document: in standard cosmology , the acoustic oscillations imprinted in the matter power spectrum at recombination have a length scale that can be accurately calculated based on measurements of the cmb anisotropy power spectrum @xcite . 
   it should then be possible to measure this `` standard ruler '' scale at low redshifts , for example in large galaxy redshift surveys , and thereby constrain the matter and energy content of the universe @xcite . 
   however , if the cmb measurements were misled by some new physics , e.g.  a new undetected relativistic particle , then the misinterpretation could potentially spread to the low - redshift application and bias the inferences .    here 
   , we show that the interpretation of the low - redshift acoustic oscillations are robust if the cmb correctly tells us the baryon - to - photon ratio and the epoch of matter - radiation equality . these quantities are robustly measured in the cmb . 
   the actual densities of matter and radiation drop out of the calculation ; only their ratio matters . 
   the result is that even if the physical matter density @xmath0 is misinterpreted from the cmb due to undetected relativistic components , the inferences for dark energy from the combined cmb and low - redshift survey data sets are unchanged . 
   knowledge of actual densities , e.g.  @xmath1 , translates into improved constraints on the hubble constant , @xmath2 . 
   the acoustic peak method depends upon measuring the sound horizon , which is the comoving distance that a sound wave can travel between the end of inflation and the epoch of recombination @xcite . 
   nearly all of this distance is accumulated just prior to the epoch of recombination at @xmath3 . 
   the sound horizon integral depends only on the hubble parameter @xmath4 and the sound speed @xmath5 in the baryon - photon plasma . if we assume dark energy is sub - dominant at @xmath6 , then @xmath7 where @xmath8 is epoch of matter - radiation equality . 
   the sound speed depends only on the baryon - to - photon ratio and is @xmath9 with @xmath10 . 
   these two produce the sound horizon @xmath11 where ` rec ' and ` eq ' refer to recombination and equality respectively . 
   one sees that the aside from a prefactor of @xmath12 , the sound horizon depends only on the baryon - to - photon ratio and the redshift of equality . 
   the epoch of recombination , being controlled by atomic physics , is very insensitive to the cosmology . for reasonable changes in the early universe and our current uncertainties of the theory of recombination @xcite , 
   any shift in @xmath13 is negligible . 
   the baryon - to - photon ratio is also exquisitely well measured in the cmb power spectrum by both the ratios of the odd and even acoustic peaks and by the silk damping tail @xcite . 
   the former effect depends only on the gravitational inertia of the baryons driven by the potentials near the epoch of recombination . 
   thus the modulation gives us a precise measurement of the baryon - to - photon ratio @xmath14 , which with our precise knowledge of @xmath15 fixes @xmath16 . 
   moreover , for the established value of @xmath17 near @xmath18 , the effect on the sound horizon is already small . 
   it seems very likely that the cmb will determine the baryon - to - photon ratio to sufficient accuracy for this portion of the sound horizon computation @xcite . 
   information about matter - radiation equality is encoded in the amplitudes of the peaks through the manner in which the potentials evolve as they cross the horizon : the potential envelope @xcite . 
   measurements of the potential envelope thus robustly constrain equality . 
   normally , one interprets this constraint as the matter density @xmath1 , on the assumption that the photons and standard neutrino background are the full radiation density . 
   however , one could imagine other relativistic components , and in this case , measuring the redshift of equality does not imply the matter density @xmath1 ( we continue to assume that the extra components are `` undetected '' in the cmb and return to this point in the next section ) . as we can see from eq . 
   ( [ eq : rsound ] ) , the dependence of @xmath19 on @xmath20 is relatively small since @xmath21 , thus even a crude determination suffices to fix @xmath19 up to an overall factor of @xmath12 , i.e. , @xmath22 is very well measured . 
   the sound horizon decreases by only 5% if @xmath20 is lowered by @xmath23 ! 
   understanding the acoustic oscillations at @xmath3 allows us to translate knowledge of the sound horizon into knowledge of wavelength of the baryonic features in the mass power spectrum up to the same normalization uncertainty . 
   we then wish to consider the measurement of this scale at lower redshift , such as could be accomplished in large galaxy surveys . 
   measuring the scale along and across the line of sight , as a redshift or angular scale , constrains @xmath24 and @xmath25 , respectively . 
   for dark energy with ( constant ) equation of state @xmath26 , the low - redshift quantities can be written as @xmath27^{-1/2},\ ] ] and ( for zero curvature ) @xmath28^{-1/2}.\ ] ] because @xmath29 is well constrained , we find that the observations actually constrain @xmath30 and @xmath31 @xcite , which contain only the terms that depend on the bare @xmath32 values , , where @xmath33 is equation [ eq : da ] . 
   but we can write @xmath34 , where @xmath35 is the usual curvature term . 
   this substitution shows that @xmath36 depends only on the bare @xmath32 s . ] 
   i.e. , @xmath37 , @xmath38 , etc . in other words , 
   the prefactors of @xmath12 have canceled out between @xmath19 and the low - redshift distances . 
   we can thus reliably predict the distance _ ratios _ between low @xmath39 and @xmath3 as a function of redshift and hence constrain cosmology . 
   what has happened is simply that the overall scale of the universe does nt affect any of the distance ratios . 
   usually this scale is labeled as the hubble constant , such that @xmath40 drops out . 
   we have rephrased the scale as @xmath1 , despite the fact that this would appear to include @xmath37 in addition to @xmath40 . another way of saying this is that the standard ruler defined by the cmb at constant redshift of equality actually scales as @xmath41 . 
   hence , even @xmath42 redshift - space measurements of this ruler do not measure @xmath40 , but instead measure @xmath43 . 
   parameter estimation for acoustic oscillations based on standard models @xcite will be unchanged by the presence of undetectable new radiation provided that the redshift of equality is measured correctly . 
   only the hubble constant would be incorrect . in the context of cmb parameter estimation , it would be more useful to report @xmath44 rather than @xmath19 itself , as this is the quantity that isolates the cosmological densities at low redshift . 
   massive neutrinos should be counted as radiation at @xmath45 but would be counted as matter at low redshift . 
   that does create a small error in the dark energy inferences . 
   one would be computing @xmath46 from the cmb , but the low - redshift distances in equations ( [ eq : h ] ) and ( [ eq : da ] ) would still have prefactors of @xmath47 . as the observations constrain @xmath25 and @xmath24 , the evaluation of these quantities in terms of bare @xmath32 s will be altered by @xmath48 . for the massive neutrino fraction inferred for non - degenerate neutrino species and the atmospheric neutrino mass 
   splitting @xcite this is a 0.2% correction ; however , it could be a few percent correction at the upper limit of the allowed masses for degenerate neutrino species @xcite . 
   fortunately , such neutrino masses should be detectable in upcoming data due to their suppression of the late - time matter power spectrum @xcite .    because the integral for the sound horizon extends to early times ( essentially to the time when the cosmic perturbations were established ) , alterations to the hubble parameter ( eq .  [ [ eq : h ] ] ) 
   could alter the sound horizon even at fixed redshift of equality . 
   for example , there might exist a non - relativistic particle that decays into relativistic unseen particles sometime prior to recombination @xcite . 
   however , such decays create alterations to the gravitational potentials that would be detectable in the cmb if the horizon scale at that epoch is visible in the primary anisotropies ( i.e. , wavenumbers @xmath49 ) . 
   this makes decays at @xmath50 difficult to hide . 
   furthermore , such decays alter the transfer function and would affect the amplitude of the late - time matter power spectrum . 
   precision measurement of the matter power spectrum out to @xmath51 from the lyman - alpha forest could push the limits on particle decays to earlier times . in the standard theory , the first 1% of the sound horizon integral 
   is contributed by @xmath52 . 
   it therefore seems very unlikely that a decaying particle could significantly affect the sound horizon ( relative to the standard theory at fixed redshift of equality ) and escape detection in the cmb or large - scale structure .    as a corollary 
   , it is interesting to note that when one measures the acoustic oscillation scale at @xmath13 with the cmb and at some low redshift @xmath53 in a galaxy survey , one can construct an observable ( the difference of the suitably scaled angular wavenumbers of the acoustic peaks ) that isolates the cosmology between @xmath53 and @xmath13 , i.e. , @xmath54 this integral is trivial when the universe is completely matter - dominated . 
   hence , if we can perform a galaxy survey at some suitably high redshift , e.g. , @xmath55 , where the dark energy is supposed to be negligible , we could search for dynamical shenanigans at @xmath56 . a photometric - redshift survey over large amount of sky 
   would be an economical route to this goal , as one can acquire very large survey volumes @xcite . 
   we have argued that only the ratios of the radiation and matter densities enter the acoustic oscillation standard ruler method , but of course it is interesting to measure the actual values of the densities as they might reveal new relativistic components or unexpected evolution . 
   the cmb is sensitive to the non - photon radiation density primarily through its effect on equality and the evolution of the potentials . 
   this encodes a sensitivity to both the amount of radiation and its quadrupole moment . in general any particle that free streams rather than behaves as a fluid will have a local quadrupole that will affect the evolution of the potentials and thus the anisotropy in the cmb 
   this breaks the degeneracy in the cmb between changes in @xmath1 and @xmath57 @xcite and allows us to constrain a `` conventional '' neutrino at the @xmath58 level @xcite . at the other extreme , extra radiation which is of the perfect fluid form leads to an increase in the small - scale power which 
   is easily discerned from a change in @xmath1 ( see fig .  [ 
   fig : cl ] ) . only a radiation component 
   whose higher moments track closely that of the traditional mix of photons and neutrinos could be confused with a change in @xmath1 . 
   altering the radiation and matter density while holding the baryon ( and photon ) densities fixed would alter the baryon fraction @xmath59 and would produce significant offsets in the late - time matter power spectrum ( e.g.  @xcite ) . 
   higher baryon fractions suppress power on small scales compared to large , with the transition occurring near the sound horizon at @xmath60 . 
   the acoustic oscillations shortward of this scale would also be increased . 
   the small - scale amplitude ( e.g. , @xmath61 ) would be reduced . 
   these changes are observable in galaxy surveys , weak lensing surveys , and cluster abundance measurements . 
   of course one can also directly measure the hubble constant @xcite .    in short , 
   although the acoustic peak method depends only on the redshift of equality , other cosmological measurements both at @xmath62 and at @xmath63 are well poised to measure the actual densities and thereby constrain the presence of unknown relativistic species . 
   we have shown that the standard ruler defined by the acoustic oscillations prior to recombination can deal gracefully with uncertainties in the matter density @xmath64 provided that the redshift of matter - radiation equality is well measured . 
   the anisotropies of the cmb have very good leverage on this quantity , and so the acoustic peak method of probing dark energy is robust . 
   in addition , it is likely that the cmb , perhaps in combination with other probes , will be able to constrain the actual matter and radiation densities . 
   acknowledgements : we thank eric linder and nikhil padmanabhan for useful discussions and the lawrence berkeley laboratory for the hospitality of its summer workshop program where this work was begun . 
   dje is supported by national science foundation grant ast-0098577 and by an alfred p.  sloan research fellowship . 
   mw is supported by the nsf and nasa . 
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summary: we discuss the systematic uncertainties in the recovery of dark energy properties from the use of baryon acoustic oscillations as a standard ruler . 
   we demonstrate that while unknown relativistic components in the universe prior to recombination would alter the sound speed , the inferences for dark energy from low - redshift surveys are unchanged so long as the microwave background anisotropies can measure the redshift of matter - radiation equality , which they can do to sufficient accuracy . 
   the mismeasurement of the radiation and matter densities themselves ( as opposed to their ratio ) would manifest as an incorrect prediction for the hubble constant at low redshift . 
   in addition , these anomalies do produce subtle but detectable features in the microwave anisotropies .