Papers by Sergei Winitzki
Lecture Notes in Computer Science, 2003
I consider an arbitrary-precision computation of the incom- plete Gamma function from the Legendr... more I consider an arbitrary-precision computation of the incom- plete Gamma function from the Legendre continued fraction. Using the method of generating functions, I compute the convergence rate of the continued fraction and find a direct estimate of the necessary number of terms. This allows to compare the performance of the continued frac- tion and of the power series methods. As
Lecture Notes in Physics, 2000
In generic models of cosmological inflation, quantum fluctuations strongly influence the spacetim... more 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 the resulting spacetime is highly inhomogeneous on scales of many Hubble sizes. The recently developed string-theoretic picture of the "landscape" presents a similar structure, where an infinite number of de Sitter, flat, and anti-de Sitter universes are nucleated via quantum tunneling. Since observers on the Earth have no information about their location within the eternally inflating universe, the main question in this context is to obtain statistical predictions for quantities observed at a random location. I describe the problems arising within this statistical framework, such as the need for a volume cutoff and the dependence of cutoff schemes on time slicing and on the initial conditions. After reviewing different approaches and mathematical techniques developed in the past two decades for studying these issues, I discuss the existing proposals for extracting predictions and give examples of their applications.
In generic models of cosmological inflation, quantum fluctuations strongly influence the spacetim... more 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 the resulting spacetime is highly inhomogeneous on scales of many Hubble sizes. The recently developed string-theoretic picture of the "landscape" presents a similar structure, where an infinite number of de Sitter, flat, and anti-de Sitter universes are nucleated via quantum tunneling. Since observers on the Earth have no information about their location within the eternally inflating universe, the main question in this context is to obtain statistical predictions for quantities observed at a random location. I describe the problems arising within this statistical framework, such as the need for a volume cutoff and the dependence of cutoff schemes on time slicing and on the initial conditions. After reviewing different approaches and mathematical techniques developed in the past two decades for studying these issues, I discuss the existing proposals for extracting predictions and give examples of their applications.
Phys Rev D, Dec 23, 2001
P and CP violation in cosmology can be manifested as large-scale helical velocity flows in the am... more P and CP violation in cosmology can be manifested as large-scale helical velocity flows in the ambient plasma and as primordial helical magnetic fields. We show that kinetic helicity at last scattering leads to temperature-polarization correlations ($C_l^{TB}$ and $C_l^{EB}$) in the cosmic microwave background radiation (CMBR) and calculate the magnitude of the effect. Helical primordial magnetic fields, expected from cosmic events such as electroweak baryogenesis, can lead to helical velocity flows and hence to non-vanishing correlations of the temperature and B-type polarization. However we show that the magnitude of the induced helical flow is unobservably small because the helical component of a magnetic field is almost force-free. We discuss an alternate scheme for extracting the helicity of a stochastically homogeneous and isotropic primordial magnetic field using observations of the CMBR. The scheme involves constructing Faraday rotation measure maps of the CMBR and thus determining the sum of the helical and non-helical components of the primordial magnetic field. The power spectrum of B-type polarization fluctuations, on the other hand, are sensitive only to the non-helical component of the primordial magnetic field. The primordial magnetic helicity can then be derived by combining these two sets of observations.
Tidal charged spherically symmetric vacuum brane black holes are characterized by their mass m an... more Tidal charged spherically symmetric vacuum brane black holes are characterized by their mass m and tidal charge q, an imprint of the 5-dimensional Weyl curvature. For q > 0 they are formally identical to the Reissner-Nordström black hole of general relativity. We study the thermodynamics and thermodynamic geometries of tidal charged black holes and discuss similarities and differences as compared to the Reissner-Nordström black hole. As a similarity, we show that (for q > 0) the heat capacity of the tidal charged black hole diverges on a set of measure zero of the parameter space, nevertheless both the regularity of the Ruppeiner metric and a Poincaré stability analysis shows no phase transition at those points. The thermodynamic state spaces being different indicates that the underlying statistical models could be different.
I consider the question of possible observability of the total number of e-folds accumulated duri... more I consider the question of possible observability of the total number of e-folds accumulated during the epoch of inflation. The total number of observable e-folds has been previously constrained by the de Sitter entropy after inflation, assuming that the null energy condition (NEC) holds. The NEC is violated by upward fluctuations of the local Hubble rate H, which occur with high probability in the fluctuation-dominated regime of inflation. These fluctuations lead at late times to the formation of black holes and thus limit the observability of inflationary evolution. I compute the average number ∆N of e-folds accumulated during the last NEC-preserving fragment of the inflationary trajectory before reheating. This is the maximum number of inflationary e-folds that can be observed in principle through measurements of the CMB at arbitrarily late times (if the dark energy disappears). The calculation also provides a reasonably precise definition of the boundary of the fluctuation-dominated regime, with an uncertainty of a few percent. In simple models of single-field inflation compatible with current CMB observations, I find ∆N of order 10 5 . This upper bound on the observable e-folds, although model-dependent, is much smaller than the de Sitter entropy after inflation. The method of calculation can be used in other models of single-field inflation.
Introduction to Quantum Effects in Gravity, 2007
Introduction to Quantum Effects in Gravity, 2007
Lecture Notes in Computer Science, 2002
Introduction to Quantum Effects in Gravity, 2007
Introduction to Quantum Effects in Gravity, 2007
Uploads
Papers by Sergei Winitzki
In this book, I discuss the long-standing technical and conceptual problems arising within this statistical framework, known collectively as the “measure problem” in multiverse cosmology. After reviewing various existing approaches and mathematical techniques developed in the past two decades for studying these issues, I describe a new proposal for a measure in the multiverse, called the reheating-volume (RV) measure. The RV measure is based on approximating an infinite multiverse by a family of progressively larger but finite multiverses. Such multiverses occur seldom but are allowed by all cosmological “multiverse” models. I give a detailed description of the new measure and its applications to generic models of eternal inflation of random-walk type and to landscape scenarios. The RV prescription is formulated differently for scenarios with eternal inflation of the random walk type and for landscape scenarios. For models of random-walk inflation, the RV cutoff considers events where one has a finite (although large) total reheating volume to the future of an initial Hubble patch. For landscape scenarios, I propose to calculate the distribution of observable quantities in a landscape that is conditioned in probability to nucleate a finite total number of bubbles to the future of an initial bubble. In each case I show in a mathematically rigorous manner that the RV measure yields well-defined results that are invari- ant with respect to general coordinate transformations, independent of the initial conditions at the beginning of inflation, and free of the “youngness paradox” and the “Boltzmann brain” problems affecting some of the previously proposed measures. I derive analytic formulas for RV-regulated probability distributions that is suitable for numerical computations.