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Motivated by the interest in models of the early universe where statistical isotropy is broken and can be revealed in cosmological observations, we consider an SU(2) theory of gauge interactions in a single scalar field inflationary…
We investigate the effect of non-symmetric relatively bounded perturbations on the spectrum of self-adjoint operators. In particular, we establish stability theorems for one or infinitely many spectral gaps along with corresponding…
Primordial scalar perturbations may be generated when complex conformal scalar field rolls down its negative quartic potential. We begin with the discussion of peculiar infrared properties of this scenario. We then consider the statistical…
In the full nonlinear cosmological perturbation theory in the leading order of the gradient expansion, all the types of the gauge invariant perturbation variables are defined. The metric junction conditions across the spacelike transition…
Random fields in nature often have, to a good approximation, Gaussian characteristics. We present the mathematical framework for a new and simple method for investigating the non-Gaussian contributions, based on counting the maxima and…
Gravitational interferometers and cosmological observations of the cosmic microwave background offer us the prospect to probe the laws of gravity in the primordial universe. To study and interpret these datasets we need to know the possible…
In single-field inflationary models with a low sound speed, the orthogonal shape of the primordial bispectrum arises due to partial cancellations between equilateral-type shapes. This fact allows for a speed of sound c_s as low as about…
Inhomogeneous random matrices with non-trivial variance profiles determined by symmetric stochastic matrices and with independent sub-Gaussian entries up to Hermitian symmetry, encompass a wide range of important models, including sparse…
Cosmological solitons are widely predicted by scenarios of the early Universe. In this work, we investigate the isotropic background and anisotropies of gravitational waves (GWs) induced by soliton isocurvature perturbations, especially…
Cosmological inflation generates a spectrum of density perturbations that can seed the cosmic structures we observe today. These perturbations are usually computed as the result of the gravitationally-induced spontaneous creation of…
The squeezed limit of the three-point function of cosmological perturbations is a powerful discriminant of different models of the early Universe. We present a conceptually simple and complete framework to relate any primordial bispectrum…
We point out that a light scalar field fluctuating around a symmetry-enhaced point can generate large non-Gaussianity in density fluctuations. We name such a particle as an "ungaussiton", a scalar field dominantly produced by the quantum…
Recent studies have shown that there is a strong interplay between quantum complexity and quantum chaos. In this work, we consider a new method to study geometric complexity for interacting non-Gaussian quantum mechanical systems to…
We study the evolution of perturbations during the domination and decay of a massive particle species whose mass and decay rate are allowed to depend on the expectation value of a light scalar field. We specialize in the case where the…
An attractive and simple hypothesis for the formation of large-scale structure is that it developed by gravitational instability from primordial fluctuations with an initially Gaussian probability distribution. Non-linear gravitational…
The evolution of cosmological large-scale perturbations is described in terms of the concordant model based on the recent discovery of cosmic vacuum. It is demonstrated that the process is robustly controlled by a few epoch-independent…
We extend the formalism to calculate non-Gaussianity of primordial curvature perturbations produced by preheating in the presence of a light scalar field. The calculation is carried out in the separate universe approximation using the…
With the developments of large galaxy surveys or cosmic shear surveys it is now possible to map the dark matter distribution at truly cosmological scales. Detailed examinations of the statistical properties of the dark matter distribution…
A description of CMB temperature fluctuations beyond the power spectrum is important for verifying models of structure formation, especially in view of forthcoming high-resolution observations. We argue that higher-order statistics of…
Since a positive future detection of non-linearity in the cosmic microwave background anisotropy pattern might allow to descriminate among different mechanisms giving rise to cosmological adiabatic perturbations, we study the evolution of…