We calculate the effect that a primordial homogeneous magnetic field, $\B_0$, will have on the different CMB power spectra due to Faraday rotation. Concentrating on the $TB$, $EB$ and $BB$ correlations, we forecast the ability for future CMB polarization experiments to constrain $\B_0$. Our results depend on how well the foregrounds can be subtracted from the CMB maps, but we find a predicted error between $σ_{\B_0} = 4 \times 10^{-11}$Gauss (for the QUIET experiment with foregrounds perfectly subtracted) and $3 \times 10^{-10}$Gauss (with the Clover experiment with no foreground subtraction). These constraints are two orders of magnitudes better than the present limits on $\B_0$.
I present here a brief overview of the effects caused by parity violating cosmological sources (such as magnetic or kinetic helicity) on the CMB fluctuations. I discuss also primordial helicity induced relic gravitational waves. All these effects can serve as cosmological tests for primordial helicity detection.
We present a set of formalisms for comparing, evolving and constraining primordial non-Gaussian models through the CMB bispectrum. We describe improved methods for efficient computation of the full CMB bispectrum for any general (non-separable) primordial bispectrum, incorporating a flat sky approximation and a new cubic interpolation. We review all the primordial non-Gaussian models in the present literature and calculate the CMB bispectrum up to l <2000 for each different model. This allows us to determine the observational independence of these models by calculating the cross-correlation of…
A primordial stochastic magnetic field will induce temperature and polarization fluctuations in the cosmic microwave background. We outline a calculation of the resulting fluctuation power spectra and present numerical results.
The details of reheating energy scale $ρ_{reh}$ is largely uncertain today, independent of inflation models. This would induce uncertainty in predicting primordial spectrum. Such uncertainty could be very large, especially for spectra with large running $n_S$. We find that for some inflation models with a large $d\ln n_S(k)/d\ln k$, $ρ_{reh}$ could be highly restricted by current CMB observations.
We have studied ways in which helical primordial magnetic fields could be constrained by measurements of the cosmic microwave background radiation (CMBR). If there were helical flows in the primordial plasma at the time of recombination, they would produce parity violating temperature-polarization correlations ($C_l^{TB}$ and $C_l^{EB}$). However, the magnitude of helical flows induced by helical magnetic fields is unobservably small. We discuss an alternate scheme for extracting the helicity of a stochastically homogeneous and isotropic primordial magnetic field using Faraday rotation measure…
We present preliminary results of an analysis into the effects of primordial voids on the cosmic microwave background (CMB). We show that an inflationary bubble model of void formation predicts excess power in the CMB angular power spectrum that peaks between 2000 < l < 3000. Therefore, voids that exist on or close to the last scattering surface at the epoch of decoupling can contribute significantly to the apparent rise in power on these scales recently detected by the Cosmic Background Imager (CBI).
When constraining the primordial non-Gaussianity parameter f_NL with cosmic microwave background anisotropy maps, the bias resulting from the covariance between primordial non-Gaussianity and secondary non-Gaussianities to the estimator of f_NL is generally assumed to be negligible. We show that this assumption may not hold when attempting to measure the primordial non-Gaussianity out to angular scales below a few tens arcminutes with an experiment like Planck, especially if the primordial non-Gaussianity parameter is around the minimum detectability level with f_NL between 5 and 10. In future…
The equation of state of the hypothetical dark energy component, which constitutes about two thirds of the critical density of the universe, may be very different from that of a cosmological constant. Employing a phenomenological model, we investigate semi-analytically the constraints imposed on the scalar quintessence by supernovae observations, and by the acoustic scale extracted from recent CMB data. We show that a universe with a quintessence-dominated phase in the dark age is consistent with the current observational constraints.
We present a new formalism, together with efficient numerical methods, to directly calculate the CMB bispectrum today from a given primordial bispectrum using the full linear radiation transfer functions. Unlike previous analyses which have assumed simple separable ansatze for the bispectrum, this work applies to a primordial bispectrum of almost arbitrary functional form, for which there may have been both horizon-crossing and superhorizon contributions. We employ adaptive methods on a hierarchical triangular grid and we establish their accuracy by direct comparison with an exact analytic sol…
We study the CMB constraints on two Dark Energy models described by scalar fields with different Lagrangians, namely a Klein-Gordon and a Born-Infeld field. The speed of sound of field fluctuations are different in these two theories, and therefore the predictions for CMB and structure formation are different. Employing the WMAP data on CMB, we make a likelihood analysis on a grid of theoretical models. We constrain the parameters of the models and compute the probability distribution functions for the equation of state. We show that the effect of the different sound speeds affects the low mul…
The role of cosmic microwave background (CMB) polarisation data in constraining the presence of primordial isocurvature modes is examined. While the MAP satellite mission will be unable to simultaneously constrain isocurvature modes and cosmological parameters, the PLANCK mission will be able to set strong limits on the presence of isocurvature modes if it makes a precise measurement of the CMB polarisation sky. We find that if we allow for the possible presence of isocurvature modes, the recently obtained BOOMERANG measurement of the curvature of the universe fails. However, a comparably sens…
After the precise observations of the Cosmic Microwave Background (CMB) anisotropy power spectrum, attention is now being focused on the higher order statistics of the CMB anisotropies. Since linear evolution preserves the statistical properties of the initial conditions, observed non-Gaussianity of the CMB will mirror primordial non-Gaussianity. Single field slow-roll inflation robustly predicts negligible non-Gaussianity so an indication of non-Gaussianity will suggest alternative scenarios need to be considered. In this paper we calculate the information on primordial non-Gaussianity encode…
We develop a new method to reconstruct the power spectrum of primordial curvature perturbations, $P(k)$, by using both the temperature and polarization spectra of the cosmic microwave background (CMB). We test this method using several mock primordial spectra having non-trivial features including the one with an oscillatory component, and find that the spectrum can be reconstructed with a few percent accuracy by an iterative procedure in an ideal situation in which there is no observational error in the CMB data. In particular, although the previous ``cosmic inversion'' method, which used only…
The identification of non-Gaussian signatures in cosmic microwave background (CMB) temperature maps is one of the main cosmological challenges today. We propose and investigate altenative methods to analyse CMB maps. Using the technique of constrained randomisation we construct surrogate maps which mimic both the power spectrum and the amplitude distribution of simulated CMB maps containing non-Gaussian signals. Analysing the maps with weighted scaling indices and Minkowski functionals yield in both cases statistically significant identification of the primordial non-Gaussianities. We demonstr…
Possible signatures of primordial magnetic fields on the Cosmic Microwave Background (CMB) temperature and polarization anisotropies are reviewed. The signals that could be searched for include excess temperature anisotropies particularly at small angular scales below the Silk damping scale, B-mode polarization, and non-Gaussian statistics. A field at a few nG level produces temperature anisotropies at the 5 micro Kelvin level, and B-mode polarization anisotropies 10 times smaller, and is therefore potentially detectable via the CMB anisotropies. An even smaller field, with B_0 < 0.1 nG, could…
We studied a constraint on the primordial helium abundance Y_p from current and future observations of CMB. Using the currently available data from WMAP, ACBAR, CBI and BOOMERANG, we obtained the constraint as Y_p = 0.25^{+0.10}_{-0.07} at 68% C.L. We also provide a forecast for the Planck experiment using the Markov chain Monte Carlo approach. In addition to forecasting the constraint on Y_p, we investigate how assumptions for Y_p affect constraints on the other cosmological parameters.
We consider for the first time the ability of present-day cosmic microwave background (CMB) anisotropies data to determine the primordial helium mass fraction, Y_p. We find that CMB data alone gives the confidence interval 0.160 < Y_p < 0.501 (at 68% c.l.). We analyse the impact on the baryon abundance as measured by CMB and discuss the implications for big bang nucleosynthesis. We identify and discuss correlations between the helium mass fraction and both the redshift of reionization and the spectral index. We forecast the precision of future CMB observations, and find that Planck alone will …
We present estimates of parameters which model the primordial density fluctuations using CMB data from the VSA, 1st year WMAP, CBI and ACBAR along with external priors from 2dF and the HST. Taken at face value there is significant evidence for a running spectral index when only scalar fluctuations are considered. The significance of this result is increased by the inclusion of tensors and, although the result is weakened by the inclusion of `running of the running', the basic trend toward significantly negative running remains. We discuss the implications of this result and how it might be str…
The analysis of the CMB anisotropies is a rich source of cosmological informations. In our study, we simulated the signals produced by the relics of a first order phase transition occured during an inflationary epoch in the early Universe. These relics are bubbles of true vacuum that leave a characteristic non-Gaussian imprint on the CMB. We use different statistical estimators in order to evaluate this non-Gaussianity. We obtain some limits on the allowed values of the bubble parameters comparing our results with the experimental data. We also predict the possibility to detect this signal wit…
We present a novel method for generation of sets of the Cosmic Microwave Background (CMB) anisotropy maps, which reproduces the $Δł=2$ correlations associated with Alfvén turbulence. The method is based on the non-linear transformation of the CMB maps, which is obtained from the Monte Carlo simulation of the statistically isotropic Gaussian signal. Our method is computationally fast and efficient. We have applied two estimators (the cross-correlation estimator in multipole domain for $ł+1,m$ and $ł-1,m$ modes and circular phase moments) to test the statistical properties of derived maps. Both …
The first-year WMAP data release showed that the reionization optical depth to CMB photons is greater than previously thought. This follows from unexpectedly high values of the C^TE_l spectrum, for l up to ~30, presumably allowing a measurement of the E-mode polarization spectrum C^E_l sooner than expected. This note aims to test the capability of large-angle polarization experiments to explore the history of the cosmological reionization, considering also the impact of cosmic variance. In particular, here we discuss how well the ionized fraction x_e and the reionization redshift z_r can be se…
We discuss upcoming opportunities with cosmic microwave background (CMB) observations during the post-WMAP era. The curl-modes of CMB polarization probe inflationary gravitational waves (IGWs). While a significant source of confusion is expected from cosmic shear conversion of polarization related to density perturbations, higher resolution observations of CMB anisotropies can be used for a lensing reconstruction and to separate gravitational-wave polarization signature from that of lensing. Separations based on current lensing reconstruction techniques allow the possibility to probe inflation…
The current enthusiam to measure fluctuations in the CMB power spectrum at angular scales between 0.1 and 1 degree is largely motivated by the expectation that CMB determinations of cosmological parameters will be of unprecedented precision. In such circumstances it is important to estimate what we can already say about the cosmological parameters. In two recent papers (Lineweaver etal 1997a & 1997b) we have compiled the most recent CMB measurements, used a fast Boltzmann code to calculate model power spectra (Seljak & Zaldarriaga 1996) and, with a chi-squared analysis, we have compared the da…
We present a new data analysis method to study rectangular T^3 ``small universes" with one or two of its dimensions significantly smaller than the present horizon (which we refer to as T^1- and T^2-models, respectively). We find that the 4 year COBE/DMR data set a lower limit on the smallest cell size for T^1- and T^2-models of 3000h^{-1} Mpc, at 95% confidence, for a scale invariant power spectrum (n=1).
Multiply connected space sections of the universe on a scale smaller than the horizon size can leave an imprint on cosmic microwave background polarization maps, in such a way that the so-called ``circles-in-the-sky'' method can be used to detect or constrain the topology. We investigate some specific cases, namely toroidal and sixth-turn spaces, in order to show the influence of topology on CMB polarization. The correlation between matched points happens to be always positive and higher than 75% regardless of the angular scale and of the cosmological parameters, except for reionization. This …
We investigate the possibility of reconstructing the initial spectrum of density fluctuations from the cosmic microwave background (CMB) anisotropy. As a first step toward this program, we consider a spatially flat, CDM dominated universe. In this case, it is shown that, with a good accuracy, the initial spectrum satisfies a first order differential equation with the source determined by the CMB angular correlation function. The equation is found to contain singularities arising from zeros of the acoustic oscillations in the transfer functions. Nevertheless, we find these singularities are not…
We discuss the polarization signature of primordial gravitational waves imprinted in cosmic microwave background (CMB) anisotropies. The high-energy physics motivated by superstring theory or M-theory generically yield parity violating terms, which may produce a circularly polarized gravitational wave background (GWB) during inflation. In contrast to the standard prediction of inflation with un-polarized GWB, circularly polarized GWB generates non-vanishing TB and EB-mode power spectra of CMB anisotropies. We evaluate the TB and EB-mode power spectra taking into account the secondary effects a…
Second-order power spectra of Cosmic Microwave Background (CMB) anisotropies due to random primordial perturbations at the matter dominant stage are studied, based on the relativistic second-order theory of perturbations in flat cosmological models and on the second-order formula of CMB anisotropies derived by Mollerach and Matarrese. So far the second-order integrated Sachs-Wolfe effect has been analyzed using the three-point correlation or bispectrum. In this paper we derive the second-order term of power spectra given using the two-point correlation of temperature fluctuations. The second-o…
A precise determination of the primordial spectrum of matter density fluctuations at super-horizon scales is essential in understanding large scale structure in the universe. Attempts to constrain or obtain the primordial spectrum using data on cosmic microwave background (CMB) anisotropies has relied on statistical and correlation analyses that assume a power-law spectrum. We propose a method to derive $P(k)$ directly from the CMB angular power spectrum which does not presuppose the need to know anything about its functional form. The method consists of a direct inversion of the Sachs-Wolfe f…
We calculate the cosmic microwave background (CMB) angular trispectrum, spherical harmonic transform of the four-point correlation function, from primordial non-Gaussianity in primordial curvature perturbations characterized by a constant non-linear coupling parameter, $f_{\rm NL}$. We fully take into account the effect of the radiation transfer function, and thus provide the most accurate estimate of the signal-to-noise ratio of the angular trispectrum of CMB temperature anisotropy. We find that the predicted signal-to-noise ratio of the trispectrum summed up to a given $l$ is approximately a…
Assuming linearity of the perturbations at the time of decoupling, we reconstruct the primordial scalar potential from the temperature and polarization anisotropies in the cosmic microwave background radiation. In doing so we derive an optimal linear filter which, when operated on the spherical harmonic coefficients of the anisotropy maps, returns an estimate of the primordial scalar potential fluctuations in a spherical slice. The reconstruction is best in a thick shell around the decoupling epoch; the quality of the reconstruction depends on the redshift of the slice within this shell. With …
Secondary anisotropies of the cosmic microwave background (CMB) can be detected by using the cross-correlation between the large-scale structure (LSS) and the CMB temperature fluctuations. In such studies, chance correlations of primordial CMB fluctuations with the LSS are the main source of uncertainty. We present a method for reducing this noise by exploiting information contained in the polarisation of CMB photons. The method is described in general terms and then applied to our recently proposed optimal method for measuring the integrated Sachs-Wolfe (ISW) effect. We obtain an expected sig…
We discuss possible distortions of the ionization history of the Universe in the model with small scale baryonic clouds. The corresponding scales of the clouds are much smaller than the typical galactic mass scales. These clouds are considered in a framework of the cosmological model with the isocurvature and adiabatic perturbations. In this model the baryonic clouds do not influence on the cosmic microwave background anisotropy formation directly as an additional sources of perturbations, but due to change of the kinetics of the hydrogen recombination . We also study the corresponding distort…
Big bang nucleosynthesis (BBN) and the cosmic microwave background (CMB) are two major pillars of cosmology. Standard BBN accurately predicts the primordial light element abundances ($^4$He, D, $^3$He and $^7$Li), depending on one parameter, the baryon density. Light element observations are used as a baryometers. The CMB anisotropies also contain information about the content of the universe which allows an important consistency check on the Big Bang model. In addition CMB observations now have sufficient accuracy to not only determine the total baryon density, but also resolve its principal …
Pursuing the original idea proposed in our previous paper (Paper I), we improve the method to determine the shape of the initial curvature perturbation spectrum $P(k)$ from the CMB data. The thickness of the last scattering surface (LSS) and the integrated Sachs-Wolfe (ISW) effect, which we neglect in Paper I, are taken into account and an iterative method is newly developed. The new method can reproduce the primordial power spectra with a high accuracy, given the correct values of the cosmological parameters. Conversely, there appear spurious peaks and dips in the reconstructed power spectrum…
Measuring the primordial matter power spectrum is our primary means of probing unknown physics in the very early universe. We allow the primordial power spectrum to be an arbitrary function, and parametrize it in terms of wavelet band powers. Current cosmological data correspond to 11 such wavelet bands. We derive constraints on these band powers as well as $H_0$, $Ω_b h^2$ and $Ω_m h^2$ from current Cosmic Microwave Background Anisotropy (CMB) data using the Markov Chain Monte Carlo (MCMC) technique. Our results indicate a feature in the primordial power spectrum at $ 0.008 \la k/(h {Mpc}^{-1…
Spatially varying primordial magnetic fields may be efficiently dissipated prior to the epoch of recombination due to the large viscosity of the baryon-photon fluid. We show that this dissipation may result in observable chemical potential mu and Compton y distortions in the cosmic microwave background radiation (CMB) spectrum. Current upper limits on mu and y from FIRAS constrain magnetic fields to have strength B_0 < 3\times 10^{-8}Gauss (scaled to the present) between comoving coherence length \approx 400 pc and \approx 0.6 Mpc. This represents the strongest upper limit on small-scale primo…
Primordial nucleosynthesis calculations are shown to be able to provide constraints on electroweak baryogenesis which produce a highly inhomogeneous distribution of the baryon-to-photon ratio. Such baryogenesis scenarios overproduce 4He and/or 7Li and can be ruled out whenever a fraction f<3*10e-6(100 GeV/T)^3 of nucleated bubbles of broken-symmetry phase contributes > 10% of the baryon number within the horizon volume.
While observations indicate that the predominant source of cosmic inhomogeneities are adiabatic perturbations, there are a variety of candidates to provide auxiliary trace effects, including inflation-generated primordial tensors and cosmic defects which both produce B-mode cosmic microwave background (CMB) polarization. We investigate whether future experiments may suffer confusion as to the true origin of such effects, focusing on the ability of Planck to distinguish tensors from cosmic strings, and show that there is no significant degeneracy.
The CMB data recently released by BOOMERANG and MAXIMA suggest that the anisotropy spectrum has a third peak in the range 800<l_3<900. A combination of this result with constraints from large-scale structure permit us to differentiate between different quintessence models. In particular, we find that inverse power law models with power α>1 are disfavoured. Models with more than 5% quintessence before last scattering require a spectral index greater than 1. These constraints are compared with supernovae observations. We also show that the CMB alone now provides strong evidence for an accelerati…
In this paper we study the effect of a magnetic field on the fluctuation spectrum of the cosmic microwave background. We find that upcoming measurements might give interesting bounds on large scale magnetic fields in the early Universe. If the effects are seen, it might be possible to establish the presence of different fields in different patches of the sky. Absence of any effect, will provide by one order of magnitude a better limit for a primordial field, now given by nucleosynthesis.
Primordial inhomogeneous magnetic fields of the right strength can leave a signature on the CMB temperature anisotropy and polarization. Potentially observable contributions to polarization B-modes are generated by vorticity and gravitational waves sourced by the magnetic anisotropic stress. We compute the corresponding CMB transfer functions in detail including the effect of neutrinos. The shear rapidly causes the neutrino anisotropic stress to cancel the stress from the magnetic field, suppressing the production of gravitational waves and vorticity on super-horizon scales after neutrino deco…
P and CP violation in cosmology can be manifested as large-scale helical velocity flows in the ambient plasma and as primordial helical magnetic fields. We show that kinetic helicity at last scattering leads to temperature-polarization correlations ($C_l^{TB}$ and $C_l^{EB}$) in the cosmic microwave background radiation (CMBR) and calculate the magnitude of the effect. Helical primordial magnetic fields, expected from cosmic events such as electroweak baryogenesis, can lead to helical velocity flows and hence to non-vanishing correlations of the temperature and B-type polarization. However we …
Tangled, primordial cosmic magnetic fields create small rotational velocity perturbations on the last scattering surface (LSS) of the cosmic microwave background radiation (CMBR). Such perturbations can contribute significantly to the CMBR temperature and polarization anisotropies at large l > 1000 or so, like the excess power detected by the CBI experiment. The magnetic contribution can be distinguished from most conventional signals, as they lead to CMBR polarization dominated by the odd parity, B-type signal. Experiments like DASI and WMAP have detected evidence for CMBR polarization at sma…
The primordial magnetic field (PMF) can strongly affect the cosmic microwave background (CMB) power spectrum and the formation of large scale structure. In this presentation, we calculate the CMB temperature anisotropies generated by including a power-law magnetic field at the photon last scattering surface (PLSS). We then deduce an upper limit on the primordial magnetic field based upon our theoretical analysis of the power excess on small angular scales. We have taken into account several important effects such as the modified matter sound speed in the presence of a magnetic field. An upper …
We investigate the possibility of constraining dark energy with the Integrated Sachs Wolfe effect recently detected by cross-correlating the WMAP maps with several Large Scale Structure surveys. In agreement with previous works, we found that, under the assumption of a flat universe, the ISW signal is a promising tool for constraining dark energy. Current available data put weak limits on a constant dark energy equation of state w. We also find no constraints on the dark energy sound speed c_e^2. For quintessence-like dark energy (c_e^2=1) we find w<-0.53, while tighter bounds are possible onl…
We discuss cosmic microwave background anisotropies in models with an unconventional primordial power spectrum. In particular, we consider an initial power spectrum with some ``spiky'' corrections. Interestingly, such a primordial power spectrum generates ``wavy'' structure in the CMB angular power spectrum.
It is shown that a subelectronvolt upper limit can be derived on the neutrino mass from the CMB data alone in the Lambda CDM model with the power-law adiabatic perturbations, without the aid of any other cosmological data. Assuming the flatness of the universe, the constraint we can derive from the current WMAP observations is \sum m_nu < 2.0 eV at the 95% confidence level for the sum over three species of neutrinos (m_nu < 0.66 eV for the degenerate neutrinos). This constraint modifies little even if we abandon the flatness assumption for the spatial curvature. We argue that it would be diffi…
The existence of a primordial magnetic field (PMF) would affect both the temperature and polarization anisotropies of the cosmic microwave background (CMB). It also provides a plausible explanation for the possible disparity between observations and theoretical fits to the CMB power spectrum. Here we report on calculations of not only the numerical CMB power spectrum from the PMF, but also the correlations between the CMB power spectrum from the PMF and the primary curvature perturbations. We then deduce a precise estimate of the PMF effect on all modes of perturbations. We find that the PMF a…
The next generation of CMB experiments should get a better handle on cosmological parameters by mapping the weak lensing deflection field, which is separable from primary anisotropies thanks to the non-Gaussianity induced by lensing. However, the generation of perturbations in the Early Universe also produces a level of non-Gaussianity which is known to be small, but can contribute to the anisotropy trispectrum at the same level as lensing. In this work, we study whether the primordial non-Gaussianity can mask the lensing statistics. We concentrate only on the ``temperature quadratic estimator…
We consider the production of gravitinos and moduli fields from quantum vacuum fluctuations induced by the presence of scalar metric perturbations at the end of inflation. We obtain the corresponding occupation numbers, up to first order in perturbation theory, in terms of the power spectrum of the metric perturbations. We compute the limits imposed by nucleosynthesis on the spectral index $n_s$ for different models with constant $n_s$. The results show that, in certain cases, such limits can be as strong as $n_s<1.12$, which is more stringent than those coming from primordial black hole produ…
Cosmic microwave background (CMB) determinations of the baryon-to-photon ratio $η\propto Ω_{\rm baryon} h^2$ will remove the last free parameter from (standard) big bang nucleosynthesis (BBN) calculations. This will make BBN a much sharper probe of early universe physics, for example, greatly refining the BBN measurement of the effective number of light neutrino species, $N_{ν,eff}$. We show how the CMB can improve this limit, given current light element data. Moreover, it will become possible to constrain $N_{ν,eff}$ independent of \he4, by using other elements, notably deuterium; this will a…
