Issue |
A&A
Volume 517, July 2010
|
|
---|---|---|
Article Number | A62 | |
Number of page(s) | 4 | |
Section | Cosmology (including clusters of galaxies) | |
DOI | https://doi.org/10.1051/0004-6361/201014215 | |
Published online | 06 August 2010 |
Constraints on variation in
and
from WMAP 7-year data
S. J. Landau1, - G. Scóccola2,
1 - Departamento de Física, FCEyN, Universidad de Buenos Aires,
Ciudad Universitaria - Pab. 1, 1428 Buenos Aires, Argentina
2 - Max-Planck-Institut für Astrophysik, Karl-Schwarzschild Str. 1, Postfach 1317,
85741 Garching, Germany
Received 8 February 2010 / Accepted 4 May 2010
Abstract
Aims. We update the constraints on the time variation of the fine structure constant
and the electron mass
,
using the latest CMB data, including the 7-yr release of WMAP.
Methods. We made statistical analyses of the variation of each
one of the constants and of their joint variation, together with the
basic set of cosmological parameters. We used a modified version of
CAMB and COSMOMC to account for these possible variations.
Results. We present bounds on the variation of the constants for
different data sets, and show how results depend on them. When using
the latest CMB data plus the power spectrum from Sloan Digital Sky
Survey LRG, we find that
at 1-
level, when the 6 basic cosmological parameters were fitted, and only variation in
was allowed. The constraints in the case of variation of both constants are
and
.
In the case of only variation in
,
the bound is
.
Key words: cosmic background radiation - cosmological parameters - early Universe
1 Introduction
The variation of fundamental constants over cosmological time scales
is a prediction of theories that attempt to unify the four
interactions in nature, like string derived field theories, related
brane-world theories and Kaluza-Klein theories (see Uzan 2003; García-Berro et al. 2007, and
references therein). Many observational and experimental efforts have
been made to put constraints on such variations. Most of the reported
data are consistent with null variation of fundamental
constants. Although there have been recent claims for time variation
of the fine structure constant ()
and of the proton to electron
mass ratio (
)
(Reinhold et al. 2006; Murphy et al. 2003), independent analyses of
similar data give null results
(Malec et al. 2010; King et al. 2008; Srianand et al. 2004; Thompson et al. 2009). On the other hand, a
recent analysis of ammonia spectra in the Milky Way suggests a spatial
variation of
(Molaro et al. 2009; Levshakov et al. 2010).
Unifying theories predict variation of all coupling constants, being
all variations related in general to the rolling of a scalar
field. Therefore, the relationship between variations of coupling
constants depends on the unifying model. In this paper we adopt a
phenomenological approach and analyse the possible variation of
and/or
at the time of the formation of neutral hydrogen
without assuming any theoretical model. Nakashima et al. (2010) have
considered also the variation in the proton mass (
). This quantity
affects mainly the baryon mass density and the baryon number
density. Their results confirm the strong degeneracy with the baryon
density. Therefore, we will not consider the variation in
in
this work.
Cosmic microwave background radiation (CMB) is one of the most
powerful tools to study the early universe and in particular, to put
bounds on possible variations in the fundamental constants between
early times and the present. Changing
or
at
recombination affects the differential optical depth of the photons
due to Thompson scattering, changing therefore Thompson scattering
cross section and the ionization fraction. The signatures on the CMB
angular power spectrum due to varying fundamental constants are similar to those
produced by changes in the cosmological parameters, i.e. changes in
the relative amplitudes of the Doppler peaks and a shift in their
positions. Moreover, an increment in
or
decreases the
high-
diffusion damping, which is due to the finite thickness of
the last-scattering surface, and thus, increases the power on very
small scales (Hannestad 1999; Kaplinghat et al. 1999).
Recent analyses of CMB data (earlier than the WMAP seven-year
release) including a possible variation in
have been
performed by Martins et al. (2010); Menegoni et al. (2009); Scóccola et al. (2009,2008); Nakashima et al. (2010),
and including a possible variation in
have been performed by
Scóccola et al. (2009); Nakashima et al. (2010); Scóccola et al. (2008).
In our previous works, we have also analyzed the dependence of the
updated recombination scenario (that includes the recombination of
helium, and was implemented in R ECFAST following Wong et al. 2008) on
and
,
and show that these dependencies are not relevant
for WMAP data.
In this paper we adopt a phenomenological approach and analyse the
possible variation in
and/or
without assuming any
theoretical model. We use WMAP seven-year release, together with other
recent CMB data. We also combine CMB data with other cosmological data
sets: i) the power spectrum of the Sloan Digital Sky Survery DR7 LRG;
ii) a recent constraint of the Hubble constant H0 with data from
the Hubble Space Telescope. In Sect. 2 we describe
the method and data sets we used in the statistical analysis. We
present and discuss our results in Sect. 3.
We conclude in Sect. 4.
2 Statistical analysis
We performed our statistical analysis by exploring the parameter space
with Monte Carlo Markov chains generated with the CosmoMC code
(Lewis & Bridle 2002) which uses the Boltzmann code CAMB (Lewis et al. 2000) and
R ECFAST to compute the CMB power spectra. We modified them in
order to include the possible variation in
and
at
recombination.
We use data from the WMAP 7-year temperature and
temperature-polarization power spectrum (Larson et al. 2010), and other CMB
experiments such as CBI (Readhead et al. 2004), ACBAR (Kuo et al. 2004),
BOOMERANG (Jones et al. 2006; Piacentini et al. 2006), BICEP (Chiang et al. 2010) and
QUAD (Brown et al. 2009). In order to reduce degeneracies of the
cosmological parameters, we combine the CMB data sets with other
cosmological data: i) the power spectrum of the Sloan Digital Sky
Survey LRG (Reid et al. 2010) and ii) the recent constraint on the Hubble
constant,
km s-1 Mpc-1, presented by
Riess et al. (2009).
We have considered a spatially-flat
cosmological model with adiabatic density fluctuations, and the
following parameters:

where






We have performed statistical analyses using the data mentioned above
and considering variation of only one constant (
or
)
and
variation of both constants. We present our results in the next
section.
3 Results and discussion
Results for the variation of the constants in the case when only one
constant is allowed to vary are shown in Table 1
and for the case when both are allowed to vary, are presented in
Table 2. The obtained values are consistent with
no variation of
or
at recombination. The obtained
errors are at the same percent level than those obtained by
Martins et al. (2010); Menegoni et al. (2009); Scóccola et al. (2009,2008) using WMAP-5 year
release. The parameter space has higher dimension when both constants
are allowed to vary. Therefore, limits on
and
are more
stringent in the case were only one constant is allowed to vary.
Results for the cosmological parameters have similar values for all
of the analyses. Therefore, we only report the values obtained in
the case where both
and
were allowed to vary and the
data from CMB and the power spectrum of the SDSS DR7 were
considered (see Table 3). The mean values and errors for
the cosmological parameters are in agreement within 1-
with
those obtained by the WMAP collaboration (Larson et al. 2010) with no
variation of fundamental constants.
Table 1:
Mean values and 1-
errors for the analysis with
variation of only
,
and only
.
Table 2:
Mean values and 1-
errors for the analysis with
the joint variation of
and
.
Table 3:
Mean values and 1
errors for the cosmological parameters using all CMB data and the SDSS DR7 power spectrum.
In Fig. 1 we show the 68% and 95% c.l. constraints
for
versus H0, for the analysis of the variation
of
alone. The results correspond to different data sets: all
the CMB data alone; all the CMB data plus the H0 prior taken from
Riess et al. (2009); and all the CMB data plus the power spectrum from
Sloan Digital Sky Survery DR7 LRG (Reid et al. 2010). The large degeneracy
between
and H0 from CMB data is reduced when
another data set is added. However, since the value of H0 obtained
from the extra data sets are different, the obtained constraint on
depends strongly on the data chosen for the
analysis. Nevertheless, the results are consistent within
1-
.
![]() |
Figure 1:
68% and 95% c.l. constraints for
|
Open with DEXTER |
In Fig. 2 we present the constraints for
versus
and in Fig. 3 we
present the constraints for
versus
.
There
are degeneracies among these parameters. The contours change because
of the different mean value of
obtained with
different data sets.
![]() |
Figure 2:
68% and 95% c.l. constraints for
|
Open with DEXTER |
![]() |
Figure 3:
68% and 95% c.l. constraints for
|
Open with DEXTER |
In Fig. 4 we present the result for the case where
only
was allowed to vary. The degeneracy between
and H0 is larger than between
and H0, making
impossible to find reliable constraints using CMB data alone. When
another data set is added, the bounds result tighter, but the mean
value for
depends strongly on which data set was
added. Results are marginally consistent at 1-
.
![]() |
Figure 4:
68% and 95% c.l. constraints for
|
Open with DEXTER |
The constraints on
versus
are shown in
Fig. 5, and on
versus
are
shown in Fig. 6. In both cases, the results depend on
the data set added to CMB data in the statistical analysis.
![]() |
Figure 5:
68% and 95% c.l. constraints for
|
Open with DEXTER |
![]() |
Figure 6:
68% and 95% c.l. constraints for
|
Open with DEXTER |
![]() |
Figure 7:
68% and 95% c.l. constraints for the joint variation of |
Open with DEXTER |
In Fig. 7 we show the posterior distribution for
and
,
for the case of joint variation
of these quantities, marginalized over the cosmological
parameters. The results correspond to different data sets. The
difference in the contours is mainly due to the large degeneracy of
and H0, and the different H0 values derived from the Sloan
power spectrum and from the H0 prior. We see that the mean value
of
is more affected than the mean value of
.
These
results can also be seen in Table 2.
A variation of
or
affects the recombination scenario
(see Scóccola et al. 2009, for example). As a consequence, the angular
diameter distance at recombination is modified if any of these
constants varies. This results in a change in the Doppler peak
positions and heights (see Kaplinghat et al. 1999, for example). This explains
the degeneracy between
and
shown in
Fig. 7 and confirmed by the correlation
coefficient. On the other hand, the degeneracy between
or
with the baryon mass density or the Hubble constant can be
explained since these effects are similar to a change in the
cosmological parameters. A variation in
and/or
at recombination, affects mainly the binding energy of
hydrogen. This quantity is proportional to
.
When
only one constant is allowed to vary, its influence on the
parameter estimation is similar, regardless of the constant. However, when a joint variation
analysis is performed, the results are different for
and
,
due to the power with which they enter the hydrogen binding
energy. In particular, in Fig. 7, we note that
the bounds on
are not affected when including additional
data sets to the CMB data. This is due to the fact that
is
no longer correlated with H0, as it was shown previously (see,
for example, Landau et al. 2008).
4 Conclusions
In this paper we have updated the constraints on the time variation of
the fine structure constant
and the electron mass
during recombination epoch, using the latest CMB data, including the
7-yr release of WMAP. We perform several statistical analyses adding
two different data sets; the H0 prior taken from Riess et al. (2009);
and the power spectrum from Sloan Digital Sky Survery DR7 LRG
(Reid et al. 2010). The bounds on the variation of the constants are
tighter than previous results because of the higher precision of the
new data used in this work.
Our results show no variation of the constants at recombination time.
We also emphasize that the constraints depend strongly on which data
set we choose in the analysis, due to the large degeneracy between
or
and H0. Yet, the results are consistent
within 1-
.
The research leading to these results has received funding from the European Community's Seventh Framework Programme ([FP7/2007-2013] under grant agreement No. 237739), and PICT 2007-02184 from Agencia Nacional de Promoción Científica y Tecnológica, Argentina. The authors would like to thank H. C. Chiang for help with compiling the BICEP dataset in COSMOMC.
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Footnotes
- ...
- Member of the Carrera del Investigador Científico y Tecnológico, CONICET.
- ...
- Marie Curie fellow.
All Tables
Table 1:
Mean values and 1-
errors for the analysis with
variation of only
,
and only
.
Table 2:
Mean values and 1-
errors for the analysis with
the joint variation of
and
.
Table 3:
Mean values and 1
errors for the cosmological parameters using all CMB data and the SDSS DR7 power spectrum.
All Figures
![]() |
Figure 1:
68% and 95% c.l. constraints for
|
Open with DEXTER | |
In the text |
![]() |
Figure 2:
68% and 95% c.l. constraints for
|
Open with DEXTER | |
In the text |
![]() |
Figure 3:
68% and 95% c.l. constraints for
|
Open with DEXTER | |
In the text |
![]() |
Figure 4:
68% and 95% c.l. constraints for
|
Open with DEXTER | |
In the text |
![]() |
Figure 5:
68% and 95% c.l. constraints for
|
Open with DEXTER | |
In the text |
![]() |
Figure 6:
68% and 95% c.l. constraints for
|
Open with DEXTER | |
In the text |
![]() |
Figure 7:
68% and 95% c.l. constraints for the joint variation of |
Open with DEXTER | |
In the text |
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