curvaton model constraints from wmap
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New Astronomy Reviews 47 (2003) 793–796
www.elsevier.com/locate/newastrev
Curvaton model constraints from WMAP
Christopher Gordon a,*, Antony Lewis b
a DAMTP, CMS, Wilberforce Road, Cambridge CB3 0WA, UKb CITA, 60 St. George St, Toronto, Ont., Canada M5S 3H8
Abstract
Simple curvaton models can generate a mixture of correlated primordial adiabatic and isocurvature perturbations.
Working numerically we use the latest WMAP observations and a variety of other data to constrain the curvaton
model. We find that models with an isocurvature contribution are not favored relative to simple purely adiabatic
models. However, a significant primordial totally correlated baryon isocurvature perturbation is not ruled out. Certain
classes of curvaton model are thereby ruled out, other classes predict enough non-Gaussianity to be detectable by the
Planck satellite.
� 2003 Elsevier B.V. All rights reserved.
1. Introduction
Recent detailed measurements of the acoustic
peaks in CMB anisotropy power spectrum by theWMAP satellite (Hinshaw et al., 2003; Peiris et al.,
2003) are consistent with the standard model of a
predominantly adiabatic, approximately scale in-
variant primordial power spectrum in a spatially
flat Universe. Frequently it is assumed the initial
power spectrum is entirely adiabatic, though there
is still no compelling justification for this as-
sumption. In particular, the recently proposedcurvaton model uses a second scalar field (the
�curvaton�) to form the perturbations (Mollerach,
1990; Lyth and Wands, 2002; Lyth et al., 2003).
The motivation for this is it makes it easier for
otherwise satisfactory particle physics models of
* Corresponding author.
E-mail addresses: c.gordon@damtp.cam.ac.uk (C. Gordon),
antony@antonylewis.com (A. Lewis).
1387-6473/$ - see front matter � 2003 Elsevier B.V. All rights reserv
doi:10.1016/j.newar.2003.07.021
inflation to produce the correct primordial spec-
trum of perturbations (Dimopoulos and Lyth,
2002).
The curvaton scenario also has the feature ofbeing able to generate isocurvature perturbations
of a similar magnitude to the adiabatic perturba-
tion without fine tuning, and therefore is open to
observational test.
We use the CMB temperature and temperature-
polarization cross-correlation anisotropy power
spectra from the WMAP 1 (Kogut et al., 2003;
Hinshaw et al., 2003; Verde et al., 2003) observa-tions, as well as seven almost independent tem-
perature band powers from ACBAR 2 (Kuo et al.,
2002) on smaller scales. In addition we use data
from the 2dF galaxy redshift survey (Percival
et al., 2002), HST Key Project (Freedman et al.,
2001), and nucleosynthesis (Burles et al., 2001)
1 http://lambda.gsfc.nasa.gov/.2 http://cosmologist.info/ACBAR.
ed.
794 C. Gordon, A. Lewis / New Astronomy Reviews 47 (2003) 793–796
using a slightly modified version of the Cos-
moMC 3 Markov-Chain Monte Carlo program, as
described in (Lewis and Bridle, 2002).
For simplicity we assume a flat universe with a
cosmological constant, uninteracting cold dark
matter, and massless neutrinos evolving accordingto general relativity.
2. Constraining the curvaton model
Primordial correlated isocurvature modes can
be generated if the baryons or CDM are generated
by, or before, the curvaton decays (Gordon andLewis, 2002). If one or both were created before the
curvaton decays, the current model assumes that
the curvaton had a negligible density when they
decayed (Lyth et al., 2003). We assume that the
curvaton is the only cosmologically relevant scalar
field after inflation decay, and that the perturba-
tions in the inflation field are negligible. Generi-
cally such models predict a very small tensor modecontribution, which we assume can be neglected.
The baryon and CDM isocurvature modes
predict proportional results (Gordon and Lewis,
2002), so we can account for Sc (the CDM iso-
curvature perturbation) by using just an effective
baryon isocurvature perturbation
Seffb ¼ Sb þ
Rc
Rb
Sc; ð1Þ
where Sb is the baryon isocurvature perturbation.
The baryon and CDM isocurvature perturba-
tions are completely correlated (or anti-correlated)
with each other and the adiabatic perturbation, so
Seffb ¼ Bf, where B measures the isocurvature mode
contribution and is taken to be scale independent 4
and f is the adiabatic perturbation. Note that our
number of degrees of freedom is actually less thangeneric inflation, because although we have in-
troduced B we now no longer have the amplitude
and slope of the tensor component to consider.
The slope of the isocurvature perturbation is pre-
3 http://cosmologist.info/cosmomc.4 Our sign convention for B differs from that in Amendola
et al. (2002). In our convention B > 0 corresponds to a positive
correlation and the modes contribute with the same sign to the
large scale CMB anisotropy.
dicted to be the same as the adiabatic perturbation
and the tensors are predicted to be negligible in the
curvaton scenario (Lyth et al., 2003).
The isocurvature modes have little effect on
small scales, but they can either raise or lower the
Sachs Wolfe plateau relative to the acoustic peaksdepending on the sign of B (Gordon and Lewis,
2002). This is in contrast to tensor perturbations
which can only raise the Sachs Wolfe plateau rel-
ative to the acoustic peaks.
We find the ratio of themean likelihood allowing
for isocurvature modes to that for purely adiabatic
models is about 0.7 (Gordon and Lewis, 2002) (for
discussion of mean likelihoods see (Lewis and Bri-dle, 2002)). Thus, the isocurvature modes do not
improve the already good fit to the data of the
standard purely adiabatic case. By the same token,
the current data is still consistent with a significant
isocurvature contribution, with the 95% marginal-
ized confidence interval�0:53 < B < 0:43 (Gordon
and Lewis, 2002). If new data favored B > 0 this
would be largely degenerate with a tensor contri-bution predicted by standard single field inflation-
ary scenarios, and would be hard to distinguish
without good CMB polarization data. Evidence for
B < 0 would be a smoking gun for an isocurvature
mode, though the large scale polarization data has
large enough cosmic variance that to distinguish it
from an adiabatic model with an unexpected initial
power spectrum shape would be difficult.If the CDM is created before the curvaton de-
cays, and while the curvaton still has negligible
energy density, its density is essentially unper-
turbed. After the curvature perturbation is gener-
ated there is therefore a relative isocurvature
perturbation, given by Lyth et al. (2003)
Sc � �3f: ð2ÞIf the curvaton decays before its energy density
completely dominates, a CDM isocurvature per-
turbation is produced (Lyth et al., 2003)
Sc � 31� rr
!f; ð3Þ
where r measures the transfer function from
fcurvaton (perturbation of the curvaton) before
curvaton decay to f after decay, f ¼ rfcurvaton.Lyth et al. (2003) find the approximate result
C. Gordon, A. Lewis / New Astronomy Reviews 47 (2003) 793–796 795
r � qcurvaton=qtotal, where q is the energy density at
curvaton decay, to an accuracy of about 10%
(Malik et al., 2003). The same formulas, Eqs. (2)
and (3), apply for the baryons with Sc replaced by
Sb. If either the CDM or the baryon number wascreated after the curvaton decayed then there
would be no isocurvature perturbation in that
quantity (Lyth et al., 2003). If both were created
after the curvaton decayed there would be no
isocurvature modes.
Various permutations of when the baryons and
CDMwere created can be considered. It was found
that models in which either the baryon number orCDM was created before the curvaton dominated
the energy density are ruled out unless counter-
balanced by the other species being created by the
curvaton decay (Gordon and Lewis, 2002).
The amount of non-Gaussianity in the CMB is
dependent on r with the conventional governing
parameter (Lyth et al., 2003)
fnl �5
4r; ð4Þ
Fig. 1. Plots of the un-normalized posterior probability distri-
bution for the amount of non-Gaussianity, fnl. The dotted line
is for CDM created before curvaton decay and baryon number
by curvaton decay. The other lines are for the other possible
permutations of the times of curvaton and baryon creation
(Gordon and Lewis, 2002).
assuming fnl � 1. Using this equation we can
convert the likelihood for r into those for fnl as isshown in Fig. 1. The current one year WMAP data
has fnl < 134 (95%) and is predicted to reach
fnl < 80 (95%) with the four year WMAP data(Komatsu et al., 2003). So if WMAP eventually
detects non-Gaussianity it will rule out all the
models considered here. The Planck satellite is
predicted to ultimately be able to detect fnl J 5
(Komatsu and Spergel, 2001). If this is realized,
Planck will be able to distinguish between the case
where the CDM is created before curvaton decay
and the baryon number by curvaton decay and theother possibilities.
3. Conclusions
The curvaton model provides a simple scenario
that can give rise to correlated adiabatic and iso-
curvature modes of similar size. The current datado not favor a large isocurvature contribution, but
a significant amplitude is still allowed.
Numerically, we found that the data was con-
sistent at the two sigma level with the presence of
an effective correlated baryon isocurvature per-
turbation of about 50% the magnitude of the adi-
abatic perturbation. The individual baryon and
CDM isocurvature modes can be even larger if theycompensate each other. Models in which either the
baryon number or CDM was created before the
curvaton dominated the energy density are ruled
out unless counter-balanced by the other species
being created by the curvaton decay. The levels of
non-Gaussianity expected for the various scenarios
were evaluated and in the case of the CDM being
created before the curvaton decayed and the bar-yon number by the curvaton decay, could be high
enough to detectable by the Planck satellite.
References
Amendola, L., Gordon, C., Wands, D., Sasaki, M., 2002.
Correlated perturbations from inflation and the cosmic
microwave background. Phys. Rev. Lett. 88, 211302.
Burles, S., Nollett, K.M., Turner, M.S., 2001. Big-bang
nucleosynthesis predictions for precision cosmology. Astro-
phys. J. 552, L1.
796 C. Gordon, A. Lewis / New Astronomy Reviews 47 (2003) 793–796
Dimopoulos, K., Lyth, D., 2002. Models of inflation liberated
by the curvaton hypothesis.
Freedman, W.L. et al., 2001. Final results from the Hubble
Space Telescope key project to measure the Hubble
constant. Astrophys. J. 553, 47.
Gordon, C., Lewis, A., 2002. Observational constraints on the
curvaton model of inflation.
Hinshaw, G. et al., 2003. First year Wilkinson Microwave
Anisotropy Probe (WMAP) observations: Data processing
and systematic errors limits.
Kogut, A. et al., 2003. First year Wilkinson microwave
anisotropy probe (WMAP) observations: Te polarization.
Komatsu, E., Spergel, D.N., 2001. Acoustic signatures in the
primary microwave background bispectrum. Phys. Rev. D
63, 063002.
Komatsu, E. et al., 2003. First year Wilkinson microwave
anisotropy probe (wmap) observations.
Kuo, C.L. et al., 2002. High resolution observations of the
CMB power spectrum with ACBAR.
Lewis, A., Bridle, S., 2002. Cosmological parameters from
CMB and other data: a Monte-Carlo approach. Phys. Rev.
D 66, 103511.
Lyth, D., Wands, D., 2002. Generating the curvature
perturbation without an inflation. Phys. Lett. B 524, 5.
Lyth, D.H., Ungarelli, C., Wands, D., 2003. The primordial
density perturbation in the curvaton scenario. Phys. Rev. D
67, 023503.
Malik, K.A., Wands, D., Ungarelli, C., 2003. Large-scale
curvature and entropy perturbations for multiple interacting
fluids. Phys. Rev. D 67, 063516.
Mollerach, S., 1990. Phys. Rev. D 42, 313.
Peiris, H.V. et al., 2003. First year Wilkinson microwave anisot-
ropy probe (wmap) observations: Implications for inflation.
Percival, W. et al., 2002. Parameter constraints for flat
cosmologies from CMB and 2dFGRS power spectra.
MNRAS 337, 1068.
Verde, L. et al., 2003. First Year Wilkinson Microwave
Anisotropy Probe (WMAP) Observations.
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