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

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

Observed parity-odd CMB temperature bispectrum

Parity-odd non-Gaussianities create a variety of temperature bispectra in the cosmic microwave background (CMB), defined in the domain: $\ell_1 + \ell_2 + \ell_3 = {\rm odd}$. These models are yet unconstrained in the literature, that so far focused exclusively on the more common parity-even scenarios. In this work, we provide the first experimental constraints on parity-odd bispectrum signals in WMAP 9-year temperature data, using a separable modal parity-odd estimator. Comparing theoretical bispectrum templates to the observed bispectrum, we place constraints on the so-called nonlineality parameters of parity-odd tensor non-Gaussianities predicted by several Early Universe models. Our technique also generates a model-independent, smoothed reconstruction of the bispectrum of the data for parity-odd configurations.Comment: 17 pages, 4 figures, 1 table. Accepted for publication in JCA

A discriminating probe of gravity at cosmological scales

The standard cosmological model is based on general relativity and includes dark matter and dark energy. An important prediction of this model is a fixed relationship between the gravitational potentials responsible for gravitational lensing and the matter overdensity. Alternative theories of gravity often make different predictions for this relationship. We propose a set of measurements which can test the lensing/matter relationship, thereby distinguishing between dark energy/matter models and models in which gravity differs from general relativity. Planned optical, infrared and radio galaxy and lensing surveys will be able to measure $E_G$, an observational quantity whose expectation value is equal to the ratio of the Laplacian of the Newtonian potentials to the peculiar velocity divergence, to percent accuracy. We show that this will easily separate alternatives such as $\Lambda$CDM, DGP, TeVeS and $f(R)$ gravity.Comment: v2: minor revisions in the main text, fig, table and references. Slightly longer than the PRL version in press. V3: update the figure (minor change due to a coding bug. No other change

Lmit and shakedown analysis based on solid shell models

The paper treats the formulation of the shakedown problem and, as special case, of the limit analysis problem, using solid shell models and ES-FEM discratization technology. In this proposal the Discrete shear gap method is applied to alleviate the shear locking phenomenon