Cosmological constraints in the presence of ionizing and resonance radiation at recombination

0.34 MB·English

by  Rachel Bean

Cosmological constraints in the presence of ionizing and resonance radiation at
recombination
Rachel Bean♯, Alessandro Melchiorri∗ and Joseph Silk ♭
♯ Dept. of Astronomy, Space Sciences Building, Cornell University, Ithaca, NY, USA.
∗ Dipartimento di Fisica e sezione INFN, Universita’ di Roma “La Sapienza”, Ple Aldo Moro 2, 00185, Rome, Italy.
♭ Astrophysics, Denys Wilkinson Building, University of Oxford, Keble Road, OX3RH, Oxford, UK.
WiththerecentmeasurementoffullskycosmicmicrowavebackgroundpolarizationfromWMAP,
key cosmological degeneracies have been broken, allowing tighter constraints to be placed on cos-
mological parameters inferred assuming a standard recombination scenario. Here we consider the
effect on cosmological constraints if additional ionizing and resonance radiation sources arepresent
at recombination. We find that the new CMB data significantly improve the constraints on the
additional radiation sources, with log [ǫ ] < −0.5 and log [ǫ ] < −2.4 at 95% c.l. for resonance
7 10 α 10 i
0 and ionizing sources respectively. Including the generalized recombination scenario, however, we
0 find that the constraints on the scalar spectral index ns are weakened to ns = 0.98±0.03, with
2 the ns = 1 case now well inside the 95% c.l.. The relaxation of constraints on tensor modes, scale
invariance, dark energy and neutrino masses are also discussed.
n
a
J
I. INTRODUCTION trino masses to mi < 0.66eV at 95% c.l. where
9
i = 1,..,3 and inPdicates the neutrino flavor. Again,

while those constraints play a very important role in
1 Therecentmeasurementsofthe CosmicMicrowave
our understanding of the darkenergy component and
v
Background (CMB) flux provided by the three year
4 neutrinophysics,theyareobtainedinanindirectway
Wilkinson Microwave Anisotropy Probe (WMAP)
2 and under several assumptions.
mission (see [1, 2, 3, 4] have confirmed several of the
2 Theimportanceofthemodeldependencyofthecos-
1 results already presented in the earlier data release,
mological constraints has been recently discussed by
0 but also pointed towards new conclusions. The bet-
several authors. The impact of isocurvature modes
7 tertreatmentofsystematicsinlargescalepolarization
0 data,inparticular,hasnowprovidedalowervaluefor on the determination of the neutrino mass [14], dark
/ energy properties [15], scalar spectral index [16] and
h the optical depth parameter τ. This, together with
baryon density [17] is just one example.
p an improvedsignalin the temperature data at higher
- multipoles, has resulted in a lower value of the spec- Hereweinvestigatepossibledeviationsinthemech-
o
tral index parameter n = 0.959± 0.016. A deter- anism on which CMB anisotropies are highly depen-
r s
t mination of this parameter can play a crucial role in dent: the process of recombination.
s
a the study of inflation. Soon after the WMAP data In a previous paper [18], we analyzed modified re-
: release, several papers have indeed investigated the combinationprocessesinlightoftheWMAPfirstyear
v
possibilityofdiscriminatingbetweensingle-fieldinfla- data. Hereweassesstheimprovementsgivenbymore
i
X tionary models by making use of this new, high qual- recent data, in particular the inclusion of CMB po-
r ity, dataset [5, 6, 7, 8, 9, 10, 11, 12, 13]. One of larization spectra, and also extend the analysis to a
a
the main conclusions of these papers is that some in- largersetofparameters. Wewillindeednotonlypro-
flationary models, such as quartic chaotic models of vide new and more stringent constraints on modified
the form V(φ) ∼ λφ4, may be considered ruled out recombination but we also consider its impact on in-
by the current data while others, such as chaotic in- flationary, dark energy and neutrino parameters,
flation with a quadratic potential V(φ) ∼ m2φ2 are The recombination process can be modified in sev-
consistent with all data sets. eral ways. For example, one could use a model-
While the WMAP result is of great importance independent, phenomenological approach such as in
for inflationary model building, one should be care- [19] where models are specified by the position and
ful in taking any conclusion as definitive since the width of the recombination surface in redshift space.
constraints on n are obtained in an indirect way Here we instead focus on theoretically motivated
s
and are, therefore, model dependent. Similar con- mechanisms based on extra sources of ionizing and
siderations applies to other cosmological constraints, resonance radiation at recombination (see e.g. [20]).
such those on the dark energy equation of state and While the method we adopt will be general enough
neutrino masses. Combining CMB anisotropies with to cover most of the models of this kind, as discussed
galaxy clustering and supernovae type Ia data, the in the next section, we remind the reader that there
dark energy equation of state parameter (dark en- exist other ways in which to modify recombination,
ergy pressure over density) has been constrained to for instance, by having a time-varying fine-structure
w = −1.08±0.12 at 95% c.l. (see [1]). Using the constant ([21]).
same dataset, but under the assumption of a cosmo- Following the seminal papers [22, 23] detailing
logical constant, it is possible to constrain the neu- the recombination process, further refinements to the
2
standard scenario were developed [24], allowing pre- decay or annihilation of massive particles [20, 32, 33,
dictions at the accuracy level found in data from 34, 35,36, 37, 38]. The decaychanneldepends onthe
the WMAP satellite and the future Planck satellite natureoftheparticles,andcould,forexample,include
[25, 26]. With this level of accuracy, it becomes charged and neutral leptons, quarks or gauge bosons.
conceivablethatdeviationsfromstandardrecombina- These particles may then decay further, leading to a
tion maybe be detectable [20, 27, 28], although fur- shower /cascade that could, amongst other products,
ther refinements could be required to get the Thom- generate a bath of lower energy photons that could
son visibility function below percent level accuracy interactwiththeprimordialgasandcosmicmicrowave
[29, 30, 31]. background. Interestingly these models, as well as
The paper proceeds as follows: in section II we de- injectingenergyatrecombination,z ∼1000,boostthe
scribeamodelwhichcanproducedeviationsfromthe ionizationfractionafterrecombinationandcandistort
standard recombination scenario. In III, we describe the ionization history of the universe at even later
how these deviations might affect the CMB temper- times, during galaxy formation and reionization z ∼
ature and polarization power spectra and conduct a 5−10 [9, 39, 40, 41, 42]. Other mechanisms include
likelihood analysis using the recent CMB data from evaporation of black holes [27, 44] or inhomogenities
WMAP and other cosmological observables. In par- in baryonic matter [27].
ticular, we will study the impact that a modified re- We employ the widely used RECFAST code [24], in
combinationscheme can have on severalcosmological thecosmomcpackage[45]modifyingthecodeasin(4)
andastrophysicalparameters. InIVwedrawtogether to include two extra constant parameters, ǫ and ǫ .
α i
the implications of the analysis. Inadditiontotheionizingsources,weassumeasingle,
swift reionization epoch at a redshift z .
re
In Figure 1 we show the effect of additional res-
II. A MODIFIED IONIZATION HISTORY
onance and ionizing radiation on the CMB TT, TE
and EE spectra, in comparison to a fiducial best fit
The evolution of the ionization fraction, xe, of model to the WMAP 3-yeardata. From identical ini-
atoms, number density n, can be modeled in a sim- tial power spectra, the inclusion of additional reso-
plified manner for the recombination of hydrogen, nance photons slighly boosts the ionization fraction
[22, 23], at and after recombination, suppressing TT power at
smallscales,whilethelargescaleEEspectraislargely
unaffected. Ionizing photons significantly boost the
dx ∆B
− dte |std =C(cid:20)acnx2e−bc(1−xe)exp(cid:18)−k T(cid:19)(cid:21)(1) ionization fraction post recombination and therefore
B aswellassignificantlysuppressingTTpoweronsmall
where a and b are the effective recombination and scales,theyalsocangenerateaboostinthelargescale
c c
photo-ionizationratesforprinciple quantumnumbers EE signal akin to an early partial reionization.
≥ 2, ∆B is the difference in binding energy between
the 1st and 2nd energy levels and
C = 1+KΛ1s2sn1s , K = λ3α (2) III. LIKELIHOOD ANALYSIS
1+K(Λ1s2s+bc)n1s 8πH(z)
Themethodweadoptisbasedonthepubliclyavail-
where λα is the wavelength of the single Ly-α transi- able Markov Chain Monte Carlo package cosmomc
tion from the 2p level, Λ1s2s is the decay rate of the [45]. We sample the following dimensional set of cos-
metastable 2s level, n1s =n(1−xe) is the number of mological parameters, adopting flat priors on them:
neutralgroundstateH atoms,andH(z)istheHubble
the physical baryon and Cold Dark Matter (CDM)
expansion factor at a redshift z. densities, ω = Ω h2 and ω = Ω h2, the ratio of the
b b c c
We include the possibility of extra photons at key
soundhorizontotheangulardiameterdistanceatde-
wavelengths that would modify this recombination
coupling, θ , the scalar spectral index, n , and the
s s
picture,namely, resonance(Ly-α) photonswith num-
optical depth to reionization, τ. As described in the
ber density, n ,which promote electrons to the 2p
α previous section, we modify recombinationby consid-
level, and ionizing photons, n ,[18, 20, 27, 28]
i eringvariationsintheε andε parameters. Further-
α i
more, we consider purely adiabatic initial conditions
dn dn
α i
= εα(z)H(z)n, =εi(z)H(z)n. (3) and we impose flatness. We also consider the possi-
dt dt
bility of having a tensor (gravity waves) component
which leads to a modified evolution of the ionization with amplitude r respect to scalar, a running of the
fraction spectral index dn /dlnk at k = 0.002h−1Mpc and a
s
dx dx non-zero,degenerate,neutrinomassofenergydensity:
e e
− = − | −Cε H −(1−C)ε H. (4)
dt dt std i α
Extraphotonsourcescanbegeneratedbyavariety Σm
of mechanisms. A widely considered process is the Ωνh2 = ν (5)
92.5eV
3
FIG.1: (From left toright) Thecomparison of ionization fraction evolution, and TT (left) ,TE (center) and EE (right)
CMB spectra comparing a best fit ΛCDM fiducial model to models with the same cosmological parameters but with
additional resonance (top) and ionizing (bottom) radiation. WMAP binned data are shown as blue shaded regions.
Finally, we will also investigate the possibility of a In the top portion of Figure 2, we consider only the
dark energy equation of state, w, different from −1 WMAP data (plus a prioronthe Hubble parameter),
but constant with redshift. The MCMC convergence while in the lower portion, we add SDSS. Let us first
diagnostics is done on 7 chains though the Gelman consider the case of WMAP alone. As we see, using
and Rubin “variance of chain mean”/“mean of chain this datasetalone,wecanputinterestingnewbounds
variances” R statistic for each parameter. Our 1D on the recombinationparameters. Marginalizing over
and 2D constraints are obtained after marginaliza- the remaining, “nuisance”, parameters we indeed ob-
tion overthe remaining “nuisance”parameters,again tain log (ǫ ) < −0.81 and log (ǫ ) < −2.31 at 95%
10 α 10 i
using the programs included in the cosmomc pack- c.l..
age. Inadditiontothe WMAPdata,wealsoconsider As suggested by Figure 1, we find ionizing photons
the constraints on the real-space power spectrum of arebetterconstrainedwithcurrentdatasincetheion-
galaxies from the Sloan Digital Sky Survey (SDSS) izationfractionissignificantlyboostedatandbeyond
[46]. We restrictthe analysisto a range of scales over the onsetofrecombination. This results in asuppres-
whichthe fluctuationsareassumedtobe inthe linear sion of TT power and boosting of EE power even on
regime (k < 0.2h−1Mpc). When combining the mat- large scales, well constrained by WMAP data. Reso-
ter power spectrum with CMB data, we marginalize nance photons have a more subtle effect only slightly
overa bias b consideredas an additionalnuisance pa- increasing the ionization fraction after the onset of
rameter. Furthermore, we make use of the Hubble recombination. This leads to a suppression of small
Space Telescope (HST) measurement of the Hubble scale TT power but little effect on large scale EE.
parameter H0 = 100h km s−1Mpc−1 [47] by multi- The constraints on both types of radiation should be
plyingthelikelihoodbyaGaussianlikelihoodfunction noticeably improved therefore by future experiments,
centered around h=0.72 and with a standard devia- such as the planned PLANCK satellite, which better
tionσ =0.08. When consideringdarkenergymodels, characterize small scale TT and EE power [28].
we also include information from luminosity distance
Moreover, there is a clear degeneracy between
measurements of type Ia Supernovae from the recent
log (ǫ )andthe spectralindexn . Indeed,amodifi-
analysisof[48]. Finally, weinclude atop-hatprioron 10 α s
cation of the recombination scheme allows us to sup-
the age of the universe: 10<t0 <20 Gyrs. press the amplitude of the peaks in the CMB power
spectruminawaysimilartoalaterrecombinationbut
without altering the large-scale polarization signal.
IV. RESULTS This changes in a drastic way the constraints on the
scalar spectral index and σ8. Marginalizing over the
recombination parameters, we get n = 0.978+0.032
Our main results are plotted in Figure 2 where we s −0.029
show the 68% and 95% c.l. on the ns − log10(ǫα), and σ8 = 0.80+−00..0089 at 95% c.l.. Those results should
σ8−log10(ǫα), ns−log10(ǫi) andσ8−log10(ǫi)plane. be compared with the constraints ns = 0.959+−00..002267
4
FIG. 3: The effect of a modified recombination scheme
on inflationary parameters in a WMAP+SDSS analysis.
In the top panel we plot the constraints in the n − r
s
plane. Thefilledcontours(68%and95%)areobtainedaf-
ter marginalization over extendedrecombination parame-
FIG. 2: The 68% and 95% likelihood contours in the n
s
terswhiletheemptycontoursassumestandardrecombina-
and σ8 vs εα plane (left) and ns and σ8 vs εi (right).
tion. Inthebottompanel,weshowthe68%and95%likeli-
Theanalysisconsiders(top/blue)the3-yearsWMAPdata
hoodcontoursinthedn /dlnk vsε plane. Non-standard
and a HST prior on the Hubble parameter, h, alone and s α
recombination shifts the∼1σ evidencefor runningin the
(bottom/red) also including SDSS galaxy matter power
standard case to a null result. Future evidence for run-
spectrum data.
ning may be interpreted as evidence for a non-standard
recombination scheme.
and σ8 =0.78+−00..0087, again at 95% c.l., obtained using
thesamedatasetandpriorsbutwithstandardrecom-
ters such as the amplitude of a tensor component r
bination.
or a running of the spectra index dn /dlnk. In Fig-
s
IncludingSDSSdata,asisshowninthelowerpanel ure 3 (toppanel) we plot the 68%and95%likelihood
in Figure 2, does not significantly improve our con- contours in the n −r plane in the standard and in
s
straints on εα and εi. The SDSS power spectrum in- the generalized recombination case. As one can see,
deed prefers a higher value of the σ8 parameter than relaxing our knowledge about recombinationstrongly
WMAP. While the tension is not strong enough to affects the final constraints: the scalar spectral index
provide any evidence for modified recombination, the can be more consistent with n > 1 and the upper
s
constraints are lowered to log10(ǫα) < −0.51 for εα limitonthetensorcomponentcanbeafactor2larger
and almost stable to log10(ǫi) < −2.24, for εi at than in the standard case. As one can see from the
95% c.l.. The constraints on ns and σ8 are also af- bottompanelofFigure3adegeneracybetweenǫαand
fected. Including SDSS we find ns = 0.994+−00..004305 and the running dns/dlnk is also present. Standard anal-
σ8 =0.87+−00..0076 at 95% c.l.. yses prefer a negative running of the spectral index
Interestingly, we find that the constraints on other with significance slightly above 1σ (see [1]). This can
key parameters (τ or Ω ) are robust to the modifica- be compensatedfor by a non-standardrecombination
b
tions in the recombination scenario. It is interesting with ǫα >0.1.
to extend the analysis to other inflationary parame- In Figure 4, we report on the impact of non-
5
bined,indicationforw <−1could,therefore,provide
a hint of a non-standard recombination process and
oneshouldbecarefulininterpretingitasevidencefor
a phantom-like dark energy component. In a more
generalized recombination scenario, we find the con-
straints on w are relaxed to w = −1.24+0.28 at 95%
−0.44
c.l..
Finally, in Figure 5, we report the constraints on
neutrino masses. As one can see, non-standard re-
combination also relaxes constraints on this parame-
ter. We find that values as large as Σm ∼ 1.2eV
ν
are consistent with the data, relaxing by ∼ 50% the
standard constraint Σm <0.72eV (see e.g. [1, 49]).
ν
FIG. 4: The impact of a modified recombination scheme V. CONCLUSIONS
on constraining a constant dark energy equation of state,
w. We show the 68% and 95% likelihood contours in
thew vsε planefrom WMAP+SDSS+HST+SN-1a(see In this paper, we update the upper bounds that
α
text). Non-standardrecombinationrelaxestheconstraints can be placed on the contribution of extra Ly-α
towards more negative values for w and ionizing photon-producing sources in light of the
new WMAP data. We find that, adopting a simple
parametrizationusing constant effective values for ε
α
and ε , the WMAP data constraints log [ε ]<−0.5
i 10 α
and log [ε ]<−2.4 at the 95%level. Physically mo-
10 i
tivated models fornon-standardrecombinationwhich
generate ionizing and resonance radiation, like those
based on primordial black hole or super-heavy dark
matter decay, remain feasible.
We findthatamodifiedrecombinationschememay
affect the current WMAP constraints on inflationary
parameterslike the spectralindex n andits running.
s
In particular, if recombination is changed, Harrison-
Zel’dovich spectra with n = 1, larger tensor modes
s
and positive running are in agreement with observa-
tions. Moreover, constraints on particle physics pa-
rameterslikethe neutrinomassarealsorelaxedwhen
non-standard recombination is considered.
Future observations in both temperature and po-
FIG. 5: The effect of a modified recombination scheme
larization, such as those expected from the Planck
on constraining neutrino masses. We show the 68% and
satellite [28],willprovidemoreprecisesmallscaleTT
95% likelihood contours in the Σm vs ε plane from
ν α
andEEmeasurementsneededtomorestringentlytest
WMAP+SDSS+HST (see text). Non-standard recombi-
these models and, crucially, will reduce the depen-
nation relax theconstraints towards larger masses
dency of other cosmologicalparameters on them.
Acknowledgments
standard recombination on the equation of state pa- RB’s work is supported by NSF grants AST-
rameter, w. We find an important degeneracy only 0607018 and PHY-0555216 and uses National Su-
with ǫ ; allowing ǫ to vary enlarges the constraints percomputing (NCSA) resources under grant TG-
α α
on w towards more negative values. A future, com- AST060029T.
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