Parity breaking signatures from a Chern-Simons coupling during inflation: the case of non-Gaussian gravitational waves

Considering high-energy modifications of Einstein gravity during inflation is an interesting issue. We can constrain the strength of the new gravitational terms through observations of inflationary imprints in the actual universe. In this paper we analyze the effects on slow-roll models due to a Chern-Simons term coupled to the inflaton field through a generic coupling function $f(\phi)$. A well known result is the polarization of primordial gravitational waves (PGW) into left and right eigenstates, as a consequence of parity breaking. In such a scenario the modifications to the power spectrum of PGW are suppressed under the conditions that allow to avoid the production of ghost gravitons at a certain energy scale, the so-called Chern-Simons mass $M_{CS}$. In general it has been recently pointed out that there is very little hope to efficiently constrain chirality of PGW on the basis solely of two-point statistics from future CMB data, even in the most optimistic cases. Thus we search if significant parity breaking signatures can arise at least in the bispectrum statistics. We find that the tensor-tensor-scalar bispectra $\langle \gamma \gamma \zeta \rangle$ for each polarization state are the only ones that are not suppressed. Their amplitude, setting the level of parity breaking during inflation, is proportional to the second derivative of the coupling function $f(\phi)$ and they turn out to be maximum in the squeezed limit. We comment on the squeezed-limit consistency relation arising in the case of chiral gravitational waves, and on possible observables to constrain these signatures.Comment: 31 pages, 1 figure. V3: references added; typos correcte

Matter waves in two-dimensional arbitrary atomic crystals

We present a general scheme to realize a cold-atom quantum simulator of bidimensional atomic crystals. Our model is based on the use of two independently trapped atomic species: the first one, subject to a strong in-plane confinement, constitutes a two-dimensional matter wave which interacts only with atoms of the second species, deeply trapped around the nodes of a two-dimensional optical lattice. By introducing a general analytic approach we show that the system Green function can be exactly determined, allowing for the investigation of the matter-wave transport properties. We propose some illustrative applications to both Bravais (square, triangular) and non-Bravais (graphene, kagom\'e) lattices, studying both ideal periodic systems and experimental-size and disordered ones. Some remarkable spectral properties of these atomic artificial lattices are pointed out, such as the emergence of single and multiple gaps, flat bands, and Dirac cones. All these features can be manipulated via the interspecies interaction, which proves to be widely tunable due to the interplay between scattering length and confinements.Comment: 14 pages, 20 figure

Matter Waves in Atomic Artificial Graphene

We present a new model to realize artificial 2D lattices with cold atoms investigating the atomic artificial graphene: a 2D-confined matter wave is scattered by atoms of a second species trapped around the nodes of a honeycomb optical lattice. The system allows an exact determination of the Green function, hence of the transport properties. The inter-species interaction can be tuned via the interplay between scattering length and confinements. Band structure and density of states of a periodic lattice are derived for different values of the interaction strength. Emergence and features of Dirac cones are pointed out, together with the appearance of multiple gaps and a non-dispersive and isolated flat band. Robustness against finite-size and vacancies effects is numerically investigated.Comment: 6 pages, 6 figure

Unified Dark Matter Scalar Field Models

In this work we analyze and review cosmological models in which the dynamics of a single scalar field accounts for a unified description of the Dark Matter and Dark Energy sectors, dubbed Unified Dark Matter (UDM) models. In this framework, we consider the general Lagrangian of k-essence, which allows to find solutions around which the scalar field describes the desired mixture of Dark Matter and Dark Energy. We also discuss static and spherically symmetric solutions of Einstein's equations for a scalar field with non-canonical kinetic term, in connection with galactic halo rotation curves.Comment: 57 pages, 6 figures, LaTeX file. Typos corrected; Added References; Revised according to reviewer's suggestions; Invited Review for the special issue "Focus Issue on Dark Matter" for Advances in Astronom

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

The Trispectrum in the Effective Theory of Inflation with Galilean symmetry

We calculate the trispectrum of curvature perturbations for a model of inflation endowed with Galilean symmetry at the level of the fluctuations around an FRW background. Such a model has been shown to posses desirable properties such as unitarity (up to a certain scale) and non-renormalization of the leading operators, all of which point towards the reasonable assumption that a full theory whose fluctuations reproduce the one here might exist as well as be stable and predictive. The cubic curvature fluctuations of this model produce quite distinct signatures at the level of the bispectrum. Our analysis shows how this holds true at higher order in perturbations. We provide a detailed study of the trispectrum shape-functions in different configurations and a comparison with existent literature. Most notably, predictions markedly differ from their P(X,\phi) counterpart in the so called equilateral trispectrum configuration. The zoo of inflationary models characterized by somewhat distinctive predictions for higher order correlators is already quite populated; what makes this model more compelling resides in the above mentioned stability properties.Comment: 24 pages, 10 figure

Measuring chiral gravitational waves in Chern-Simons gravity with CMB bispectra

Chern-Simons gravity coupled to the scalar sector through a generic coupling function $f(\phi)$ can be tested at the very high energies of the inflationary period. In 1706.04627, we computed the theoretical parity breaking signatures of the $\langle \gamma \gamma \zeta \rangle$ primordial bispectrum which mixes two gravitons and one scalar curvature perturbation. We defined a parameter $\Pi$ which measures the level of parity breaking of the corresponding bispectrum. In this work we forecast the expected $1 \sigma$ error on $\Pi$ using the cosmic microwave background (CMB) angular bispectra. We find that, given the angular resolution of an experiment like $Planck$, $\Pi \sim 10^6$ is detectable via the measurement of $BBT$ or $BBE$ angular bispectra if the tensor-to-scalar ratio $r = 0.01$. We also show that, from the theoretical point of view, $\Pi$ can be greater than $10^6$. Thus, our conclusion is that $BBT$ or $BBE$ CMB angular bispectra can become an essential observable for testing Chern-Simons gravity in the primordial universe.Comment: 16 pages, 1 figure; version matching publication in JCA

The Effective Field Theory of Inflation Models with Sharp Features

We describe models of single-field inflation with small and sharp step features in the potential (and sound speed) of the inflaton field, in the context of the Effective Field Theory of Inflation. This approach allows us to study the effects of features in the power-spectrum and in the bispectrum of curvature perturbations, from a model-independent point of view, by parametrizing the features directly with modified "slow-roll" parameters. We can obtain a self-consistent power-spectrum, together with enhanced non-Gaussianity, which grows with a quantity $\beta$ that parametrizes the sharpness of the step. With this treatment it is straightforward to generalize and include features in other coefficients of the effective action of the inflaton field fluctuations. Our conclusion in this case is that, excluding extrinsic curvature terms, the only interesting effects at the level of the bispectrum could arise from features in the first slow-roll parameter $\epsilon$ or in the speed of sound $c_s$. Finally, we derive an upper bound on the parameter $\beta$ from the consistency of the perturbative expansion of the action for inflaton perturbations. This constraint can be used for an estimation of the signal-to-noise ratio, to show that the observable which is most sensitive to features is the power-spectrum. This conclusion would change if we consider the contemporary presence of a feature and a speed of sound $c_s < 1$, as, in such a case, contributions from an oscillating folded configuration can potentially make the bispectrum the leading observable for feature models.Comment: 31 pages, 11 figures; references added, accepted version 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

Cosmic Microwave Background Anisotropies up to Second Order

These lecture notes present the computation of the full system of Boltzmann equations describing the evolution of the photon, baryon and cold dark matter fluids up to second order in perturbation theory, as recently studied in (Bartolo, Matarrese & Riotto 2006, 2007). These equations allow to follow the time evolution of the cosmic microwave background anisotropies at all angular scales from the early epoch, when the cosmological perturbations were generated, to the present, through the recombination era. The inclusion of second-order contributions is mandatory when one is interested in studying possible deviations from Gaussianity of cosmological perturbations, either of primordial (e.g. inflationary) origin or due to their subsequent evolution. Most of the emphasis in these lectures notes will be given to the derivation of the relevant equations for the study of cosmic microwave background anisotropies and to their analytical solutions.Comment: 53 pages, LaTeX file. Lectures given by S.M. at Les Houches Summer School - Session 86: Particle Physics and Cosmology: The Fabric of Spacetime, Les Houches, France, 31 Jul - 25 Aug 2006. To appear in the Proceedings. Second version with minor misprints correcte