Related papers: The empirical process on Gaussian spherical harmon…
We consider several ways to test for topology directly in harmonic space by comparing the measured a_lm with the expected correlation matrices. Two tests are of a frequentist nature while we compute the Bayesian evidence as the third test.…
We address the characterization of classical fractional random noise via quantum probes. In particular, we focus on estimation and discrimination problems involving the fractal dimension of the trajectories of a system subject to fractional…
Identifying the anisotropies in a cosmologically sourced stochastic gravitational wave background (SGWB) would be of significance in shedding light on the nature of primordial inhomogeneities. For example, if SGWB carries isocurvature…
Recent measurements of the cosmic microwave background radiation by the Boomerang experiment indicate that the universe is spatially flat. Here some simple back-of-the-envelope calculations are used to explain their result. The main result…
We study the concentration of ladder sequences of spherical harmonics on caustic latitude circles. We prove that they have Airy scaling asymptotics. We also determine the weak* limit of certain empirical measures of $L^2$ norms of…
This paper studies random fields on the unit sphere. Traditionally, isotropic Gaussian random fields are considered as the underlying statistical model of the cosmic microwave background (CMB) data. This paper discusses the generalized…
The interferometry-based experimental tests of quantum properties of space-time which the author sketched out in a recent short Letter [Nature 398 (1999) 216] are here discussed in self-contained fashion. Besides providing detailed…
We investigate the ability to constrain oscillatory features in the primordial power spectrum using current and future cosmic microwave background observations. In particular, we study the observability of an oscillation arising from…
We study the representations of tensor random fields on the sphere basing on the theory of representations of the rotation group. Introducing specific components of a tensor field and imposing the conditions of weak isotropy and mean square…
The Stochastic Gravitational Wave Background (SGWB) is expected to be a key observable for Gravitational Wave (GW) interferometry. Its detection will open a new window on early universe cosmology and on the astrophysics of compact objects.…
The current effort to test General Relativity employs multiple disparate formalisms for different observables, obscuring the relations between laboratory, astrophysical and cosmological constraints. To remedy this situation, we develop a…
Recent gravitational wave observations show evidence for the presence of higher harmonics, thus possibly indicating that these waves were generated in the inspiral of compact objects with asymmetric mass ratios. Signals with higher…
Gravitational waves in isotropic cosmologies were recently studied using the gauge-invariant approach of Ellis-Bruni. We now construct the linearised metric perturbations of the background Robertson-Walker space-time which reproduce the…
This paper discusses sparse isotropic regularization for a random field on the unit sphere $\mathbb{S}^2$ in $\mathbb{R}^{3}$, where the field is expanded in terms of a spherical harmonic basis. A key feature is that the norm used in the…
We present a topological multiple testing scheme for detecting peaks on the sphere under isotropic Gaussian noise, where tests are performed at local maxima of the observed field filtered by the spherical needlet transform. Our setting is…
Pulsar timing arrays aim to detect nanohertz-frequency gravitational waves (GWs). A background of GWs modulates pulsar arrival times and manifests as a stochastic process, common to all pulsars, with a signature spatial correlation. Here we…
Limit theorems are proved for quadratic forms of Gaussian random fields in presence of long memory. We obtain a non central limit theorem under a minimal integrability condition, which allows isotropic and anisotropic models. We apply our…
We investigate a particular form of weak convergence of the local empirical process.
In the framework of the recently proposed asymptotically finite gauge models the cosmological constant is essentially weakened by quantum effects. The next (and more general) claim is that the coupling between quantum fields may suppress…
The claim by Gurzadyan et al. that the cosmological sky is a weakly random one where "the random perturbation is a minor component of mostly regular signal" has given rise to a series of useful exchanges. The possibility that the Cosmic…