values of @xmath27 are illustrated in fig .
[ figgf ] .     and @xmath2 within current _ planck _ constraints parametrized by the curvaton parameter @xmath26 .
( right ) normalized likelihood distributions for @xmath26 in a two - dimensional test case in the sachs - wolfe limit with data generated from @xmath28 .
figures taken from ( ( * ? ? ?
* dorn et al .  2014)).[figgf],title="fig : " ] and @xmath2 within current _ planck _ constraints parametrized by the curvaton parameter @xmath26 .
( right ) normalized likelihood distributions for @xmath26 in a two - dimensional test case in the sachs - wolfe limit with data generated from @xmath28 .
figures taken from ( ( * ? ? ?
* dorn et al .  2014)).[figgf],title="fig : " ]
we presented a novel and generic method to infer inflationary parameters from observations ( cmb , lss ) by local non - gaussianity .
the method is fully analytic and thereby avoids expensive sampling techniques .
the introduced approximation , necessary to conserve the analyticity , has been validated successfully .
2013 , _ apjs _  208  20 , arxiv : astro - ph/12125225 2013 , arxiv : astro - ph/13035076 2013 , arxiv : astro - ph/13035084 2011 , _ phys .  rev .
d _  80  105005 , arxiv : astro - ph/08063474 2013 , _ phys .
d _  88  103516 ,
arxiv : astro - ph/13073884 2014 , arxiv : astro - ph/14035067 2013 , _ phys .
e _  88  053303 ,
arxiv : astro - ph/13073889
the presence of multiple fields during inflation might seed a detectable amount of non - gaussianity in the curvature perturbations , which in turn becomes observable in present data sets like the cosmic microwave background ( cmb ) or the large scale structure ( lss ) . within this proceeding 
 we present a fully analytic method to infer inflationary parameters from observations by exploiting higher - order statistics of the curvature perturbations . to keep this analyticity , and thereby to dispense with numerically expensive sampling techniques , 
 a saddle - point approximation is introduced whose precision has been validated for a numerical toy example . applied to real data , this approach might enable to discriminate among the still viable models of inflation .