arXiv subjects

Siméon Vareilles

Publications and source records attributed to Siméon Vareilles.

4 recordsLinked to original sources

arXiv2026

Universal CMB Phase Coherence from Single-Field Inflation

The phase coherence of primordial perturbations shapes the acoustic peaks of the CMB and is regarded as a key signature of inflation. Inflationary scenarios at different energy scales, thus with different durations, are commonly expected to leave different levels of coherence. We show this expectation fails: because the curvature perturbation is conserved on super-Hubble scales, the coherence at recombination inherits a value fixed by the observed primordial spectrum alone. This holds irrespective of the inflationary energy scale and the subsequent expansion history.

astro-ph.CO↗

arXiv2026

Closed-form linear moments of the two-dimensional angular central Gaussian distribution

The polar-angle marginal of a centred bivariate Gaussian distribution, obtained after integrating out the radial coordinate, gives the two-dimensional angular central Gaussian (ACG) distribution of Tyler. While its trigonometric and vector-valued moments have been studied in detail, to our knowledge there are no explicit closed-form expressions for the \emph{linear} moments $\mathbf{E}[θ]$ and $\mathbf{E}[θ^{2}]$ on the natural domain $θ\in\left]-π/2,π/2\right[$. Here \textit{linear} refers to the ordinary moments $\intθ^{k}f(θ)\,dθ$ of the angle regarded as a real-valued variable, in contrast to the circular (trigonometric) moments $\mathbf{E}[e^{ikθ}]$ customary in directional statistics. We provide such expressions: the mean is a simple arctangent of the parameters, while the second moment is given by the real part of a dilogarithm. The derivation, based on a contour integration around the branch cut of $\arctan z$, is elementary. These quantities naturally arise in physics, where $θ$ is interpreted as a real-valued phase rather than a circular variable.

math.ST↗

arXiv2026

Time as a test-field: the no-boundary universe in motion and a smooth radiation bounce

The proper time of an observer can be introduced as a degree of freedom in quantum cosmology, additional to the existing fields. We review two arguments for using the Schrödinger equation to evolve the corresponding wavefunction. We restrict to solutions in which time acts as a component with negligible backreaction on the metric -- that is, it plays the role of a test field. We apply this idea to various minisuperspace models. In the semiclassical regime we recover expected results: the wavefunction peaks on the classical solution and, in models with a scalar field, the variance of $ζ$ (a mini-superspace analogue of the comoving curvature perturbation) is conserved. Applied to the no-boundary wavefunction, our model recovers the bouncing behavior of classical global de Sitter space, with small corrections associated to the evolving variance of the wavefunction. Other bouncing solutions do not have any classical analogue. This is the case of a radiation dominated universe, which classically leads to a big-bang singularity but corresponds quantum mechanically to an $s$-wave scattering off a central potential of the form $-r^{-2/3}$. As much as the hydrogen atom, this potential is famously made stable by the Heisenberg uncertainty principle. We study the unitary evolution of the wavepacket numerically. During the bounce, the uncertainty and the expectation value of the scale factor become comparable. By selecting a large initial variance, the bounce can be made arbitrarily smooth, the mean value of the Hubble parameter correspondingly soft.

hep-th↗

arXiv2025

Cosmological perturbations meet Wheeler DeWitt

We study approximate solutions of the Wheeler DeWitt (WdW) equation and compare them with the standard results of cosmological perturbation theory. In mini-superspace, we introduce a dimensionless gravitational coupling $α$ that is typically very small and functions like $\hbar$ in a WKB expansion. We seek solutions of the form $Ψ= e^{iS/α} ψ$ that are the closest quantum analog of a given classical background spacetime. The function $S$ satisfies the Hamilton-Jacobi equation, while $ψ$ obeys a Schrödinger-like equation and can be given a probabilistic interpretation. The semiclassical limit suggests a specific relation between $ψ$ and the standard perturbation-theory wavefunction $ψ_P$. We verify this relation in two main examples: a scalar field with a purely exponential potential, of which simple scaling solutions are known and a slow-roll scenario expanded in the vicinity of the origin in field space. Each example is worked out in two different gauges, that are the minisuperspace equivalent of unitary gauge and spatially flat gauge. We discuss possible deviations from the classical background trajectory as well as the higher ``time" derivative terms that are present in the WdW equation but not in the perturbative approach. We clarify the \emph{conditional probability} content of the wavefunctions and how this is related with the standard gauge fixing procedure in perturbation theory.

hep-th↗