Cosmic Microwave Background Spectrum Research Articles

A joint study of early and late spectral distortions of the cosmic microwave background and of the millimetric foreground

In this work we have compared the absolute temperature data of the cosmic microwave background (CMB) spectrum with models of CMB spectra distorted by a single or two heating processes at different cosmic times. The constraints on the fractional energy injected in the radiation field, Δe/ei, are mainly provided by the precise measures of the FIRAS instrument on board the COBE satellite, while long-wavelength measures are crucial to set constraints on free–free distortions. We find that the baryon density does not influence the limits on Δe/ei derived from current data for cosmic epochs corresponding to the same dimensionless time yh of dissipation epoch, although the redshift corresponding to the same yh decreases with the baryon density. Under the hypothesis that two heating processes have occurred at different epochs, the former at any yh in the range 5 ≥yh≥ 0.01 (this joint analysis is meaningful for yh≳ 0.1) and the latter at yh≪ 1, the limits on Δe/ei are relaxed by a factor ∼2 for both the earlier and the later process with respect to the case in which a single energy injection in the thermal history of the Universe is considered. In general, the constraints on Δe/ei are weaker for early processes (5 ≳yh≳ 1) than for relatively late processes (yh≲ 0.1), because of the subcentimetric wavelength coverage of FIRAS data, relatively more sensitive to Comptonization than to Bose–Einstein like distortions. While from a widely conservative point of view the FIRAS calibration as revised recently by Battistelli et al. only implies a significant relaxation of the constraints on the Planckian shape of the CMB spectrum, the favoured calibrator emissivity law proposed by the authors, quite different from a constant emissivity, implies significant deviations from a Planckian spectrum. An astrophysical explanation of this, although intriguing, seems difficult. We find that an interpretation in terms of CMB spectral distortions should require a proper balance between the energy exchanges at two very different cosmic times or a delicate fine tuning of the parameters characterizing a dissipation process at intermediate epochs, while an interpretation in terms of a relevant millimetric foreground, produced by cold dust, should imply a too large involved mass and/or an increase of the fluctuations at subdegree angular scales. Future precise measurements at longer wavelengths as well as current and future CMB anisotropy space missions will provide independent, direct or indirect, cross-checks. This work is related to Planck-LFI activities.

Cosmological Nucleosynthesis in the Big-Bang and Supernovae

Recent observation of the power spectrum of Cosmic Microwave Background (CMB) Radiation has exhibited that the flat cosmology is most likely. This suggests too large universal baryon-density parameter Ωbh2 ≈ 0.022 ~ 0.030 to accept a theoretical prediction, Ωbh2 ≤ 0.017, in the homogeneous Big-Bang model for primordial nucleosynthesis. Theoretical upper limit arises from the sever constraints on the primordial 7Li abundance. We propose two cosmological models in order to resolve the descrepancy; lepton asymmetric Big-Bang nucleosynthesis model, and baryon inhomogeneous Big-Bang nucleosynthesis model. In these cosmological models the nuclear processes are similar to those of the r-process nucleosynthesis in gravitational collapse supernova explosions.Massive stars ≥ 10M⊙ culminate their evolution by supernova explosions which are presumed to be the most viable candidate site for the r-process nucleosynthesis. Even in the nucleosynthesis of heavy elements, initial entropy and density at the surface of proto-neutron stars are so high that nuclear statistical equilibrium favors production of abundant light nuclei. In such explosive circumstances many neutron-rich radioactive nuclei of light-to-intermediate mass as well as heavy mass nuclei play the significant roles.

Cosmological perturbations and short distance physics from Noncommutative Geometry

We investigate the possible effects on the evolution of perturbations in the inflationary epoch due to short distance physics. We introduce a suitable non local action for the inflaton field, suggested by Noncommutative Geometry, and obtained by adopting a generalized star product on a Friedmann-Robertson-Walker background. In particular, we study how the presence of a length scale where spacetime becomes noncommutative affects the gaussianity and isotropy properties of fluctuations, and the corresponding effects on the Cosmic Microwave Background spectrum.

Effect of the minimal length uncertainty relation on the density of states and the cosmological constant problem

We investigate the effect of the minimal length uncertainty relation, motivated by perturbative string theory, on the density of states in momentum space. The relation is implemented through the modified commutation relation [x_i,p_j]=i hbar[(1 + beta p^2) delta_{ij} + beta' p_i p_j]. We point out that this relation, which is an example of an UV/IR relation, implies the finiteness of the cosmological constant. While our result does not solve the cosmological constant problem, it does shed new light on the relation between this outstanding problem and UV/IR correspondence. We also point out that the blackbody radiation spectrum will be modified at higher frequencies, but the effect is too small to be observed in the cosmic microwave background spectrum.

The location of cosmic microwave background peaks in a universe with dark energy

The locations of the peaks of the cosmic microwave background (CMB) spectrum are sensitive indicators of cosmological parameters, yet there is no known analytic formula which accurately describes their dependence on them. We parametrize the location of the peaks as l m = l A (m - φ m ), where l A is the analytically calculable acoustic scale and m labels the peak number. Fitting formulae for the phase shifts φ m for the first three peaks and the first trough are given. It is shown that in a wide range of parameter space, the acoustic scale l A can be retrieved from actual CMB measurements of the first three peaks within 1 per cent accuracy. This can be used to speed up likelihood analysis. We describe how the peak shifts can be used to distinguish between different models of dark energy.

Constraining the quintessence equation of state with SnIa data and CMB peaks

Quintessence has been introduced as an alternative to the cosmological constant scenario to account for the current acceleration of the universe. This new dark energy component allows values of the equation of state parameter ${w}_{Q}^{0}>~\ensuremath{-}1$ and in principle measurements of cosmological distances to type Ia supernovae can be used to distinguish between these two types of models. Assuming a flat universe, we use the supernovae data and measurements of the position of the acoustic peaks in the cosmic microwave background spectra to constrain a rather general class of quintessence potentials, including inverse power law models and recently proposed supergravity inspired potentials. In particular we use a likelihood analysis, marginalizing over the dark energy density ${\ensuremath{\Omega}}_{Q},$ the physical baryon density ${\ensuremath{\Omega}}_{b}{h}^{2}$ and the scalar spectral index n, to constrain the slopes of our quintessence potential. Considering only the first Doppler peak the best fit in our range of models gives ${w}_{Q}^{0}\ensuremath{\sim}\ensuremath{-}0.8.$ However, including the SnIa data and the three peaks, we find an upper limit on the present value of the equation of state parameter, $\ensuremath{-}1<~{w}_{Q}^{0}<~\ensuremath{-}0.93$ at $2\ensuremath{\sigma},$ a result that appears to rule out a class of recently proposed potentials.

Relic dark energy from the trans-Planckian regime

As yet, there is no underlying fundamental theory for the trans-Planckian regime. There is a need to address the issue of how the observables in our present Universe are affected by processes that may have occurred at super-Planckian energies (referred to as the trans-Planckian regime). Specifically, we focus on the impact the trans-Planckian regime has on two observables: namely, dark energy and the cosmic microwave background radiation (CMBR) spectrum. We model the trans-Planckian regime by introducing a 1-parameter family of smooth non-linear dispersion relations which modify the frequencies at very short distances. A particular feature of the family of dispersion functions chosen is the production of ultralow frequencies at very high momenta k (for $k>{M}_{P}).$ We name the range of the ultralow energy modes (of very short distances) that have frequencies equal to or less than the current Hubble rate ${H}_{0}$ as the tail modes. These modes are still frozen today due to the expansion of the Universe. We calculate their energy today and show that the tail provides a strong candidate for the dark energy of the Universe. During inflation, their energy is about 122 to 123 orders of magnitude smaller than the total energy, for any random value of the free parameter in the family of dispersion relations. For this family of dispersions, we present the exact solutions and show that the CMBR spectrum is that of a (nearly) blackbody, and that the adiabatic vacuum is the only choice for the initial conditions.

ChandraObservations of Two High‐Redshift Quasars

We report the first high-resolution X-ray spectra of two high-redshift quasars, S5 0836+710 and PKS 2149-306, obtained with the Chandra High-Energy Transmission Grating Spectrometer (HETGS). The primary goal of this observation is to use the high spectral resolving power of the HETGS to detect X-ray absorption produced by a hot intergalactic medium (IGM). The continuum of both quasars can be fitted by absorbed power laws. The power-law photon index (Γ) of S5 0836+710 is consistent with that found in previous observations with ROSAT and ASCA, while the power law of PKS 2149-306 is harder than found in a previous observation by ASCA. Excess continuum absorption above the Galactic value is found in S5 0836+710, as evidenced in ASCA and ROSAT observations. No significant emission or absorption feature is detected in either source at the ±3 σ level. Based on the detection limits we constrain the properties of possible emitters and absorbers. The upper limit of the equivalent width of Fe-K emission lines could be as low as ~10 eV. Absorbers with a column density higher than 8 × 1016 cm-2 for O VIII or 5 × 1016 cm-2 for Si XIV would have been detected. We propose a method to constrain the cosmological parameters (namely, Ω0 and Ωb) via the X-ray forest theory, but current data do not give significant constraints. However, we estimate that observing about seven bright quasars should give at least one O VIII and more O VII absorption lines at 95% possibility. We also find that combined with the constraints from the distortion of the cosmic microwave background spectrum, the X-ray Gunn-Peterson test can marginally constrain a uniform, enriched IGM.

Hydrodynamic Simulations of the Sunyaev‐Zeldovich Effect(s)

We have performed a sequence of high-resolution hydrodynamic simulations of structure formation in a ΛCDM model to study the thermal and kinetic Sunyaev-Zeldovich (SZ) effects. Including only adiabatic gas physics, we demonstrate that our simulations for the thermal effect are converged down to subarcminute scales. In this model, the angular power spectrum of cosmic microwave background (CMB) anisotropies induced by the thermal effect peaks at l ≃ 104, and reaches an amplitude just below current observational upper limits. Fluctuations due to the kinetic effect are a factor of ≃30 lower in power and peak at slightly smaller angular scales. We identify individual SZ sources and compute their counts as a function of source strength and angular size. We present a preliminary investigation of the consequences of an early epoch of energy injection, which tends to suppress power on small angular scales, while giving rise to additional power on large scales from the reheated intergalactic matter (IGM) at high redshift.

Fitting BOOMERANG and MAXIMA-1 data with a Einstein–Yang–Mills cosmological model

We analyse the implications of recent Cosmic Microwave Background (CMB) data for a specific cosmological model, based on the higher-dimensional Einstein–Yang–Mills system compactified on a R× S 3× S d topology and conclude that the model parameters are tightly constrained by CMB spectra. Moreover, the model predicts a relationship between the deceleration parameter at present, q 0, and some characteristic features of CMB spectra, namely, the height of the first peak and the the location of the second peak, that is consistent with the observations and which can be further tested by future CMB and other experiments.

The standard and degenerate primordial nucleosynthesis versus recent experimental data

We report the results on Big Bang Nucleosynthesis (BBN) based on an updated code, with accuracy of the order of 0.1 % on 4He abundance, compared with the predictions of other recent similar analysis. We discuss the compatibility of the theoretical results, for vanishing neutrino chemical potentials, with the observational data. Bounds on the number of relativistic neutrinos and baryon abundance are obtained by a likelihood analysis. We also analyze the effect of large neutrino chemical potentials on primordial nucleosynthesis, motivated by the recent results on the Cosmic Microwave Background Radiation spectrum. The BBN exclusion plots for electron neutrino chemical potential and the effective number of relativistic neutrinos are reported. We find that the standard BBN seems to be only marginally in agreement with the recent BOOMERANG and MAXIMA-1 results, while the agreement is much better for degenerate BBN scenarios for large effective number of neutrinos, Nν ~ 10. For the low D data, standard BBN is still viable for η ~ (5÷6) 10−10.

Self-interacting warm dark matter

It has been shown by many independent studies that the cold dark matter scenario produces singular galactic dark halos, in strong contrast with observations. Possible remedies are that either the dark matter is warm so that it has significant thermal motion or that the dark matter has strong self-interactions. We combine these ideas to calculate the linear mass power spectrum and the spectrum of cosmic microwave background (CMB) fluctuations for self-interacting warm dark matter. Our results indicate that such models have more power on small scales than is the case for the standard warm dark matter model, with a CMB fluctuation spectrum which is nearly indistinguishable from standard cold dark matter. This enhanced small-scale power may provide better agreement with the observations than does standard warm dark matter. (c) 2000 The American Physical Society.

Limit on primordial small-scale magnetic fields from cosmic microwave background distortions

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 &mgr; and Compton y distortions in the cosmic microwave background spectrum. Current upper limits on &mgr; and y from FIRAS constrain magnetic fields to have strength B0<3x10(-8) G (scaled to the present) between comoving coherence length approximately 400 pc and approximately 0.6 Mpc. These represent the strongest upper limits on small-scale primordial magnetic fields to date.

Contributions to the Power Spectrum of Cosmic Microwave Background from Fluctuations Caused by Clusters of Galaxies

We estimate the contributions to the cosmic microwave background radiation (CMBR) power spectrum from the static and kinematic Sunyaev-Zeldovich (SZ) effects, and from the moving cluster of galaxies (MCG) effect. We conclude, in agreement with other studies, that at sufficiently small scales secondary fluctuations caused by clusters provide important contributions to the CMBR. At l 3000, these secondary fluctuations become important relative to lensed primordial fluctuations. Gravitational lensing at small angular scales has been proposed as a way to break the geometric degeneracy in determining fundamental cosmological parameters. We show that this method requires the separation of the static SZ effect, but the kinematic SZ effect and the MCG effect are less important. The power spectrum of secondary fluctuations caused by clusters of galaxies, if separated from the spectrum of lensed primordial fluctuations, might provide an independent constraint on several important cosmological parameters.

Microwave polarization in the direction of galaxy clusters induced by the CMB quadrupole anisotropy

Electron scattering induces a polarization in the cosmic microwave background (CMB) signal measured in the direction of a galaxy cluster due to the presence of a quadrupole component in the CMB temperature distribution. Measuring the polarization towards distant clusters provides the unique opportunity to observe the evolution of the CMB quadrupole at moderate redshifts, z~0.5-3. We demonstrate that for the local cluster population the polarization degree will depend on the cluster celestial position. There are two extended regions in the sky, which are opposite to each other, where the polarization is maximal, 0.1(tau/0.02) microK in the Rayleigh-Jeans part of the CMB spectrum (tau being the Thomson optical depth across the cluster) exceeding the contribution from the cluster transverse peculiar motion if v_t<1300 km/s. One can hope to detect this small signal by measuring a large number of clusters, thereby effectively removing the systematic contribution from other polarization components produced in clusters. These polarization effects, which are of the order of (v_t/c)^2 tau, (v_t/c) tau^2 and (kT_e/m_ec^2) tau^2, as well as the polarization due to the CMB quadrupole, were previously calculated by Sunyaev and Zel'dovich for the Rayleigh-Jeans region. We fully confirm their earlier results and present exact frequency dependencies for all these effects. The polarization is considerably higher in the Wien region of the CMB spectrum.

Cosmic Microwave Background and Density Fluctuations from Strings plus Inflation

In cosmological models where local cosmic strings are formed at the end of a period of inflation, the perturbations are seeded both by the defects and by the quantum fluctuations, with similar amplitudes. In a flat cosmology with zero cosmological constant and 5% baryonic component, strings plus inflation fit the observational data much better than each component individually. The large-angle cosmic microwave background spectrum is mildly tilted, for Harrison-Zeldovich inflationary fluctuations. It then rises to a thick Doppler bump, covering $\ensuremath{\ell}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}200--600$, modulated by soft secondary undulations. The standard cold dark matter antibiasing problem is cured.

Observational tests of x-matter models

We study gravitational lensing statistics, matter power spectra and the angular power spectra of the cosmic microwave background (CMB) radiation in x-matter models. We adopt an equation of state of x-matter which can express a wide range of matter from pressureless dust to the cosmological constant. A new ingredient in this model is the sound speed of the x-component, in addition to the equation of state w0 = px0/ρx0. Except for the cosmological constant case, the perturbations of x-matter itself are considered. Our primary interest is in the effect of non-zero sound speed on the structure formation and the CMB spectra. It is found that there exist parameter ranges where x-matter models are consistent with all current observations. The x-matter generally leaves imprints in the CMB anisotropy and the matter power spectrum, which should be detectable in future observations.

Excitation of the 3.071 mm Hyperfine Line in Li‐like57Fe in Astrophysical Plasmas

As noted first by Sunyaev & Churazov, the 3.071 mm hyperfine line from 57Fe+23 might be observable in astrophysical plasmas. We assess the atomic processes that might contribute to the excitation of this line. The distorted wave approximation was used to compute the direct electron collision strength between the two hyperfine sublevels of the ground configuration; it was found to be small. Proton collisional excitation was calculated and found to be negligible. We determine the rate of line excitation by electron collisional excitation of more highly excited levels, followed by radiative cascades. The branching ratios for hyperfine sublevels for allowed radiative decays and electron collisional excitation or deexcitation are derived. We show that the dominant line excitation process is electron collisional excitation of the 2p levels followed by radiative decay, as first suggested by Sunyaev & Churazov. We calculate an effective collision strength for excitation of the hyperfine line, including all of these effects and correcting for resonances. Because the hyperfine line is near the peak in the cosmic microwave background radiation spectrum, induced radiative processes are also very important. The effect of background radiation on the level populations and line excitation is determined. We determine the intensity of the hyperfine line from an isothermal, coronal plasma in collisional ionization equilibrium. Because of the variation in the ionization fraction of Fe+23, the emissivity peaks at a temperature of about 1.8 × 107 K. We have also derived the hyperfine line luminosity emitted by a coronal plasma cooling isobarically by its own radiation. Comparisons of the hyperfine line to other lines emitted by the same ion, Fe+23, are shown to be useful for deriving the isotopic fraction of 57Fe. We calculate the ratios of the hyperfine line to the 2s-2p EUV lines at 192 A and 255 A and the 2s-3p X-ray doublet at 10.6 A.

The microwave background anisotropies: observations.

Most cosmologists now believe that we live in an evolving universe that has been expanding and cooling since its origin about 15 billion years ago. Strong evidence for this standard cosmological model comes from studies of the cosmic microwave background radiation (CMBR), the remnant heat from the initial fireball. The CMBR spectrum is blackbody, as predicted from the hot Big Bang model before the discovery of the remnant radiation in 1964. In 1992 the cosmic background explorer (COBE) satellite finally detected the anisotropy of the radiation-fingerprints left by tiny temperature fluctuations in the initial bang. Careful design of the COBE satellite, and a bit of luck, allowed the 30 microK fluctuations in the CMBR temperature (2.73 K) to be pulled out of instrument noise and spurious foreground emissions. Further advances in detector technology and experiment design are allowing current CMBR experiments to search for predicted features in the anisotropy power spectrum at angular scales of 1 degrees and smaller. If they exist, these features were formed at an important epoch in the evolution of the universe--the decoupling of matter and radiation at a temperature of about 4,000 K and a time about 300,000 years after the bang. CMBR anisotropy measurements probe directly some detailed physics of the early universe. Also, parameters of the cosmological model can be measured because the anisotropy power spectrum depends on constituent densities and the horizon scale at a known cosmological epoch. As sophisticated experiments on the ground and on balloons pursue these measurements, two CMBR anisotropy satellite missions are being prepared for launch early in the next century.

Anisotropies in the cosmic microwave background: Theoretical foundations

The analysis of anisotropies in the cosmic microwave background (CMB) has become an extremely valuable tool for cosmology. There is even hope that planned CMB anisotropy experiments may revolutionize cosmology. Together with determinations of the CMB spectrum, they represent the first precise cosmological measurements. The value of CMB anisotropies lies in large part in the simplicity of the theoretical analysis. Fluctuations in the CMB can be determined almost fully within linear cosmological perturbation theory and are not severely influenced by complicated nonlinear physics. In this contribution the different physical processes causing or influencing anisotropies in the CMB are discussed: the geometry perturbations at and after last scattering, the acoustic oscillations in the baryon-photon plasma prior to recombination, and the diffusion damping during the process of recombination. The perturbations due to the fluctuating gravitational field, the so-called Sachs-Wolfe contribution, is described in a very general form using the Weyl tensor of the perturbed geometry.