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current cosmological observations are very precise to give us a lot of information on the evolution and present state of the universe . we usually extract the information by constraining cosmological parameters such as energy densities of baryon , dark matter and dark energy , the hubble constant , reionization optical depth , spectral index of primordial fluctuation and so on . among them , in this paper , we focus on the primordial helium abundance @xmath0 , which has been of great interest in cosmology . one of the reasons why the primordial helium abundance has been considered to be interesting and important is that , in the context of the standard big bang nucleosynthesis ( sbbn ) , we can know the baryon density once @xmath0 is determined from observations . however , it has been discussed that a significant systematic error dominates when one infers the value of @xmath0 from measurements in low - metallicity extragalactic hii region @xcite . furthermore , there have been some discussions that there may be a large uncertainty in the neutron lifetime @xcite , which results in uncertainties in the predictions for the abundances of light elements . in this respect , the study of other independent measurements of the helium abundance would be interesting . recent precise measurements of cosmic microwave background ( cmb ) such as wmap can now enable us to constrain cosmological parameters with great accuracies . however , the helium abundance has not been discussed much in the literature when one study of cosmological constraints from cmb since @xmath0 has been considered to have little effect on cmb power spectrum . in most of analyses , @xmath0 is fixed to be @xmath6 which is probably motivated from a somewhat old value of the observed primordial helium abundance of @xmath7 @xcite @xcite . ] . but , in fact , there have been some works which discuss the effects of @xmath0 on cmb and some constraints were given @xcite . since the helium abundance affects the recombination history , the cmb power spectrum can be affected mainly through the diffusion damping . although the constraint is not so severe , it is important to notice that they are obtained independently from bbn , which can be used to cross - check our understanding of the helium abundance . furthermore , the value of @xmath0 at the time of bbn may be different from that at late time when cmb observations can probe - balls , the decay of @xmath8-balls produce extra baryon after bbn has completed @xcite . in a model of this kind , the value of @xmath0 can vary at different epochs . ] . after we studied the constraint on @xmath0 in @xcite , the data from wmap has been updated @xcite . in addition , the data at higher multipoles where the effects of @xmath0 become significant have been updated by acbar @xcite and cbi @xcite . thus it is a good time to investigate the constraint on the helium abundance using these cmb data , which is one of the aims of this paper . furthermore , we expect a more precise measurement of cmb from the future planck satellite @xcite , which can give us a much better constraint on @xmath0 . in fact , future constraint on @xmath0 has already been studied using the fisher matrix formalism @xcite . although this method is fast and usually adopted to predict the precision of the future measurements of cosmological parameters , it can give some inaccurate predictions in some cases , for example , when the likelihoods does not respect a gaussian form . in addition , the fisher matrix formalism predicts only the uncertainty for the parameter estimation since it just concerns with the derivatives with respect to parameters around the fiducial values . however , since some parameters are correlated in general , fixing the values of some parameters can bias the estimation of other parameters . namely , priors we assume on some parameters can cause the estimated central values to deviate from the input fiducial values , but such effects can not be quantified by the fisher matrix approach . thus , in this paper , we use the markov chain monte carlo ( mcmc ) approach to extract reliable future constraints on @xmath0 and other cosmological parameters . in particular , when we forecast the sensitivity for other cosmological parameters , we assume some different priors on @xmath0 and investigate to what extent the information of @xmath0 is important to determine other cosmological parameters .    the organization of this paper is as follows . in the next section , the effects of @xmath0 on cmb power spectrum are briefly discussed . then in section [ sec : current ] , we study the constraint on @xmath0 using cmb data currently available including acbar , boomerang and cbi as well as wmap5 . in section [ sec : planck ] , we investigate a constraint on @xmath0 and other cosmological parameters from the future planck experiment . in addition , we also study how the prior on @xmath0 affects the determination of other cosmological parameters . a brief discussion on the significance of the uncertainties of the recombination theory in deriving cosmological constraint is given too . the final section is devoted to the summary of this paper . here we briefly discuss the effects of the primordial helium abundance @xmath0 on cmb power spectrum where @xmath9 with @xmath10 and @xmath11 being the number density of hydrogen and helium-4 respectively . as has been discussed in @xcite , the value of @xmath0 can affect the recombination history , which changes the structure of acoustic peaks . the effects of @xmath0 on acoustic peaks mainly come from the diffusion damping which suppresses the power on small scales and the shift of the position of acoustic peaks due to the change of the recombination epoch . before recombination , the number density of electron @xmath12 can be given by @xmath13 , where @xmath14 is the baryon number density . thus the increase of @xmath0 indicates the decrease of the number of electrons . when the number of electrons is reduced , the mean free path of the compton scattering becomes larger , which means that fluctuations on larger scales can be more affected by the diffusive mixing and rescattering . thus the damping scale below which fluctuation of photon is exponentially suppressed becomes larger . furthermore , due to the change of the number density of electrons , the epoch of recombination is also affected even though its effect is not so significant . this effect shifts the position of acoustic peaks slightly . in fig . [ fig : cl ] , we show the cmb @xmath15 spectrum with several values of @xmath0 . for reference , we also plot the current data ( left panel ) and the expected data from the future planck experiment ( right panel ) . as mentioned above , by increasing the value of @xmath0 , the power on small scales is damped more . in addition , it is noticeable that the position of acoustic peaks also shifts slightly .    to characterize the effects of the change in @xmath0 and other cosmological parameters on cmb @xmath15 power spectrum @xmath16 , we consider some useful quantities @xcite . first of all , to see how cosmological parameters affect the position of acoustic peaks , we investigated the response of the position of the first peak by the change of the parameters , which we denote @xmath17 . in addition , to see the effects of the diffusion damping and some other effects by cosmological parameters , we study the height of the first peak relative to that at @xmath18 and the height of the second peak ( and higher peaks up to 5th peak ) relative to the first peak , which are denoted as @xmath19 , @xmath20 , @xmath21 , @xmath22 and @xmath23 , respectively . for clarity , we give the definitions of these quantities . the definition of @xmath19 is @xmath24 and the height of the @xmath25-th peak relative to the first peak is defined as @xmath26 where @xmath27 . we varied cosmological parameters including @xmath0 around a fiducial model and obtained partial derivatives by fitting linearly around the fiducial value . for the fiducial cosmological values , we assumed the mean values of the wmap 5-yr result ( wmap5 ) for a power - law @xmath28cdm model . regarding @xmath0 , we take @xmath29 which corresponds to the value obtained in the sbbn for the wmap5 baryon density . the resulting derivatives are : @xmath30 where @xmath31 and @xmath32 are energy densities of baryon and matter , @xmath33 is the scalar spectral index of primordial fluctuation , @xmath34 is the hubble constant in units of @xmath35 . in the formula for @xmath19 , we do not show the dependence on @xmath36 since its effect on @xmath19 is very small compared to that of the other parameters . as seen from the negative signs of @xmath37 for @xmath38 - 5 , the diffusion damping becomes more efficient as @xmath0 increases . we can also see the correlation of @xmath0 with other cosmological parameters , which can be useful when we interpret the results , in particular , for a planck forecast . the prior ranges for the parameters used in the analysis . priors shown in the 1st and 2nd columns are adopted for current and expected planck data , respectively . note that we adopt the prior range for @xmath0 shown above only in the cases with @xmath0 being treated as a free parameter whereas @xmath0 is a derived parameter in the case where we assume the sbbn relation . for the analysis with the current data , we also vary the amplitude of the sunyaev - zeldovich effect @xmath39 , which is omitted in the planck data analysis . we also include two additional parameters @xmath40 and @xmath41 which represent uncertainties in the theory of recombination ( see section  [ sec : planck ] for more details ) . [ cols="<,^,^ " , ] we studied the constraint on @xmath0 and the effects of the priors for @xmath0 on constraining other cosmological parameters using current cmb data from wmap5 , acbar , boomerang and cbi , and also from the future planck experiment . after briefly reviewing the effects of @xmath0 on cmb , we studied current constraints on the primordial helium abundance . we obtained the current limit on @xmath0 from wmap5 alone as @xmath42 at 95%c.l . , which is improved to be @xmath43 at 68% ( 95% ) c.l . by adding the data of acbar , boomerang and cbi around the damping tail . we have also considered how the prior of @xmath0 can affects the constraints on other cosmological parameters using currently available data . we found that , at the present precision level of cmb measurements , the prior on @xmath0 has little effect for determinations of other cosmological parameters . we have also investigated the future constraint from the planck experiment . by performing a mcmc analysis , we derived an expected error for the helium abundance from the future planck experiment and found that it will be well measured with the accuracy of @xmath44 ( 68% c.l . ) in the planck experiment , which is 10 times smaller values compared with current data . furthermore , it may be interesting to notice that this precision is comparable to that obtained by hii region observations . as for the effects of the prior on @xmath0 on the determination of other cosmological parameters , we found that , with the precision of planck , the assumption on @xmath0 can affect the constraints on other cosmological parameters such as @xmath31 and @xmath33 . in this respect , the prior on @xmath0 can be important for determining the other parameters . in addition , the constraint on @xmath0 from cmb itself can be an independent test from other methods such as using hii region observations .    in the near future , we can have more precise measurements of cmb . such upcoming data would give us more precise information of the primordial helium abundance . at the same time , it is necessary to study the effects of the helium abundance more rigorously in order to extract information of other cosmological parameters . * acknowledgments : * this work is supported in part by the sumitomo foundation ( t.t . ) and the grant - in - aid for scientific research from the ministry of education , science , sports , and culture of japan , no.18840010 ( k.i . ) and no.19740145 ( t.t . ) . t.s . would like to thank the japan society for the promotion of science for financial support . k.  a.  olive and e.  d.  skillman , astrophys . j.   * 617 * , 29 ( 2004 ) [ arxiv : astro - ph/0405588 ] ; r.  h.  cyburt , b.  d.  fields , k.  a.  olive and e.  skillman , astropart . * 23 * , 313 ( 2005 ) [ arxiv : astro - ph/0408033 ] . m.  fukugita and m.  kawasaki , astrophys .  j.   * 646 * , 691 ( 2006 ) . m.  peimbert , v.  luridiana and a.  peimbert , arxiv : astro - ph/0701580 . y.  i.  izotov , t.  x.  thuan and g.  stasinska , astrophys .  j.   * 662 * , 15 ( 2007 ) [ arxiv : astro - ph/0702072 ] . a.  serebrov _ et al . _ , phys . b * 605 * , 72 ( 2005 ) [ arxiv : nucl - ex/0408009 ] . g.  j.  mathews , t.  kajino and t.  shima , phys . d * 71 * , 021302 ( 2005 ) [ arxiv : astro - ph/0408523 ] . a.  p.  serebrov , phys .  lett . b * 650 * , 321 ( 2007 ) [ arxiv : nucl - ex/0611038 ] . b.  d.  fields and k.  a.  olive , astrophys . j.   * 506 * , 177 ( 1998 ) [ arxiv : astro - ph/9803297 ] . r.  trotta and s.  h.  hansen , phys .  rev . d * 69 * , 023509 ( 2004 ) [ arxiv : astro - ph/0306588 ] . g.  huey , r.  h.  cyburt and b.  d.  wandelt , phys . d * 69 * , 103503 ( 2004 ) [ arxiv : astro - ph/0307080 ] . k.  ichikawa and t.  takahashi , phys . d * 73 * , 063528 ( 2006 ) [ arxiv : astro - ph/0601099 ] . k.  ichikawa , m.  kawasaki and f.  takahashi , phys .  lett . b * 597 * , 1 ( 2004 ) [ arxiv : astro - ph/0402522 ] . e.  komatsu _ et al . _ [ wmap collaboration ] , arxiv:0803.0547 [ astro - ph ] . j.  dunkley _ et al . _ [ wmap collaboration ] , arxiv:0803.0586 [ astro - ph ] . g.  hinshaw _ et al . _ [ wmap collaboration ] , arxiv:0803.0732 [ astro - ph ] . r.  s.  hill _ [ wmap collaboration ] , arxiv:0803.0570 [ astro - ph ] . m.  r.  nolta _ et al . _ [ wmap collaboration ] , arxiv:0803.0593 [ astro - ph ] . c.  l.  reichardt _ et al . _ , arxiv:0801.1491 [ astro - ph ] . j.  l.  sievers _ et al . _ , arxiv : astro - ph/0509203 . 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we studied a constraint on the primordial helium abundance @xmath0 from current and future observations of cmb . using the currently available data from wmap , acbar , cbi and boomerang 
 , we obtained the constraint as @xmath1 at 68% c.l . 
 we also provide a forecast for the planck experiment using the markov chain monte carlo approach . 
 in addition to forecasting the constraint on @xmath0 , we investigate how assumptions for @xmath0 affect constraints on the other cosmological parameters . 
 may 2008 + .5 in    * primordial helium abundance from cmb : + a constraint from recent observations and a forecast *    .45 in    kazuhide ichikawa@xmath2 , toyokazu sekiguchi@xmath3 , and tomo takahashi@xmath4    .45 in    _ 
 @xmath3 institute for cosmic ray research , university of tokyo , kashiwa 277 - 8582 , japan + @xmath5 department of physics and astronomy , university college london , gower street , london , wc1e 6bt , u.k . 
 + @xmath4 department of physics , saga university , saga 840 - 8502 , japan _ 
 .4 in