# The Case for Dark Radiation

###### Abstract

Combined analyses of recent cosmological data are showing interesting hints for the presence of an extra relativistic component, coined Dark Radiation. Here we perform a new search for Dark Radiation, parametrizing it with an effective number of relativistic degrees of freedom parameter, . We show that the cosmological data we considered are clearly suggesting the presence for an extra relativistic component with at c.l.. Performing an analysis on Dark Radiation sound speed and viscosity parameters, we found and at c.l., consistent with the expectations of a relativistic free streaming component (==). Assuming the presence of relativistic neutrinos we constrain the extra relativistic component with and at c.l. while results as unconstrained. Assuming a massive neutrino component we obtain further indications for Dark Radiation with at c.l. .

## I Introduction

Since almost a decade, observations from Cosmic Microwave Background (CMB hereafter) satellite, balloon-borne and ground based experiments (wmap7 , act , acbar , spt ), galaxy redshift surveys red and luminosity distance measurements, are fully confirming the theoretical predictions of the standard CDM cosmological model. This not only permits to place stringent constraints on the parameters of the model but can be fruitfully used to constrain non standard physics at the fundamental level, such as classes of elementary particle models predicting a different radiation content in the Universe.

One of the major theoretical predictions of the standard scenario is the existence of a relativistic energy component ( see e.g. kolb ), beside CMB photons, with a current energy density given by :

(1) |

where is the energy density of the CMB photons background at temperature and is in principle a free parameter, defined as the effective number of relativistic degrees of freedom. Assuming standard electroweak interactions, three active massless neutrinos and including the (small) effect of neutrino flavour oscillations the expected value is with a deviation from that takes into account effects from the non-instantaneous neutrino decoupling from the primordial photon-baryon plasma (see e.g. mangano3046 ).

In recent years, thanks to the continuous experimental advancements, the value of has been increasingly constrained from cosmology (bowen , seljak06 , cirelli , mangano07 , ichikawa07 , wmap7 , hamann10 , giusarma11 , krauss , reid , riess , knox11 ), ruling out at high significance.

However, especially after the new ACT act and SPT spt CMB results, the data seem to suggest values higher than the ”standard” one, with (see e.g. hamann10 , giusarma11 , riess , knox11 , zahn ) in tension with the expected standard value at about two standard deviations.

The number of relativistic degrees of freedom obviously depends on the decoupling process of the neutrino background from the primordial plasma. However, a value of is difficult to explain in the three neutrino framework since non-standard neutrino decoupling is expected to maximally increase this value up to (see e.g. mangano06 ). A possible explanation could be the existence of a fourth (or fifth) sterile neutrino. The hypothesis of extra neutrino flavour is interesting since recent results from short-baseline neutrino oscillation data from LSND lsnd and MiniBooNE minibun experiments are consistent with a possible fourth (or fifth) sterile neutrino specie (see hamann10 ; giusarma11 and references therein). Moreover, a larger value for could arise from a completely different physics, related to axions (see e.g. axions ), gravity waves (gw ), decaying particles (see e.g. decay ), extra dimensions extra ; Hebecker:2001nv and dark energy (see e.g. ede and references therein).

As a matter of fact, any physical mechanism able to produce extra ”dark” radiation produces the same effects on the background expansion of additional neutrinos, yielding a larger value for from observations.

Since there is a large number of models that could enhance it is clearly important to investigate the possible ways to discriminate among them. If Dark Radiation is made of relativistic particles as sterile neutrinos it should behave as neutrinos also from the point of view of perturbation theory, i.e. if we consider the set of equations that describes perturbations in massless neutrino (following the definition presented in gdm ):

(2) | |||

(3) | |||

(4) | |||

(5) |

it should have an effective sound speed and a viscosity speed such that . Free streaming of relativistic neutrino will indeed produce anisotropies in the neutrino background yielding a value of while a smaller value would indicate possible non standard interactions (see e.g. couplings ). A value of different from zero, as expected in the standard scenario, has been detected in trotta and confirmed in subsequent papers dopo . More recently, the analysis of zahn confirmed the presence of anisotropies from current cosmological data but also suggested the presence of a lower value for the effective sound speed with ruled out at more than two standard deviations.

Given the current situation and the experimental hints for is therefore timely to perform a new analysis for (and the perturbation parameters and ) with the most recent cosmological data. This is the kind of analysis we perform in this paper, organizing our work as follows: in Sec. II we describe the data and the data analysis method adopted. We present our results in the first two subsections of Sec. III, depending on two adopted different parametrizations for the Dark Radiation. Moreover a model independent analysis is also discussed in the last subsection of Sec. III. Finally we conclude in Sec. IV.

## Ii Analysis Method

We perform a COSMOMC Lewis:2002ah analysis combining the following CMB datasets: WMAP7 wmap7 , ACBAR acbar , ACT act , and SPT spt , and we analyze datasets using out to . We also include information on dark matter clustering from the galaxy power spectrum extracted from the SDSS-DR7 luminous red galaxy sample red . Finally, we impose a prior on the Hubble parameter based on the last Hubble Space Telescope observations hst .

The analysis method we adopt is based on the publicly available Monte Carlo Markov Chain package cosmomc Lewis:2002ah with a convergence diagnostic done through the Gelman and Rubin statistic. We sample the following six-dimensional standard set of cosmological parameters, adopting flat priors on them: the baryon and cold dark matter densities and , the ratio of the sound horizon to the angular diameter distance at decoupling , the optical depth to reionization , the scalar spectral index , and the overall normalization of the spectrum at . We consider purely adiabatic initial conditions and we impose spatial flatness. We vary the effective number of relativistic degrees of freedom , the effective sound speed , and the viscosity parameter . In some cases, we consider only variations in the extra dark radiation component , varying the perturbation parameters and only for this extra component and assuming for the standard neutrino component.

In our analysis we always fix the primordial Helium abundance to the observed value . This procedure is different from the one adopted, for example, in spt , where the parameter is varied assuming Big Bang Nucleosynthesis for each values of and in the chain. Since the cosmological epoch and the energy scales probed by BBN are dramatically different from the ones probed by CMB and large scale structure we prefer to do not assume standard BBN in our analysis and to leave the primordial Helium abundance as fixed to a value consistent with current observations.

We account for foregrounds contributions including three extra amplitudes: the SZ amplitude , the amplitude of clustered point sources , and the amplitude of Poisson distributed point sources . We marginalize the contribution from point sources only for the ACT and SPT data, based on the templates provided by spt . We quote only one joint amplitude parameter for each component (clustered and Poisson distributed). Instead, the SZ amplitude is obtained fitting the WMAP data with the WMAP own template, while for SPT and ACT it is calculated using the Trac:2010sp SZ template at 148 GHz. Again, this is different from the analysis performed in spt where no SZ contribution was considered for the WMAP data.

## Iii Results

As stated in the previous section, we perform two different analyses. In the first analysis we vary the amplitude of the whole relativistic contribution changing and the corresponding perturbation parameters and . In the second analysis we assume the existence of a standard neutrino background and vary only the extra component considering only in this extra component the variations in and .

### iii.1 Varying the number of relativistic degrees of freedom .

In Table 1 we report the constraints on the cosmological parameters varying with and without variations in perturbation theory. We consider two cases: first we run our analysis fixing the perturbation parameters to the standard values, i.e. , then we let those parameters to vary freely.

As we can see from the results in the left column of Table 1, the WMAP7+ACT+SPT+DR7+H0 analysis is clearly suggesting the presence for Dark Radiation with at c.l.. When considering variations in the perturbation parameters (right column) the constraint is somewhat shifted towards smaller values with . The constraint on the sound speed, is fully consistent with the expectations of a free streaming component. Anisotropies in the neutrino background are detected at high statistical significance with improving previous constraints presented in trotta .

It is interesting to consider the possible degeneracies between and other ”indirect” (i.e. not considered as primary parameters in MCMC runs) model parameters. In Figure 1 we therefore plot the 2D likelihood constraints on versus the Hubble constant , the age of the universe and the amplitude of r.m.s. mass fluctuations on spheres of , .

As we can see from the three panels in the figure, there is a clear degeneracy between and those three parameters. Namely, an extra radiation component will bring the cosmological constraints (respect to the standard neutrino case) to higher values of the Hubble constant and of and to lower values of the age of the universe . These degeneracies have been already discussed in the literature (see e.g. nuage ) and could be useful to estimate the effect of additional datasets on our result. The determination of the Hubble constant from the analysis of riess plays a key role in our analysis in shifting the constraints towards larger values of . If future analyses will point towards lower values of the Hubble constant, this will make the standard neutrino case more consistent with observations. If future observations will point towards values of the age of the universe significantly larger than Gyrs, this will be against an extra dark radiation component, since it prefers . Clearly, adding cluster mass function data as presented in clusters and that points towards lower values of renders the standard case more consistent with observations. A future and precise determination of from clusters or Lyman- surveys could be crucial in ruling out dark radiation.

### iii.2 Varying only the excess in the relativistic component and assuming standard neutrinos.

In Table 2 we report the constraints considering only an excess in the number of relativistic degrees of freedom over a standard neutrinos background.

Model : | varying , | , varying |
---|---|---|

(A) | (B) | |

As we can see for the results in the table, the evidence for an extra background is solid with at c.l. when only variations in the component are considered, while the constraint is when also variations in are considered. Again, the data provide a good determination for with at c.l., in marginal agreement at about with the standard value. This lower value of , also found in zahn , could hint for a dark radiation component with a varying equation of state, ruling out a a massless sterile neutrino. It will be certainly interesting to investigate if this signal remains in future analyses. No significant constraint is obtained on .

In Figure 2 we show the degeneracy between the parameters , , and by plotting the 2D likelihood contours between them. As we can see a degeneracy is present between and : models with lower values of are more compatible with since the effect of on the CMB spectrum is smaller. No apparent degeneracy is present between and the remaining parameters since is weakly constrained by current data.

Since oscillation experiments have clearly established that neutrino are massive, it is interesting to perform a similar analysis but letting the neutrino standard background with to be massive, and varying the parameter that consider the sum of masses of the active neutrinos. The extra dark radiation component is assumed massless and we treat the perturbations in it as in the previous sections. In Table 3 we report the results of this analysis.

As we can see, when masses in the active neutrinos are considered, there is a slightly stronger evidence for the extra background with . This is can be explained by the degeneracy present between and , well known in the literature (see e.g. hamann10 ) and clearly shown in Figure 3 where we report the 2D marginalized contours in the plane .

### iii.3 Profile likelihood analysis

Recently, in verdex , a model-independent analysis for the extra relativistic degrees of freedom in cosmological data has been performed claiming no statistically significant evidence for it. This simple analysis consists in extracting the maximum likelihood value as a function of over the parameter space sampled in the chains, with a bin width of and constructing a profile likelihood ratio by considering as a function of ; where is the maximum likelihood in the entire chains.

Here we perform a similar analysis, using however a smaller bin width of and considering the case where the whole number of relativistic degrees of freedom is varied while . The resulting likelihood ratio , plotted in Figure 4, clearly indicates a preference for a dark radiation component finding that the best fit model has with a respect to the best fit model with .

We should however point out that the ratio presented in Figure 4 is rather noisy. Bayesian methods such as MCMC are indeed known to be inaccurate for this purpose (see for example the discussion in akrami ). Other methods more appropriate for a frequentist analysis have been presented, for example, in others .

## Iv Conclusions

In this paper we performed a new search for Dark Radiation, parametrizing it with an effective number of relativistic degrees of freedom . We have shown that the cosmological data we considered are clearly suggesting the presence for an extra dark radiation component with at c.l. . Performing an analysis on its effective sound speed and viscosity parameters, we found and at c.l., consistent with the expectations of a relativistic free streaming component (==). Assuming the presence of standard relativistic neutrinos we constrain the extra dark radiation component with and at c.l. while is practically unconstrained. Assuming a mass in the neutrino component we obtain further indications for the dark radiation component with at c.l. . From these results we conclude that Dark Radiation currently represents one of the most relevant anomaly for the -CDM scenario.

## V Acknowledgments

We thank Ryan Keisler for providing us with the likelihood code for the SPT data. We thank Luca Pagano for help. This work is supported by PRIN-INAF, ”Astronomy probes fundamental physics”. Support was given by the Italian Space Agency through the ASI contracts Euclid- IC (I/031/10/0).

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