Parity violation of primordial magnetic fields in the CMB bispectrum

We study the parity violation in the cosmic microwave background (CMB) bispectrum induced by primordial magnetic fields (PMFs). Deriving a general formula for the CMB bispectrum generated from not only non-helical but also helical PMFs, we find that helical PMFs produce characteristic signals, which disappear in parity-conserving cases, such as the intensity-intensity-intensity bispectra arising from $\sum_{n=1}^3 \ell_n = {\rm odd}$. For fast numerical calculation of the CMB bispectrum, we reduce the one-loop formula to the tree-level one by using the so-called pole approximation. Then, we show that the magnetic anisotropic stress, which depends quadratically on non-helical and helical PMFs and acts as a source of the CMB fluctuation, produces the local-type non-Gaussianity. Comparing the CMB bispectra composed of the scalar and tensor modes with the noise spectra, we find that assuming the generation of the nearly scale-invariant non-helical and helical PMFs from the grand unification energy scale ($10^{14} {\rm GeV}$) to the electroweak one ($10^{3} {\rm GeV}$), the intensity-intensity-intensity bispectrum for $\sum_{n=1}^3 \ell_n = {\rm odd}$ can be observed by the WMAP experiment under the condition that $B_{1 \rm Mpc}^{2/3} {\cal B}_{1 \rm Mpc}^{1/3} > 2.7 - 4.5 {\rm nG}$ with $B_{1 \rm Mpc}$ and ${\cal B}_{1 \rm Mpc}$ being the non-helical and helical PMF strengths smoothed on 1 Mpc, respectively.Comment: 18 pages, 2 figures. Accepted for publication in JCA

Probing the Early Universe with the CMB Scalar, Vector and Tensor Bispectrum

Although cosmological observations suggest that the fluctuations of seed fields are almost Gaussian, the possibility of a small deviation of their fields from Gaussianity is widely discussed. Theoretically, there exist numerous inflationary scenarios which predict large and characteristic non-Gaussianities in the primordial perturbations. These model-dependent non-Gaussianities act as sources of the Cosmic Microwave Background (CMB) bispectrum; therefore, the analysis of the CMB bispectrum is very important and attractive in order to clarify the nature of the early Universe. Currently, the impacts of the primordial non-Gaussianities in the scalar perturbations, where the rotational and parity invariances are kept, on the CMB bispectrum have been well-studied. However, for a complex treatment, the CMB bispectra generated from the non-Gaussianities, which originate from the vector- and tensor-mode perturbations and include the violation of the rotational or parity invariance, have never been considered in spite of the importance of this information. On the basis of our current studies, this thesis provides the general formalism for the CMB bispectrum sourced by the non-Gaussianities not only in the scalar-mode perturbations but also in the vector- and tensor-mode perturbations. Applying this formalism, we calculate the CMB bispectrum from two scalars and a graviton correlation and that from primordial magnetic fields, and we then outline new constraints on these amplitudes. Furthermore, this formalism can be easily extended to the cases where the rotational or parity invariance is broken. We also compute the CMB bispectra from the non-Gaussianities of the curvature perturbations with a preferred direction and the graviton non-Gaussianities induced by the parity-violating Weyl cubic terms. We also present some unique impacts to the violation of these invariances on the CMB bispectrum.Comment: The final version will be published in Springer Theses http://www.springer.com/astronomy/book/978-4-431-54179-

Violation of the Rotational Invariance in the CMB Bispectrum

We investigate a statistical anisotropy on the Cosmic Microwave Background (CMB) bispectrum, which can be generated from the primordial non-Gaussianity induced by quantum fluctuations of a vector field. We find new configurations in the multipole space of the CMB bispectrum given by $\ell_1 = \ell_2 + \ell_3 + 2, |\ell_2 - \ell_3| - 2$ and their permutations, which violate the rotational invariance, such as an off-diagonal configuration in the CMB power spectrum. We also find that in a model presented by Yokoyama and Soda (2008), the amplitude of the statistically anisotropic bispectrum in the above configurations becomes as large as that in other configurations such as $\ell_1 = \ell_2 + \ell_3$. As a result, it might be possible to detect these contributions in future experiments, which would give us novel information about the physics of the early Universe.Comment: 13 pages, 2 figures. Accepted for publication in PT

Parity violation in the CMB bispectrum by a rolling pseudoscalar

We investigate parity-violating signatures of temperature and polarization bispectra of the cosmic microwave background (CMB) in an inflationary model where a rolling pseudoscalar produces large equilateral tensor non-Gaussianity. By a concrete computation based on full-sky formalism, it is shown that resultant CMB bispectra have nonzero signals in both parity-even $(\ell_1 + \ell_2 + \ell_3 = {\rm even})$ and parity-odd $(\ell_1 + \ell_2 + \ell_3 = {\rm odd})$ spaces, and are almost uncorrelated with usual scalar-mode equilateral bispectra. These characteristic signatures and polarization information help to detect such tensor non-Gaussianity. Use of both temperature and E-mode bispectra potentially improves of $400\%$ the detectability with respect to an analysis with temperature bispectrum alone. Considering B-mode bispectrum, the signal-to-noise ratio may be able to increase by 3 orders of magnitude. We present the $1\sigma$ uncertainties of a parameter depending on a coupling constant and a rolling condition for the pseudoscalar expected in the ${\it Planck}$ and the proposed PRISM experiments.Comment: 19 pages, 5 figures. Accepted for publication in JCA

Angular dependence of primordial trispectra and CMB spectral distortions

Under the presence of anisotropic sources in the inflationary era, the trispectrum of the primordial curvature perturbation has a very specific angular dependence between each wavevector that is distinguishable from the one encountered when only scalar fields are present, characterized by an angular dependence described by Legendre polynomials. We examine the imprints left by curvature trispectra on the $TT\mu$ bispectrum, generated by the correlation between temperature anisotropies (T) and chemical potential spectral distortions ($\mu$) of the Cosmic Microwave Background (CMB). Due to the angular dependence of the primordial signal, the corresponding $TT\mu$ bispectrum strongly differs in shape from $TT\mu$ sourced by the usual $g_{\rm NL}$ or $\tau_{\rm NL}$ local trispectra, enabling us to obtain an unbiased estimation. From a Fisher matrix analysis, we find that, in a cosmic-variance-limited (CVL) survey of $TT\mu$, a minimum detectable value of the quadrupolar Legendre coefficient is $d_2 \sim 0.01$, which is 4 orders of magnitude better than the best value attainable from the $TTTT$ CMB trispectrum. In the case of an anisotropic inflationary model with a $f(\phi)F^2$ interaction (coupling the inflaton field $\phi$ with a vector kinetic term $F^2$), the size of the curvature trispectrum is related to that of quadrupolar power spectrum asymmetry, $g_*$. In this case, a CVL measurement of $TT\mu$ makes it possible to measure $g_*$ down to $10^{-3}$.Comment: 20 pages, 5 figures; version matching publication in JCA

Signatures of anisotropic sources in the trispectrum of the cosmic microwave background

Soft limits of $N$-point correlation functions, in which one wavenumber is much smaller than the others, play a special role in constraining the physics of inflation. Anisotropic sources such as a vector field during inflation generate distinct angular dependence in all these correlators. In this paper we focus on the four-point correlator (the trispectrum $T$). We adopt a parametrization motivated by models in which the inflaton $\phi$ is coupled to a vector field through a $I^2 \left( \phi \right) F^2$ interaction, namely $T_{\zeta}({\bf k}_1, {\bf k}_2, {\bf k}_3, {\bf k}_4) \equiv \sum_n d_n [ P_n(\hat{\bf k}_1 \cdot \hat{\bf k}_3) + P_n(\hat{\bf k}_1 \cdot \hat{\bf k}_{12}) + P_n(\hat{\bf k}_3 \cdot \hat{\bf k}_{12}) ] P_{\zeta}(k_1) P_{\zeta}(k_3) P_\zeta(k_{12}) + (23~{\rm perm})$, where $P_n$ denotes the Legendre polynomials. This shape is enhanced when the wavenumbers of the diagonals of the quadrilateral are much smaller than the sides, ${\bf k}_i$. The coefficient of the isotropic part, $d_0$, is equal to $\tau_{\rm NL}/6$ discussed in the literature. A $I^2 \left( \phi \right) F^2$ interaction generates $d_2 = 2 d_0$ which is, in turn, related to the quadrupole modulation parameter of the power spectrum, $g_*$, as $d_2 \approx 14 |g_*| N^2$ with $N \approx 60$. We show that $d_0$ and $d_2$ can be equally well-constrained: the expected $68 \%$ CL error bars on these coefficients from a cosmic-variance-limited experiment measuring temperature anisotropy of the cosmic microwave background up to $\ell_{\rm max}=2000$ are $\delta d_2 \approx 4 \delta d_0 = 105$. Therefore, we can reach $|g_*|=10^{-3}$ by measuring the angle-dependent trispectrum. The current upper limit on $\tau_{\rm NL}$ from the ${\it Planck}$ temperature maps yields $|g_*|<0.02$ ($95 \%$ CL).Comment: 15 pages, 5 figure

Primordial trispectra and CMB spectral distortions

We study the $TT\mu$ bispectrum, generated by correlations between Cosmic Microwave Background temperature (T) anisotropies and chemical potential ($\mu$) distortions, and we analyze its dependence on primordial local trispectrum parameters $g_{\rm NL}$ and $\tau_{\rm NL}$. We cross-check our results by comparing the full bispectrum calculation with the expectations from a general physical argument, based on predicting the shape of $\mu$-T correlations from the couplings between short and long perturbation modes induced by primordial non-Gaussianity. We show that $both$ $g_{\rm NL}$ and $\tau_{\rm NL}$-parts of the primordial trispectrum source a non-vanishing $TT\mu$ signal, contrary to the $\mu\mu$ auto-correlation function, which is sensitive only to the $\tau_{\rm NL}$-component. A simple Fisher matrix-based forecast shows that a futuristic, cosmic-variance dominated experiment could in principle detect $g_{\rm NL} \sim 0.4$ and $\tau_{\rm NL} \sim 40$ using $TT\mu$.Comment: 21 pages, 4 figures. Accepted for publication in JCA