Fractional calculus analysis of the cosmic microwave background

Cosmic microwave background (CMB) radiation is the imprint from an early stage of the Universe and investigation of its properties is crucial for understanding the fundamental laws governing the structure and evolution of the Universe. Measurements of the CMB anisotropies are decisive to cosmology, since any cosmological model must explain it. The brightness, strongest at the microwave frequencies, is almost uniform in all directions, but tiny variations reveal a spatial pattern of small anisotropies. Active research is being developed seeking better interpretations of the phenomenon. This paper analyses the recent data in the perspective of fractional calculus. By taking advantage of the inherent memory of fractional operators some hidden properties are captured and described.

Cosmic microwave background and large-scale structure constraints on a simple quintessential inflation model

We derive constraints on a simple quintessential inflation model, based on a spontaneously broken Phi(4) theory, imposed by the Wilkinson Microwave Anisotropy Probe three-year data (WMAP3) and by galaxy clustering results from the Sloan Digital Sky Survey (SDSS). We find that the scale of symmetry breaking must be larger than about 3 Planck masses in order for inflation to generate acceptable values of the scalar spectral index and of the tensor-to-scalar ratio. We also show that the resulting quintessence equation of state can evolve rapidly at recent times and hence can potentially be distinguished from a simple cosmological constant in this parameter regime.

Testing gaussianity, homogeneity, and isotropy with the cosmic microwave background

We review the basic hypotheses which motivate the statistical framework used to analyze the cosmic microwave background, and how that framework can be enlarged as we relax those hypotheses. In particular, we try to separate as much as possible the questions of gaussianity, homogeneity, and isotropy from each other. We focus both on isotropic estimators of nongaussianity as well as statistically anisotropic estimators of gaussianity, giving particular emphasis on their signatures and the enhanced cosmic variances that become increasingly important as our putative Universe becomes less symmetric. After reviewing the formalism behind some simple model-independent tests, we discuss how these tests can be applied to CMBdata when searching for large-scale anomalies. Copyright © 2010 L. Raul Abramo and Thiago S. Pereira.

Signature of the scattering between dark sectors in large scale cosmic microwave background anisotropies

We study the interaction between dark sectors by considering the momentum transfer caused by the dark matter scattering elastically within the dark energy fluid. Describing the dark scattering analogy to the Thomson scattering which couples baryons and photons, we examine the impact of the dark scattering in CMB observations. Performing global fitting with the latest observational data, we find that for a dark energy equation of state w < -1, the CMB gives tight constraints on dark matter-dark energy elastic scattering. Assuming a dark matter particle of proton mass, we derive an elastic scattering cross section of sigma(D) < 3.295 x 10(-10)sigma(T) where sigma(T) is the cross section of Thomson scattering. For w > -1, however, the constraints are poor. For w = -1, sigma(D) can formally take any value.

Cosmic microwave background theory

A long-standing goal of theorists has been to constrain cosmological parameters that define the structure formation theory from cosmic microwave background (CMB) anisotropy experiments and large-scale structure (LSS) observations. The status and future promise of this enterprise is described. Current band-powers in ℓ-space are consistent with a ΔT flat in frequency and broadly follow inflation-based expectations. That the levels are ∼(10−5)2 provides strong support for the gravitational instability theory, while the Far Infrared Absolute Spectrophotometer (FIRAS) constraints on energy injection rule out cosmic explosions as a dominant source of LSS. Band-powers at ℓ ≳ 100 suggest that the universe could not have re-ionized too early. To get the LSS of Cosmic Background Explorer (COBE)-normalized fluctuations right provides encouraging support that the initial fluctuation spectrum was not far off the scale invariant form that inflation models prefer: e.g., for tilted Λ cold dark matter sequences of fixed 13-Gyr age (with the Hubble constant H0 marginalized), ns = 1.17 ± 0.3 for Differential Microwave Radiometer (DMR) only; 1.15 ± 0.08 for DMR plus the SK95 experiment; 1.00 ± 0.04 for DMR plus all smaller angle experiments; 1.00 ± 0.05 when LSS constraints are included as well. The CMB alone currently gives weak constraints on Λ and moderate constraints on Ωtot, but theoretical forecasts of future long duration balloon and satellite experiments are shown which predict percent-level accuracy among a large fraction of the 10+ parameters characterizing the cosmic structure formation theory, at least if it is an inflation variant.

Non-standard signatures from Cosmic Microwave Background polarisation

In this Thesis we focus on non-standard signatures from CMB polarisation, which might hint at the existence of new phenomena beyond the standard models for Cosmology and Particle physics. With the Planck ESA mission, CMB temperature anisotropies have been observed at the cosmic variance limit, but polarisation remains to be further investigated. CMB polarisation data are important not only because they contribute to provide tighter constraints of cosmological parameters but also because they allow the investigation of physical processes that would be precluded if just the CMB temperature maps were considered. We take polarisation data into account to assess the statistical significance of the anomalies currently observed only in the CMB temperature map and to constrain the Cosmic Birefringence (CB) effect, which is expected in parity-violating extensions of the standard electromagnetism. In particular, we propose a new one-dimensional estimator for the lack of power anomaly capable of taking both temperature and polarisation into account jointly. With the aim of studying the anisotropic CB we develop and perform two different and complementary methods able to evaluate the power spectrum of the CB. Finally, by employing these estimators and methodologies on Planck data we provide new constraints beyond what already known in literature. The measure of CMB polarisation represents a technological challenge and to make accurate estimates, one has to keep an exquisite control of the systematic effects. In order to investigate the impact of spurious signal in forthcoming CMB polarisation experiments, we study the interplay between half-wave plates (HWP) non-idealities and the beams. Our analysis suggests that certain HWP configurations, depending on the complexity of Galactic foregrounds and the beam models, significantly impacts the B-mode reconstruction fidelity and could limit the capabilities of next-generation CMB experiments. We provide also a first study of the impact of non-ideal HWPs on CB.

Spectral distortions of the cosmic microwave background and small-scale gravitational waves as new windows on the Early Universe

In this thesis, we explore constraints which can be put on the primordial power spectrum of curvature perturbations beyond the scales probed by anisotropies of the cosmic microwave background and galaxy surveys. We exploit present and future measurements of CMB spectral distortions, and their synergy with CMB anisotropies, as well existing and future upper limits on the stochastic background of gravitational waves. We derive for the first time phenomenological templates that fit small-scale bumps in the primordial power spectrum generated in multi-field models of inflation. By using such templates, we study for the first time imprints of primordial peaks on anisotropies and spectral distortions of the cosmic microwave background and we investigate their contribution to the stochastic background of gravitational waves. Through a Monte Carlo Markov Chain analysis we infer for the first time the constraints on the amplitude, the width and the location of such bumps using Planck and FIRAS data. We also forecast how a future spectrometer like PIXIE could improve FIRAS boundaries. The results derived in this thesis have implications for the possibility of primordial black holes from inflation.

Forecasting cosmic doomsday from CMB-LSS cross-correlations.

A broad class of dark energy models, which have been proposed in attempts at solving the cosmological constant problems, predict a late time variation of the equation of state with redshift. The variation occurs as a scalar field picks up speed on its way to negative values of the potential. The negative potential energy eventually turns the expansion into contraction and the local universe undergoes a big crunch. In this paper we show that cross-correlations of the cosmic microwave background anisotropy and matter distribution, in combination with other cosmological data, can be used to forecast the imminence of such cosmic doomsday.

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 μK 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° 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.

New coupled quintessence cosmology

A component of dark energy has been recently proposed to explain the current acceleration of the Universe. Unless some unknown symmetry in Nature prevents or suppresses it, such a field may interact with the pressureless component of dark matter, giving rise to the so-called models of coupled quintessence. In this paper we propose a new cosmological scenario where radiation and baryons are conserved, while the dark energy component is decaying into cold dark matter. The dilution of cold dark matter particles, attenuated with respect to the usual a(-3) scaling due to the interacting process, is characterized by a positive parameter epsilon, whereas the dark energy satisfies the equation of state p(x) = omega rho(x) (omega < 0). We carry out a joint statistical analysis involving recent observations from type Ia supernovae, baryon acoustic oscillation peak, and cosmic microwave background shift parameter to check the observational viability of the coupled quintessence scenario here proposed.

Dynamics and constraints of the massive graviton dark matter flat cosmologies

We discuss the dynamics of the Universe within the framework of the massive graviton cold dark matter scenario (MGCDM) in which gravitons are geometrically treated as massive particles. In this modified gravity theory, the main effect of the gravitons is to alter the density evolution of the cold dark matter component in such a way that the Universe evolves to an accelerating expanding regime, as presently observed. Tight constraints on the main cosmological parameters of the MGCDM model are derived by performing a joint likelihood analysis involving the recent supernovae type Ia data, the cosmic microwave background shift parameter, and the baryonic acoustic oscillations as traced by the Sloan Digital Sky Survey red luminous galaxies. The linear evolution of small density fluctuations is also analyzed in detail. It is found that the growth factor of the MGCDM model is slightly different (similar to 1-4%) from the one provided by the conventional flat Lambda CDM cosmology. The growth rate of clustering predicted by MGCDM and Lambda CDM models are confronted to the observations and the corresponding best fit values of the growth index (gamma) are also determined. By using the expectations of realistic future x-ray and Sunyaev-Zeldovich cluster surveys we derive the dark matter halo mass function and the corresponding redshift distribution of cluster-size halos for the MGCDM model. Finally, we also show that the Hubble flow differences between the MGCDM and the Lambda CDM models provide a halo redshift distribution departing significantly from the those predicted by other dark energy models. These results suggest that the MGCDM model can observationally be distinguished from Lambda CDM and also from a large number of dark energy models recently proposed in the literature.

Confronting dark energy models using galaxy cluster number counts

The mass function of cluster-size halos and their redshift distribution are computed for 12 distinct accelerating cosmological scenarios and confronted to the predictions of the conventional flat Lambda CDM model. The comparison with Lambda CDM is performed by a two-step process. First, we determine the free parameters of all models through a joint analysis involving the latest cosmological data, using supernovae type Ia, the cosmic microwave background shift parameter, and baryon acoustic oscillations. Apart from a braneworld inspired cosmology, it is found that the derived Hubble relation of the remaining models reproduces the Lambda CDM results approximately with the same degree of statistical confidence. Second, in order to attempt to distinguish the different dark energy models from the expectations of Lambda CDM, we analyze the predicted cluster-size halo redshift distribution on the basis of two future cluster surveys: (i) an X-ray survey based on the eROSITA satellite, and (ii) a Sunayev-Zeldovich survey based on the South Pole Telescope. As a result, we find that the predictions of 8 out of 12 dark energy models can be clearly distinguished from the Lambda CDM cosmology, while the predictions of 4 models are statistically equivalent to those of the Lambda CDM model, as far as the expected cluster mass function and redshift distribution are concerned. The present analysis suggests that such a technique appears to be very competitive to independent tests probing the late time evolution of the Universe and the associated dark energy effects.

Constraints on cold dark matter accelerating cosmologies and cluster formation

We discuss the properties of homogeneous and isotropic flat cosmologies in which the present accelerating stage is powered only by the gravitationally induced creation of cold dark matter (CCDM) particles (Omega(m) = 1). For some matter creation rates proposed in the literature, we show that the main cosmological functions such as the scale factor of the universe, the Hubble expansion rate, the growth factor, and the cluster formation rate are analytically defined. The best CCDM scenario has only one free parameter and our joint analysis involving baryonic acoustic oscillations + cosmic microwave background (CMB) + SNe Ia data yields (Omega) over tilde = 0.28 +/- 0.01 (1 sigma), where (Omega) over tilde (m) is the observed matter density parameter. In particular, this implies that the model has no dark energy but the part of the matter that is effectively clustering is in good agreement with the latest determinations from the large- scale structure. The growth of perturbation and the formation of galaxy clusters in such scenarios are also investigated. Despite the fact that both scenarios may share the same Hubble expansion, we find that matter creation cosmologies predict stronger small scale dynamics which implies a faster growth rate of perturbations with respect to the usual Lambda CDM cosmology. Such results point to the possibility of a crucial observational test confronting CCDM with Lambda CDM scenarios through a more detailed analysis involving CMB, weak lensing, as well as the large-scale structure.

CMB in a box: Causal structure and the Fourier-Bessel expansion

This paper makes two points. First, we show that the line-of-sight solution to cosmic microwave anisotropies in Fourier space, even though formally defined for arbitrarily large wavelengths, leads to position-space solutions which only depend on the sources of anisotropies inside the past light cone of the observer. This foretold manifestation of causality in position (real) space happens order by order in a series expansion in powers of the visibility gamma = e(-mu), where mu is the optical depth to Thomson scattering. We show that the contributions of order gamma(N) to the cosmic microwave background (CMB) anisotropies are regulated by spacetime window functions which have support only inside the past light cone of the point of observation. Second, we show that the Fourier-Bessel expansion of the physical fields (including the temperature and polarization momenta) is an alternative to the usual Fourier basis as a framework to compute the anisotropies. The viability of the Fourier-Bessel series for treating the CMB is a consequence of the fact that the visibility function becomes exponentially small at redshifts z >> 10(3), effectively cutting off the past light cone and introducing a finite radius inside which initial conditions can affect physical observables measured at our position (x) over right arrow = 0 and time t(0). Hence, for each multipole l there is a discrete tower of momenta k(il) (not a continuum) which can affect physical observables, with the smallest momenta being k(1l) similar to l. The Fourier-Bessel modes take into account precisely the information from the sources of anisotropies that propagates from the initial value surface to the point of observation-no more, no less. We also show that the physical observables (the temperature and polarization maps), and hence the angular power spectra, are unaffected by that choice of basis. This implies that the Fourier-Bessel expansion is the optimal scheme with which one can compute CMB anisotropies.