Related papers: Towards a gauge invariant volume-weighted probabil…
In this work, we study convergence in probability and almost sure convergence for weighted partial sums of random variables that are related to the class of generalized Oppenheim expansions. It is worth noting that the random variables…
The phenomenon of stochastic eternal inflation is studied for a chaotic inflation potential in a Bianchi Type I spacetime background. After deriving the appropriate stochastic Klein-Gordon equation, we give details on the conditions for…
We give a formal proof that the space-time average of the vacuum condensate of mass dimension two, i.e., the vacuum expectation value of the squared potential $\mathscr{A}_\mu^2$, is gauge invariant in the weak sense that it is independent…
It is well known that the space of invariant probability measures for transitive sub-shifts of finite type is a Poulsen simplex. In this article we prove that in the non-compact setting, for a large family of transitive countable Markov…
Motivated by the gauge theory of gravity with local scaling symmetry proposed recently in 1712.04537 and 1506.01807, we investigate whether the scalar field therein can be responsible for the inflation. We show that the classical theory…
We propose a topological inflation model in the framework of supergravity with $R$ invariance. This topological inflation model is not only free from the initial value problem of the inflaton field but also gives low reheating temperature…
Current bounds from the polarization of the CMB predict the scale-invariant gravitational wave (GW) background of inflation to be out of reach for upcoming GW interferometers. This prospect dramatically changes if the inflaton is a…
In this article, we study the pressure at infinity of potentials defined over countable Markov shifts. We establish an upper semi-continuity result concerning the limiting behaviour of the pressure of invariant probability measures, where…
We construct ergodic probability measures with infinite metric entropy for typical continuous maps and homeomorphisms on compact manifolds. We also construct sequences of such measures that converge to a zero-entropy measure.
Experiments and simulations in solid-state high harmonic generation often make use of the distinction between interband and intraband currents. These two contributions to the total current have been associated with qualitatively different…
In generic models of cosmological inflation, quantum fluctuations strongly influence the spacetime metric and produce infinitely many regions where the end of inflation (reheating) is delayed until arbitrarily late times. The geometry of…
We address the question how to adapt cosmological constant $\Lambda$ for description of a vacuum dark energy density jumping from the big initial value to the small today value suggested by observations. We find such a possibility in the…
We study an inflationary scenario in supergravity model with a gauge kinetic function. We find exact anisotropic power-law inflationary solutions when both the potential function for an inflaton and the gauge kinetic function are…
Let $k \ge 1$ be an integer and $f$ a holomorphic endomorphism of $\mathbb P^k (\mathbb C)$ of algebraic degree $d\geq 2$. We introduce a volume dimension for ergodic $f$-invariant probability measures with strictly positive Lyapunov…
We investigate gauge invariant scalar fluctuations of the metric during inflation in a non-perturbative formalism in the framework of a recently introduced scalar-tensor theory of gravity formulated on a Weyl-Integrable geometry. We found…
This paper introduces a measure or statistics invariant through the flow of the Benjamin-Bona-Mahony equation and studies its stability, regarding a specific class of perturbation and in the idea of the wave turbulence theory.
Cosmological inflation, if it occurred, radically alters the picture of the `big bang', which would merely point to reheating at the end of inflation. Moreover, this reheating may be only local, so that inflation continues elsewhere and…
Problems with uniform probabilities on an infinite support show up in contemporary cosmology. This paper focuses on the context of inflation theory, where it complicates the assignment of a probability measure over pocket universes. The…
A direct detection of primordial gravitational waves is the ultimate probe for any inflation model. While current CMB bounds predict the generic scale-invariant gravitational wave spectrum from slow-roll inflation to be below the reach of…
In this pedagogical note, I present a method for constructing a fully covariant normal coordinate expansion of the gauge potential on a curved space-time manifold. Although the content of this paper is elementary, the results may prove…