Cosmic Microwave Background Spectrum Research Articles

Optimising Boltzmann codes for the PLANCK era

High precision measurements of the Cosmic Microwave Background (CMB)anisotropies, as can be expected from the PLANCK satellite, willrequire high-accuracy theoretical predictions as well. One possiblesource of theoretical uncertainty is the numerical error in the outputof the Boltzmann codes used to calculate angular power spectra. Inthis work, we carry out an extensive study of the numerical accuracyof the public Boltzmann code CAMB, and identify a set ofparameters which determine the error of its output. We show that atthe current default settings, the cosmological parameters extractedfrom data of future experiments like Planck can be biased by severaltenths of a standard deviation for the six parameters of the standardΛCDM model, and potentially more seriously for extendedmodels. We perform an optimisation procedure that leads the code toachieve sufficient precision while at the same time keeping thecomputation time within reasonable limits. Our conclusion is that thecontribution of numerical errors to the theoretical uncertainty ofmodel predictions is well under control—the main challenges formore accurate calculations of CMB spectra will be of an astrophysicalnature instead.

THE COSMIC MICROWAVE BACKGROUND SPECTRUM AND AN UPPER LIMIT FOR FRACTAL SPACE DIMENSIONALITY

The possibility to constrain fractal space dimensionality from Astrophysics and other areas is briefly reviewed. Assuming such dimensionality to be $3 + \epsilon$, a limit to $\epsilon$ can be inferred from COBE satellite data. The available data for the cosmic microwave background radiation spectrum are fitted by a Planck's radiation distribution generalized to non integer space dimensionality. Our analysis shows that the shape of the CMBR spectrum, which does not depend on the absolute normalization, is correctly described from this distribution provided the absolute temperature is equal to 2.726 $\pm$ $0.003\times 10^{-2}$ K and $\epsilon = - (0.957 \pm 0.006) \times 10^{-5}$. This value for $\epsilon$ is shown to be consistent with what is found on a very different spatial scale based on a quantum field phenomenon. The $|\epsilon|$ is interpreted as an upper limit for how much space dimensionality could have deviated from three. In other words, this is the maximum fluctuation space dimensionality should have experienced in a spatial and temporal scale compared to that of the decoupling era.

Needlet detection of features in the WMAP CMB sky and the impact on anisotropies and hemispherical asymmetries

We apply spherical needlets to the Wilkinson Microwave Anisotropy Probe 5-year cosmic microwave background (CMB) data set, to search for imprints of nonisotropic features in the CMB sky. We use the needlets' localization properties to resolve peculiar features in the CMB sky and to study how these features contribute to the anisotropy power spectrum of the CMB. In addition to the now well-known 'cold spot' of the CMB map in the southern hemisphere, we also find two hot spots at greater than 99% confidence level, again in the southern hemisphere and closer to the Galactic plane. While the cold spot contributes to the anisotropy power spectrum in the multipoles between l=6 to l=33, the hot spots are found to be dominating the anisotropy power in the range between l=6 and l=18. Masking both the cold and the two hot spots results in a reduction by about 15% in the amplitude of the angular power spectrum of CMB around l=10. The resulting changes to the cosmological parameters when the power spectrum is estimated masking these features (in addition to the WMAP team's KQ85 mask) are within the 1{sigma} errors published with the WMAP mask only. We also study the asymmetry betweenmore » the angular power spectra evaluated on the northern and southern hemispheres. When the features detected by needlets are masked, we find that the difference in the power, measured in terms of the anisotropy variance between l=4 and l=18, is reduced by a factor 2. We make available a mask related to needlet features for more detailed studies on asymmetries in the CMB anisotropy sky.« less

Gravitational waves from the big bounce

In this paper we investigate gravitational wave production during the big bounce phase,inspired by loop quantum cosmology. We consider the influence of the holonomy correctionsto the equation for tensor modes. We show that they act like additional effective gravitonmass, suppressing gravitational wave creation. However, such effects can be treatedperturbatively. We investigate a simplified model without holonomy corrections to theequation for modes and find its exact analytical solution. Assuming the form for matter we calculate the full spectrum of the gravitational waves from the big bounce phase. Thespectrum obtained decreases to zero for the low energy modes. On the basis of thisobservation we infer that this effect can lead to low cosmic microwave background (CMB)multipole suppression and gives a potential way for testing loop quantum cosmologymodels. We also consider a scenario with a post-bounce inflationary phase. The powerspectrum obtained gives a qualitative explanation of the CMB spectra, including lowmultipole suppression.

Quantum slow-roll and quantum fast-roll inflationary initial conditions: CMB quadrupole suppression and further effects on the low CMB multipoles

Quantum fast-roll initial conditions for the inflaton which are different from the classical fast-roll conditions and from the quantum slow-roll conditions can lead to inflation that lasts long enough. These quantum fast-roll initial conditions for the inflaton allow for kinetic energies of the same order of the potential energies and nonperturbative inflaton modes with nonzero wave numbers. Their evolution starts with a transitory epoch where the redshift due to the expansion succeeds to assemble the quantum excited modes of the inflaton in a homogeneous (zero mode) condensate, and the large value of the Hubble parameter succeeds to overdamp the fast roll of the redshifted inflaton modes. After this transitory stage the effective classical slow-roll epoch is reached. Most of the e-folds are produced during the slow-roll epoch, and we recover the classical slow-roll results for the scalar and tensor metric perturbations plus corrections. These corrections are important if scales which are horizon size today exited the horizon by the end of the transitory stage and, as a consequence, the lower cosmic microwave background (CMB) multipoles get suppressed or enhanced. Both for scalar and tensor metric perturbations, fast roll leads to a suppression of the amplitude of the perturbations (and of the low CMB multipoles), while the quantum precondensate epoch gives an enhancement of the amplitude of the perturbations (and of the low CMB multipoles). These two types of corrections can compete and combine in a scale dependent manner. They turn out to be smaller in new inflation than in chaotic inflation. These corrections arise as natural consequences of the quantum nonperturbative inflaton dynamics, and can allow a further improvement of the fitting of inflation plus the $\ensuremath{\Lambda}\mathrm{CMB}$ model to the observed CMB spectra. In addition, the corrections to the tensor metric perturbations will provide an independent test of this model. Thus, the effects of quantum inflaton fast-roll initial conditions provide a consistent and contrastable model for the origin of the suppression of the quadrupole and for other departures of the low CMB multipoles from the slow-roll inflation-$\ensuremath{\Lambda}\mathrm{CMB}$ model, which are to be contrasted with the TE and EE multipoles and with the forthcoming and future CMB data.

A Test of the Copernican Principle

The blackbody nature of the cosmic microwave background (CMB) radiation spectrum is used in a modern test of the Copernican principle. The reionized universe serves as a mirror to reflect CMB photons, thereby permitting a view of ourselves and the local gravitational potential. By comparing with measurements of the CMB spectrum, a limit is placed on the possibility that we occupy a privileged location, residing at the center of a large void. The Hubble diagram inferred from lines of sight originating at the center of the void may be misinterpreted to indicate cosmic acceleration. Current limits on spectral distortions are shown to exclude the largest voids which mimic cosmic acceleration. More sensitive measurements of the CMB spectrum could prove the existence of such a void or confirm the validity of the Copernican principle.

Testing cosmology with cosmic sound waves

Wilkinson Microwave Anisotropy Probe (WMAP) observations have accurately determined the position of the first two peaks and dips in the cosmic microwave background (CMB) temperature power spectrum. These encode information on the ratio of the distance to the last scattering surface to the sound horizon at decoupling. However prerecombination processes can contaminate this distance information. In order to assess the amplitude of these effects, we use the WMAP data and evaluate the relative differences of the CMB peak and dip multipoles. We find that the position of the first peak is largely displaced with respect to the expected position of the sound horizon scale at decoupling. In contrast, the relative spacings of the higher extrema are statistically consistent with those expected from perfect harmonic oscillations. This provides evidence for a scale dependent phase shift of the CMB oscillations which is caused by gravitational driving forces affecting the propagation of sound waves before recombination. By accounting for these effects we have performed a Markov Chain Monte Carlo likelihood analysis of the location of WMAP extrema to constrain, in combination with recent BAO data, a constant dark energy equation of state parameter $w$. For a flat universe we find a strong $2\ensuremath{\sigma}$ upper limit $wl\ensuremath{-}1.10$, and including the Hubble Space Telescope prior, we obtain $wl\ensuremath{-}1.14$, which is only marginally consistent with limits derived from the Supernova Legacy Survey sample. On the other hand, we infer larger limits for nonflat cosmologies. From the full CMB likelihood analysis, we also estimate the values of the shift parameter $R$ and the multipole ${l}_{a}$ of the acoustic horizon at decoupling for several cosmologies, to test their dependence on model assumptions. Although the analysis of the full CMB spectra should always be preferred, using the position of the CMB peaks and dips provides a simple and consistent method for combining CMB constraints with other data sets.

Lines in the cosmic microwave background spectrum from the epoch of cosmological helium recombination

The main goal of this work is to calculate the contributions of bound-bound transitions of helium to the cosmological recombination spectrum. We show that helium in the early Universe causes unique features to appear in the total cosmological recombination spectrum. These may provide a unique observational possibility to determine the relative abundance of primordial helium, well before the formation of first stars. We include the effect of the tiny fraction of neutral hydrogen atoms on the dynamics of He II He I recombination at redshifts z ~ 2500. As discussed recently, this process significantly accelerates He II He I recombination, resulting in rather narrow and distinct features in the associated recombination spectrum. In addition this process induces some emission within the hydrogen Lyman-α line, before the actual epoch of hydrogen recombination around z ~ 1100-1500. We also show that some of the fine-structure transitions of neutral helium appear in absorption, again leaving unique traces in the cosmic microwave background blackbody spectrum, which may allow confirmation of our understanding of the early Universe and of detailed atomic physics.

Is there a need and another way to measure the cosmic microwave background temperature more accurately?

The recombination history of the Universe depends exponentially on the temperature, T0, of the cosmic microwave background. Therefore tiny changes of T0 are expected to lead to significant changes in the free electron fraction. Here we show that even the current 1σ-uncertainty in the value of T0 results in more than half a percent ambiguity in the ionization history, and more than 0.1% uncertainty in the TT and EE power spectra at small angular scales. We discuss how the value of T0 affects the highly redshifted cosmological hydrogen recombination spectrum and demonstrate that T0 could, in principle, be measured by looking at the low frequency distortions of the cosmic microwave background spectrum. For this no absolute measurements are necessary, but sensitivities on the level of ∼30 nK are required to extract the quasi-periodic frequency-dependent signal with typical ∆ν/ν ∼ 0.1 coming from cosmological recombination. We also briefly mention the possibility of obtaining additional information on the specific entropy of the Universe, and other cosmological parameters.

Trans‐Planckian signatures in the cosmic microwave background?

AbstractWith the increasingly precise measurement of the cosmic microwave background (CMB), cosmology has entered an era where a model's predictions become testable to percent‐level accuracy. In particular, the CMB spectrum has so far provided impressive support for the scenario of inflation, first invented to solve outstanding problems of standard cosmology. While current data (COBE, WMAP etc.) have already constrained cosmological parameters like Ω0 to high precision, next generation instruments such as the PLANCK satellite should give access to specific characteristics of the inflationary mechanism itself. Another tantalizing idea has been discussed in this context: Given the enormous expansion of the Universe during the phase of inflation, could it be that even Planck scale physics has been stretched to observable distances and is therefore within grasp in the CMB observations? In this contribution, I discuss the possibility of carrying through the calculation of the perturbation spectrum from an ansatz for short distance physics right to its imprint in the CMB. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Dark matter and dark energy from a single scalar field: the cosmic microwave backgroundspectrum and matter transfer function

The dual axion model (DAM), yielding both dark matter and darkenergy forming a Peccei–Quinn-like scalar field solving the strongCP problem, is known to allow a fair fit of cosmic microwave background (CMB) data.Recently, however, it was shown that its transfer function exhibits significant anomalies,causing difficulties for fitting deep galaxy sample data. Here we show how the DAM can bemodified to agree with the latter data set. The modification follows the pattern suggestedfor reconciling any Peccei–Quinn-like approach with gravity. The modified DAM allowsprecise predictions which could be tested against future CMB and/or deep sampledata.

Constraining interacting dark energy models with flux destabilization

A destabilization in the transfer energy flux from the vacuum to radiation, for two vacuum decay laws relevant to the dark energy problem, is analyzed using the Landau–Lifshitz fluctuation hydrodynamic theory. Assuming thermal (or near thermal) equilibrium between the vacuum and radiation, at the earliest epoch of the Universe expansion, we show that the law due to renormalization-group running of the cosmological constant term, with parameters chosen not to spoil the primordial nucleosynthesis scenario, does soon drive the flux to fluctuate beyond its statistical average value thereby distorting the cosmic background radiation spectrum beyond observational limits. While the law coming from the saturated holographic dark energy does not lead the flux to wildly fluctuate, a more realistic non-saturated form shows again such anomalous behavior.

Relativistic modified Newtonian dynamics from string theory?

We argue that TeVeS-like vector fields appear naturally in certain string theory backgrounds involving D0-branes, as a result of the recoil velocity field, expressing the interaction of neutrino string matter with point-like branes. However, the similarity with TeVeS models is restricted only to the bi-metric properties of space–time, namely the difference of the background metric from the one felt by (some) matter fields interacting, in a topologically non-trivial manner, with the D0-brane defects. In our approach, neutrinos appear as dark matter candidates that could be “captured” by the D0-branes, as a result of stringy properties, and thus couple with the recoil-vector fields. Moreover, we argue in support of a possibly preferential rôle of neutrinos in inducing novel non-perturbative contributions to “vacuum” (dark) energy, in addition to their ordinary dark matter contribution. In fact, the rôle of neutrinos as providing substantial contributions to dark matter and dark energy components of the Universe, suggested by our approach, appears also to be necessitated by the need to reproduce the peaks in the Cosmic Microwave Background radiation spectrum, as claimed recently in the literature. Thus, our framework may be viewed as providing a microscopic explanation of such phenomenological conclusions concerning TeVeS-like, Lorentz-violating models.

Rapid He ii→He i recombination and radiation arising from this process

Abstract Recombination of the primordial helium plasma (He ii → He i, z≃ 1500–3000) is considered. This process has an effect on the cosmic microwave background radiation (CMBR) anisotropy and CMBR spectrum distortion. In this work the influence of neutral hydrogen on the kinetics of He ii → He i recombination is investigated in the framework of the standard cosmological model. It is shown that a small amount of neutral hydrogen (a fraction 10−5–10−2 of the total number of hydrogen ions and atoms) leads to the acceleration of He ii → He i recombination at z≲ 2000, and at z≲ 1600 quasi-equilibrium He ii → He i recombination (according to the Saha formula) becomes valid.

Probing inflation with cosmic microwave background polarization: the weak lensing effecton the covariance of cosmic microwave background spectra

Cosmic microwave background (CMB) anisotropies are modified by the weaklensing effect of intervening large scale structures on the photon path from the lastscattering surface to the observer. This has to be accounted for when observationaldata from sensitive experiments are used to constrain cosmological models. Acommon approximation for analysing the CMB angular power spectra is includingonly the Gaussian part of the lensing correction and ignoring the non-Gaussianterms in the error covariance matrix of the spectra. In order to investigate thevalidity of this approximation, we computed these non-Gaussian terms by using aperturbative expansion method. We present a graphical method for writing down anyN point correlation functions at any order in lensing. We use a pedagogical approach to demonstratethat neglecting non-Gaussian terms is an accurate approximation for all polarizations butB, and it will remain so even for the analysis of very sensitive post-Planck experiments. For theB polarization, non-Gaussian contributions up to order 4 must be taken into account.

Ellipticity in cosmic microwave background as a tracer of large-scale universe

Wilkinson Microwave Anisotropy Probe (WMAP) 3-year data confirm the ellipticity of anisotropies of Cosmic Microwave Background (CMB) maps, found previously for Boomerang and WMAP 1-year high sensitivity maps. The low noise level of the WMAP latter data enable also to show that, the ellipticity is a property not described by the conventional cosmological model fitting the power spectrum of CMB. As a large scale anomaly, the ellipticity characteristics are consistent with the effect of geodesics mixing occurring in hyperbolic universe. Its relation to other large scale effects, i.e. to suppressed low multipoles, as well as to dark energy if the latter is due to vacuum fluctuations, is then an arising issue.

CMB and matter power spectra of earlyf(R)cosmology in the Palatini formulation

We calculate in this article the cosmic microwave background (CMB) and matter power spectra of a class of early $f(R)$ cosmologies, which takes the form of $f(R)=R+{\ensuremath{\lambda}}_{1}{H}_{0}^{2}\mathrm{exp}[R/({\ensuremath{\lambda}}_{2}{H}_{0}^{2})]$. Unlike the late-time $f(R)$ cosmologies such as $f(R)=R+\ensuremath{\alpha}(\ensuremath{-}R{)}^{\ensuremath{\beta}}$ ($\ensuremath{\beta}l0$), the deviation from $\ensuremath{\Lambda}\mathrm{CDM}$ of this model occurs at a higher redshift (thus the name ``early $f(R)$ cosmology''), and this important feature leads to rather different integrated Sachs-Wolfe (ISW) effect and CMB spectrum. The matter power spectrum of this model is, however, again very sensitive to the chosen parameters, and large scale structure (LSS) observations such as Sloan digital sky survey (SDSS) should constrain the parameter space stringently. We expect that our results are applicable at least qualitatively to other models that produce $f(R)$ modification to GR at earlier times (e.g., redshifts $\mathcal{O}(10)\ensuremath{\lesssim}z\ensuremath{\lesssim}\mathcal{O}(1)$) than when dark energy begins to dominate---such models are strongly disfavored by data on CMB and matter power spectra.

Structure formation and CMBR anisotropy spectrum in the inflessence model

The inflessence model has recently been proposed in an attempt to explain both early inflation and present day accelerated expansion within a single mechanism. The model has been successfully tested against the Hubble diagram of Type Ιa Supernovae, the shift parameter, and the acoustic peak parameter. As a further mandatory test, we investigate here structure formation in the inflessence model determining the evolution of matter density contrast 6 = δρ M /ρ M in the linear regime. We compare the growth factor D(a) ≡ 6/a and the growth index f(z) ≡ dlnδ/dlnα to these same quantities for the successful concordance ACDM model with a particular emphasis on the role of the inflessence parameters (γ,z Q ). We also evaluate the anisotropy spectrum of the cosmic microwave background radiation (CMBR) to check whether the inflessence model may be in agreement with the observations. We find that, for large values of (γ, z Q ). structure formation proceeds in a similar way to that in the ACDM scenario, and it is also possible to nicely fit the CMBR spectrum.

Constraining isocurvature initial conditions with WMAP 3-year data

We present constraints on the presence of isocurvature modes from the temperature and polarization cosmic microwave background (CMB) spectrum data from the WMAP satellite alone, and in combination with other data sets including SDSS galaxy survey and SNLS supernovae. We find that the inclusion of polarization data allows the WMAP data alone, as well as in combination with complementary observations, to place improved limits on the contribution of CDM and neutrino density isocurvature components individually. With general correlations, the upper limits on these subdominant isocurvature components are reduced to $\ensuremath{\sim}60%$ of the first year WMAP results, with specific limits depending on the type of fluctuations. If multiple isocurvature components are allowed, however, we find that the data still allow a majority of the initial power to come from isocurvature modes. As well as providing general constraints we also consider their interpretation in light of specific theoretical models like the curvaton and double inflation.

Lines in the cosmic microwave background spectrum from the epoch of cosmological hydrogen recombination

We compute the spectral distortions of the cosmic microwave background (CMB) arising during the epoch of cosmological hydrogen recombination within the standard cosmological (concordance) model for frequencies in the range 1–3500 GHz. We follow the evolution of the populations of the hydrogen levels including states up to principle quantum number n= 30 in the redshift range 500 ≤z≤ 3500. All angular momentum substates are treated individually, resulting in a total number of 465 hydrogen levels. The evolution of the matter temperature and the fraction of electrons coming from He ii are also included. We present a detailed discussion of the distortions arising from the main dipolar transitions, for example Lyman and Balmer series, as well as the emission due to the two-photon decay of the hydrogen 2s level. Furthermore, we investigate the robusteness of the results against changes in the number of shells considered. The resulting spectral distortions have a characteristic oscillatory behaviour, which might allow experimentalists to separate them from other backgrounds. The relative distortion of the spectrum exceeds a value of 10−7 at wavelengths longer than 21 cm. Our results also show the importance of detailed follow-up of the angular momentum substates, and their effect on the amplitude of the lines. The effect on the residual electron fraction is only moderate, and mainly occurs at low redshifts. The CMB angular power spectrum is changed by less than 1 per cent. Finally, our computations show that if the primordial radiation field is described by a pure blackbody, then there is no significant emission from any hydrogen transition at redshifts greater than z∼ 2000. This is in contrast to some earlier works, where the existence of a ‘pre-recombination’ peak was claimed.