Narrow Results

In this paper, we address quantum systems isospectral to the harmonic oscillator, as those found within the framework of supersymmetric quantum mechanics, as potential resources for continuous variable quantum information. These deformed oscillator potentials share the equally spaced energy levels of the shifted harmonic oscillator but differ significantly in that they are nonharmonic. Consequently, their ground states and thermal equilibrium states are no longer Gaussian and exhibit nonclassical properties. We quantify their non-Gaussianity and evaluate their nonclassicality using various measures, including quadrature squeezing, photon number squeezing, Wigner function negativity, and quadrature coherence scale. Additionally, we employ quantum estimation theory to identify optimal measurement strategies and establish ultimate precision bounds for inferring the deformation parameter. Our findings prove that quantum systems isospectral to the harmonic oscillator may represent promising platforms for quantum information with continuous variables. In turn, non-Gaussian and nonclassical stationary states may be obtained and these features persist at nonzero temperature.

Analysis of the criticality in finance and economics is an important topic for scholars. The crises are conditions in which unpredictable behavior have been emerged. On the other hand, the contagion from one market to another one due to the complex nature of them is a crucial concept. Therefore, we should consider economies and financial markets as entangled systems that interact with each other, and studying one’s behavior without considering its interacting structures will not provide us with adequate information. In this paper, we have considered the critical states of some emerging and mature markets’ indices. S&P500 and Nikkei 225 as representatives of mature markets, and SSE Composite and TEDPIX as representatives of emerging markets have been analyzed. Coupled criticality emerges when two interacting systems reach their critical state due to their interactions. One of the efficient methods to study the coupled criticality is the bi-variate multifractal random walk model. This method is useful to assess the correlation of rare events and coupled criticality in entangled systems such as financial markets. The observations in this paper show that TEDPIX and S&P500 have higher critical states among others in most time lags by assessing criticality parameter explained in the model, and in longer time lags criticality parameter decreases in all indices. Coupled criticality parameter explained in the model is assessed between each index mentioned and TEDPIX. Results show that TEDPIX and S&P500 have the highest level of coupled criticality. To figure out how long-range time correlation between rare events in each index affect its critical behavior, the data of each index are shuffled, and the criticality parameter is calculated for the shuffled data. From the observations, it can be concluded that this matter has more substantial effect on mature markets. As it is known, shuffling removes the effect of the long-range time correlations. Therefore, the coupled criticality parameter is calculated for the shuffled S&P500 data and TEDPIX. Results show that the long-range correlation of S&P500 data has a significant effect on the coupled criticality behavior of S&P500 and TEDPIX.

We investigate the physical implications of the noncommutative geometry in inflationary scenario. Firstly we study the noncommutative inflation with a time-dependent noncommutativity between space and time and find that the scalar perturbation power spectrum depends sensitively on the time varying of the spacetime noncommutativity. Secondly, we discuss the spatially noncommutative effect on the non-Gaussianities of primordial cosmological perturbation. In the lowest order of noncommutativity and slow-roll parameter, we find that in the models with small speed of sound the noncommutative modifications could be observable if assuming a relatively low string scale. It turns out that the corrections are sensitive to the speed of sound and the choice of string length scale, and the shapes of the corrected non-Gaussianities are distinct from that of ordinary ones.

In this paper, we explore the parameter space for a Right-Handed (RH) sneutrino curvaton that can generate large non-Gaussianity without assuming any particular inflation sector. The mass of the RH sneutrino is suggested from a discussion on the initial condition of the curvaton field. It is shown that a small Yukawa coupling is generally required for a successful RH sneutrino curvaton. However, the Yukawa coupling can be larger if we consider the braneworld scenario. Some general discussion about the spectral index in curvaton scenario is also provided.

In this paper, we investigate the idea that the decay of a curvaton is kinematically blocked and show that the coupling constant for curvaton decay can be as large as . We also find in this case the lower bound of the Hubble parameter at horizon exit from big bang nucleosynthesis (BBN) is H_* ≳ 7.2 × 10^-9M_P ~ 10¹⁰GeV. Similar to conventional curvaton scenario, the nonlinear parameter can be as large as f_NL = 100.

We consider inflationary models in which vector fields (VF) are responsible for part or eventually all of the primordial curvature perturbation ζ. Such models are phenomenologically interesting since they naturally introduce anisotropies in the probability distribution function of the primordial fluctuations that can leave a measurable imprint in the cosmic microwave background. Assuming that non-Gaussianity (NG) is generated due to the superhorizon evolution, we use the δN formalism to do a complete tree level calculation of the NG parameters f_NL and τ_NL in the presence of VF. We isolate the isotropic pieces of the NG parameters, which anyway have contributions from the VF, and show that they obey the Suyama–Yamaguchi (SY) consistency relation . Other ways of defining the NG parameters, which could be observationally relevant, are stated and the respective SY-like consistency relations are obtained.

There are possibilities to violate symmetries (e.g. parity and rotational invariance) in the primordial cosmological fluctuations. Such symmetry breakings can imprint very rich signatures in late-time phenomena, which may be possible to observe. Especially, Cosmic Microwave Background (CMB) will change its face drastically, corresponding to the symmetry-breaking types, since the harmonic-space representation is very sensitive to the statistical, spin and angular dependences of cosmological perturbations. Here, we discuss (1) general responses of CMB to the symmetry breakings, (2) some theoretical models creating interesting CMB signatures, and (3) aspects of the estimation from observational data.

Cosmological Collider Physics gives us the opportunity to probe high-energy physics from observing the space–time fluctuations generated during inflation imprinted on the cosmic microwave background. In other words, it is a method to investigate physics on energy scales that cannot be reached by terrestrial accelerators by means of precise observations of the universe. In this paper, we focus on the case where the GUT scale is close to the energy scale of inflation, and calculate three-point function of inflaton by exchanging the Higgs boson in GUT at tree level. The results are found to be consistent with the current observed restrictions on non-Gaussianity without a drastic fine-tuning of parameters, and it might be possible to detect the signature of the Higgs boson in GUT by 21 cm spectrum, future LSS and future CMB depending on our model parameters.

An orthogonal state of coherent state is produced by applying an orthogonalizer related with Hermite-excited superposition operator $H_m(x{a}^{†}+ya)$. Using some technique, we cleverly deal with the normalization and discuss the nonclassical and non-Gaussian characters of the orthogonal state. The analytical expressions for the Wigner functions of the orthogonal state are derived in detail. Numerical results show that the orthogonal state will exhibit its richly nonclassical and non-Gaussian character by changing the interaction parameters.

The detection of non-Gaussianity in the CMB data would rule out a number of inflationary models. A null detection of non-Gaussianity, instead, would exclude alternative models for the early universe. Thus, a detection or non-detection of primordial non-Gaussianity in the CMB data is crucial to discriminate among inflationary models, and to test alternative scenarios. However, there are various non-cosmological sources of non-Gaussianity. This makes important to employ different indicators in order to detect distinct forms of non-Gaussianity in CMB data. Recently, we proposed two new indicators to measure deviation from Gaussianity on large angular scales, and used them to study the Gaussianity of the raw band WMAP maps with and without the KQ75 mask. Here we extend this work by using these indicators to perform similar analyses of deviation from Gaussianity of the foreground-reduced Q, V, and W band maps. We show that there is a significant deviation from Gaussianity in the considered full-sky maps, which is reduced to a level consistent with Gaussianity when the KQ75 mask is employed.

Certain inflation models are shown to have large non-Gaussianity in special cases. Namely, slow-roll inflation models with an effective higher derivative interaction, in which the length of inflation is finite and a scalar-matter-dominated period or power inflation is adopted as pre-inflation, are considered. Using Holman and Tolley's formula of the nonlinearity parameter in the flattened triangle configurations , we calculate the value of . The value of is found to be largest when the inflation length is approximately 60 e-folds, and is found to depend strongly on the length of inflation and the cut-off scale.

The vector curvaton paradigm is reviewed. The mechanism allows a massive vector boson field to contribute to or even generate the curvature perturbation in the Universe. Contribution of vector bosons is likely to generate statistical anisotropy in the spectrum and bispectrum of the curvature perturbation, which will soon be probed observationally. Two specific models for the generation of superhorizon spectra for the components of an Abelian vector field are analyzed. Emphasis is put on the observational signatures of the models when the vector fields play the role of vector curvatons. If future observations support the vector curvaton mechanism this will open a window into the gauge field content of theories beyond the standard model.

I compute the bispectrum of maps of cosmic microwave background (CMB) fluctuations seeded by cosmic strings from large to 30 arcminute scales. Examining the distribution of triangle configurations and comparing with Gaussian realizations with the same power spectrum, I conclude that the CMB bispectrum cannot pick up the mild non-Gaussianity present in the maps and thus that it cannot characterize cosmic string induced non-Gaussianity produced in the regimes probed by these maps.

Inflation models are numerous. It is extremely difficult, if possible at all, to identify the actual underlying inflation model of our primordial universe. Thus, for the purpose of proving/falsifying inflation and using inflation to probe new physics, model-independent approaches are crucial. Massive fields play a uniquely important role in those missions. This short review is based on a talk by one of the authors (YW) in the 2nd LeCosPA Symposium.

We study a nonminimal inflation which is driven by a superpotential. By adopting the Arnowitt–Deser–Misner formalism, we explore the primordial perturbations and its non-Gaussianity in this framework. By expanding the action up to the second-order in perturbations, we seek the scalar spectral index, its running and the tensor-to-scalar ratio. In this regard, we find the ranges of the nonminimal coupling and superpotential parameters which lead to the observationally viable perturbations parameters. The non-Gaussian feature in both the equilateral and orthogonal configurations in this setup, is studied by exploring the third-order action. We show that in some ranges of the nonminimal and superpotential parameters, the model predicts large non-Gaussianity. By comparing the numerical results with Planck2015 data, we test the viability of the model and find some constraints on the model’s parameters space.

We address truncated states of continuous variable systems and analyze their statistical properties numerically by generating random states in finite-dimensional Hilbert spaces. In particular, we focus to the distribution of purity and non-Gaussianity for dimension up to d = 21. We found that both quantities are distributed around typical values with variances that decrease for increasing dimension. Approximate formulas for typical purity and non-Gaussianity as a function of the dimension are derived.

We generate sub-Poissonian non-Gaussian conditional states from pulsed multimode twin beams (TWBs) by measuring with photon-number-resolving detectors. Links among twin-beam non-classicality and the properties of the conditional states are discussed.

In this paper, we study the non-Gaussian character in generalized coherent states in the framework of a noncommutative space by adding photons to deformed coherent states, which is called the photon-added nonlinear coherent states (PANCSs). We find that the non-Gaussianity of PANCSs is enhanced with the increase of the photon-added number and it increases monotonically with the amplitude of the coherent states. Interestingly, we obtain that the maximal value of non-Gaussianity measure occurs at a certain critical value of the coherent state amplitude, where this critical value is determined by the kind of the deformation. Using the Mandel’s parameter, we examine the statistical properties for the PANCSs and show that the Mandel’s parameter may take positive and negative values depending on the choice of the amplitude and deformation parameter, exhibiting sub-Poissonian distribution and super-Poissonian distribution.

We study the non-gaussianity from the bispectrum in multi-field inflation models with a general kinetic term. The models include the multi-field K-inflation and the multi-field Dirac-Born-Infeld (DBI) inflation as special cases. We derive the three-point function for the curvature perturbation which depends on both adiabatic and entropy perturbations, in the small sound speed limit and at leading order in the slow-roll expansion. The contribution from the entropy perturbations has a different momentum dependence if the sound speed for the entropy perturbations is different from the adiabatic one, which provides a possibility to distinguish the multi-field models from single field models.

A detection or nondetection of primordial non-Gaussianity by using the cosmic microwave background radiation (CMB) offers a way of discriminating inflationary scenarios and testing alternative models of the early universe. This has motivated the considerable effort that has recently gone into the study of theoretical features of primordial non-Gaussianity and its detection in CMB data. Among such attempts to detect non-Gaussianity, there is a procedure that is based upon two indicators constructed from the skewness and kurtosis of large-angle patches of CMB maps, which have been proposed and used to study deviation from Gaussianity in the WMAP data (see Refs. 1 and 2). Simulated CMB maps equipped with realistic primordial non-Gaussianity are essential tools to test the viability of non-Gaussian indicators in practice, and also to understand the effect of systematics, foregrounds and other contaminants. In this work we extend and complement the results Refs. 1 and 2 by performing an analysis of non-Gaussianity of the high-angular resolution simulated CMB temperature maps endowed with non-Gaussianity of the local type, for which the level of non-Gaussianity is characterized by the dimensionless parameter .