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Shell models provide a simplified mathematical framework that captures essential features of incompressible fluid turbulence, such as the energy cascade and scaling of the fluid observables. We perform a precision analysis of the direct and inverse cascades in shell models of turbulence, where the velocity field is a real-valued function. We calculate the leading hundred anomalous scaling exponents, the marginal probability distribution functions of the velocity field at different shells, as well as the correlations between different shells. We find that the structure functions in both cascades exhibit a linear Kolomogorov scaling in the inertial range. We argue that the underlying reason for having no intermittency, is the strong correlations between the velocity fields at different shells. We analyze the tails of velocity distribution functions, which offer new insights to the structure of fluid turbulence.

We study the decay of the false vacuum in the regime where the quantum field theory analysis is not valid, since gravitational effects become important. This happens when the height of the barrier separating the false and the true vacuum is large, and it has implications for the instability of de Sitter, Minkowski and anti-de Sitter vacua. We carry out the calculations for a scalar field with a potential coupled to gravity, and work within the thin-wall approximation, where the bubble wall is thin compared to the size of the bubble. We show that the false de Sitter vacuum is unstable, independently of the height of the potential and the relative depth of the true vacuum compared to the false vacuum. The false Minkowski and anti-de Sitter vacua can be stable despite the existence of a lower energy true vacuum. However, when the relative depth of the true and false vacua exceeds a critical value, which depends on the potential of the false vacuum and the height of the barrier, then the false Minkowski and anti-de Sitter vacua become unstable. We calculate the probability for the decay of the false de Sitter, Minkowski and anti-de Sitter vacua, as a function of the parameters characterizing the field potential., Comment: 18 pages, 4 figures

Shell model turbulence is a simplified mathematical framework that captures essential features of incompressible fluid turbulence such as the energy cascade, intermittency and anomalous scaling of the fluid observables. We perform a precision analysis of shell model of a complex velocity field in the steady state turbulent regime, including a calculation of the leading hundred anomalous scaling exponents, the probability distribution function of the magnitude and phase of the velocity and the correlations among them at different shells. We analyze the tail of velocity distribution function and find that the high moments exhibit a linear scaling that differs from Kolomogorov's. We explain the origin of this asymptotic scaling that offers a new insight to the structure of fluid turbulence., Comment: 9 pages, 9 figures

It is shown how self-reproduction can be easily avoided in the inflationary universe, even when inflation starts at Planck scales. This is achieved by a simple coupling of the inflaton potential with a mimetic field. In this case, the problem of fine-tuning of the initial conditions does not arise, while eternal inflation and the multiverse with all their widely discussed problems are avoided., Comment: 19 pages, 1 figure

We identify an infinite class of unbounded potentials for which the Coleman instantons do not exist in D-dimensional spacetime. For such potentials, the decay of a false vacuum is described by the new instantons introduced in [5,6,4]. For each spacetime dimension D, we also construct the two different classes of potentials for which the instanton equations are exactly solvable., Comment: 5 pages, LaTeX

We assume that the points in volumes smaller than an elementary volume (which may have a Planck size) are indistinguishable in any physical experiment. This naturally leads to a picture of a discrete space with a finite number of degrees of freedom per elementary volume. In such discrete spaces, each elementary cell is completely characterized by displacement operators connecting a cell to the neighboring cells and by the spin connection. We define the torsion and curvature of the discrete spaces and show that in the limiting case of vanishing elementary volume the standard results for the continuous curved differentiable manifolds are completely reproduced., Comment: 13 pages

We consider new instantons that appear as a result of accounting for quantum fluctuations. These fluctuations naturally regularize the O(4) singular solutions abandoned in Coleman's theory. In the previous works [3,4] we showed how new instantons modify the widely accepted picture of false vacuum decay in two particular examples of exactly solvable potentials. Here we generalize our consideration to arbitrary potentials and provide a general theory of these new instantons with quantum cores in which vacuum fluctuations dominate. We develop a method that allows us to determine the parameters of instantons for generic potentials not only in the thin-wall approximation but also in the cases where this approximation fails. Unlike the Coleman instantons, the instantons with quantum cores always exist in the cases where the vacuum must be unstable., Comment: 20 pages, LaTeX, 8 figures

We identify infinite classes of potentials for which the Coleman instantons do not exist. For these potentials, the decay of a false vacuum must be described by the new instantons introduced in [7,8]., Comment: 6 pages, LaTeX, 2 figures

We study the fate of a false vacuum in the case of a potential that contains a portion which is quartic and unbounded. We first prove that an $O(4)$ invariant instanton with the Coleman boundary conditions does not exist in this case. This, however, does not imply that the false vacuum does not decay. We show how the quantum fluctuations may regularize the singular classical solutions. This gives rise to a new class of $O(4)$ invariant regularized instantons which describe the vacuum instability in the absence of the Coleman instanton. We derive the corresponding solutions and calculate the decay rate they induce., Comment: 13 pages, LaTeX, 2 figures

We consider the decay of a false vacuum in circumstances where the methods suggested by Coleman run into difficulties. We find that in these cases quantum fluctuations play a crucial role. Namely, they naturally induce both an ultraviolet and infrared cutoff scales, determined by the parameters of the classical solution, beyond which this solution cannot be trusted anymore. This leads to the appearance of a broad class of new $O(4)$ invariant instantons, which would have been singular in the absence of an ultraviolet cutoff. We apply our results to a case where the potential is unbounded from below in a linear way and in particular show how the problem of small instantons is resolved by taking into account the inevitable quantum fluctuations., Comment: 16 pages, LaTeX, 3 figures

The recently proposed theory of "Asymptotically Free Mimetic Gravity" is extended to the general non-homogeneous, spatially non-flat case. We present a modified theory of gravity which is free of higher derivatives of the metric. In this theory asymptotic freedom of gravity implies the existence of a minimal black hole with vanishing Hawking temperature. Introducing a spatial curvature dependent potential, we moreover obtain non-singular, bouncing modifications of spatially non-flat Friedmann and Bianchi universes., Comment: 55 pages, 3 figures

We show that in asymptotically free mimetic gravity with limiting curvature the black hole singularity can be resolved and replaced by a static patch of de Sitter space. As a result of Hawking evaporation of these non-singular black holes, there remain stable remnants with vanishing Hawking temperature., Comment: 4 pages

We show that the scalar field of mimetic gravity could be used to construct diffeomorphism invariant models that reduce to Horava gravity in the synchronous gauge. The gradient of the mimetic field provides a timelike unit vector field that allows to define a projection operator of four-dimensional tensors to three-dimensional spatial tensors. Conversely, it also enables us to write quantities invariant under space diffeomorphisms in fully covariant form without the need to introduce new propagating degrees of freedom., Comment: 8 pages, comments about renormalizability of the model added. Matches version to be published in Physics Letters B

The idea of "asymptotically free" gravity is implemented using a constrained mimetic scalar field. The effective gravitational constant is assumed to vanish at some limiting curvature. As a result singularities in contracting spatially flat Friedmann and Kasner universes are avoided. The solutions in both cases approach de Sitter metric with a limiting curvature.We show that quantum metric fluctuations vanish when this limiting curvature is approached., Comment: 14 pages

In 1974 Jacob Bekenstein has noticed that the area of the black hole behaves as adiabatic invariant and hence most likely must be quantized in integers of the Planckian area. In these notes I will present the arguments which led him and myself to such conclusion and will discuss the consequences of the black hole quantization., Comment: Jacob Bekenstein Memorial Volume, to be published by World Scientific Publishing

We present a theory of ghost-free massive gravity where the mass of the graviton is generated through the Brout-Englert-Higgs (BEH) mechanism and one of the four scalar fields used is that of mimetic gravity. The mass term is not of the Fierz-Pauli type and the constraint eliminates the Boulware-Deser ghost which is absent to all orders. We perform a detailed analysis using the methods of cosmological perturbation theory and consider quantum fluctuations of the degrees of freedom of massive graviton and mimetic matter. It is shown that for three of the degrees of freedom of the graviton of mass $m$ the nonlinear corrections become comparable to the linear terms already at a length scale of order $m^{-\frac{1}{2}}$. Thus, at smaller scales they become strongly coupled and the graviton remains with two transverse degrees of freedom which get strongly coupled only at Planck scale. The mimetic field behaves as cold particles of half of the graviton mass and could well explain the source of dark matter in our universe. In the weakly coupled domain mimetic matter is completely decoupled from the massive graviton., Comment: 25 pages

The mass of the graviton can be generated using a Brout-Englert-Higgs mechanism with four scalar fields. We show that when one of these fields is costrained as in mimetic gravity, the massive gravity obtained is ghost free and consistent. The mass term is not of the Fierz-Pauli type. There are only five degrees of freedom and the sixth degree of freedom associated with the Boulware-Deser ghost is constrained and replaced by mimetic matter to all orders. The van Dam-Veltman-Zakharov discontinuity is also absent., Comment: 3 pages. One sentence corrected in abstract and one reference added

We consider the Schwarzschild black hole and show how, in a theory with limiting curvature, the physical singularity "inside it" is removed. The resulting spacetime is geodesically complete. The internal structure of this nonsingular black hole is analogus to Russian nesting dolls. Namely, after falling into the black hole of radius $r_{g}$, an observer, instead of being destroyed at the singularity, gets for a short time into the region with limiting curvature. After that he re-emerges in the near horizon region of a spacetime described by the Schwarzschild metric of a gravitational radius proportional to $r_{g}^{1/3}$. In the next cycle, after passing the limiting curvature, the observer finds himself within a black hole of even smaller radius proportional to $r_{g}^{1/9}$, and so on. Finally after few cycles he will end up in the spacetime where he remains forever at limiting curvature., Comment: 21 pages

We find a simple modification of the longitudinal mode in General Relativity which incorporates the idea of limiting curvature. In this case the singularities in contracting Friedmann and Kasner universes are avoided, and instead, the universe has a regular bounce which takes place during the time inversely proportional to the square root of the limiting curvature. Away from the bounce, corrections to General Relativity are negligible. In addition the non-singluar modification of General Relativity delivers for free a realistic candidate for Dark Matter., Comment: 15 pages

Considering a higher dimensional Lorentz group as the tangent symmetry, we unify gravity and gauge interactions in a natural way. The spin connection of the gauged Lorentz group is then responsible for both gravity and gauge fields, and the action for the gauged fields becomes part of the spin curvature squared. The realistic group which unifies all known particles and interactions is the $SO(1,13)$ Lorentz group whose gauge part leads to $SO(10)$ grand unified theory and contains double the number of required fermions in the fundamental spinor representation. Mirror fermions could acquire mass utilizing a mechanism employed for topological superconductors. Family unification could be achieved by considering the $SO(1,21)$ Lorentz group., Comment: 17 pages. Mirror fermions now acquire masses utilizing a mechanism employed for topological superconductors

We modify Einstein General Relativity by adding non-dynamical scalar fields to account simultaneously for both dark matter and dark energy. The dark energy in this case can be distributed in-homogeneously even within horizon scales. Its inhomogeneities can contribute to the late time integrated Sachs-Wolfe effect, possibly removing some of the low multipole anomalies in the temperature fluctuations of the CMB spectrum. The presence of the inhomogeneous dark matter also influences structure formation in the universe., Comment: 11 pages

We study the validity of the Newtonian description of cosmological perturbations using the Lemaitre model, an exact spherically symmetric solution of Einstein's equation. This problem has been investigated in the past for the case of a dust fluid. Here, we extend the previous analysis to the more general case of a fluid with non-negligible pressure, and, for the numerical examples, we consider the case of radiation (P=\rho/3). We find that, even when the density contrast has a nonlinear amplitude, the Newtonian description of the cosmological perturbations using the gravitational potential \psi and the curvature potential \phi is valid as long as we consider sub-horizon inhomogeneities. However, the relation \psi+\phi={\cal O}(\phi^2), which holds for the case of a dust fluid, is not valid for a relativistic fluid and effective anisotropic stress is generated. This demonstrates the usefulness of the Lemaitre model which allows us to study in an exact nonlinear fashion the onset of anisotropic stress in fluids with non-negligible pressure. We show that this happens when the characteristic scale of the inhomogeneity is smaller than the sound horizon and that the deviation is caused by the nonlinear effect of the fluid's fast motion. We also find that \psi+\phi= \max[{\cal O}(\phi^2),{\cal O}(c_s^2\phi \, \delta)] for an inhomogeneity with density contrast \delta whose characteristic scale is smaller than the sound horizon, unless w is close to -1, where w and c_s are the equation of state parameter and the sound speed of the fluid, respectively. On the other hand, we expect \psi+\phi={\cal O}(\phi^2) to hold for an inhomogeneity whose characteristic scale is larger than the sound horizon, unless the amplitude of the inhomogeneity is large and w is close to -1., Comment: 23 pages, 7 figures. Version accepted for publication in JCAP

Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation appears in two versions, one sided and two sided. It implies the quantization of the volume. In the one-sided case it implies that the manifold decomposes into a disconnected sum of spheres which will represent quanta of geometry. The two sided version in dimension 4 predicts the two algebras M_2(H) and M_4(C) which are the algebraic constituents of the Standard Model of particle physics. This taken together with the non-commutative algebra of functions allows one to reconstruct, using the spectral action, the Lagrangian of gravity coupled with the Standard Model. We show that any connected Riemannian Spin 4-manifold with quantized volume >4 (in suitable units) appears as an irreducible representation of the two-sided commutation relations in dimension 4 and that these representations give a seductive model of the "particle picture" for a theory of quantum gravity in which both the Einstein geometric standpoint and the Standard Model emerge from Quantum Mechanics. Physical applications of this quantization scheme will follow in a separate publication., Comment: 33 pages, 2 figures

In the construction of spectral manifolds in noncommutative geometry, a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of real scalar fields naturally appears and implies, by equality with the index formula, the quantization of the volume. We first show that this condition implies that the manifold decomposes into disconnected spheres which will represent quanta of geometry. We then refine the condition by involving the real structure and two types of geometric quanta, and show that connected spin-manifolds with large quantized volume are then obtained as solutions. The two algebras M_2(H) and M_4(C) are obtained which are the exact constituents of the Standard Model. Using the two maps from M_4 to S^4 the four-manifold is built out of a very large number of the two kinds of spheres of Planckian volume. We give several physical applications of this scheme such as quantization of the cosmological constant, mimetic dark matter and area quantization of black holes., Comment: 4 pages. Title modified. Letter rewritten to be understandable by a wider audience. To appear in Physical Review Letters

We find a rather unique extension of inflationary scenario which avoids selfreproduction and thus resolves the problems of multiverse, predictability and initial conditions. In this theory the amplitude of the cosmological perturbations is expressed entirely in terms of the total duration of inflation.

We consider minimal extensions of the recently proposed Mimetic Dark Matter and show that by introducing a potential for the mimetic non-dynamical scalar field we can mimic nearly any gravitational properties of the normal matter. In particular, the mimetic matter can provide us with inflaton, quintessence and even can lead to a bouncing nonsingular universe. We also investigate the behaviour of cosmological perturbations due to a mimetic matter. We demonstrate that simple mimetic inflation can produce red-tilted scalar perturbations which are largely enhanced over gravity waves., Comment: 19 pages

We reformulate Einstein's theory of gravity, isolating the conformal degree of freedom in a covariant way. This is done by introducing a physical metric defined in terms of an auxiliary metric and a scalar field appearing through its first derivatives. The resulting equations of motion split into a traceless equation obtained through variation with respect to the auxiliary metric and an additional differential equation for the trace part. As a result the conformal degree of freedom becomes dynamical even in the absence of matter. We show that this extra degree of freedom can mimic cold dark matter., Comment: 5 pages

General relativity can be unambiguously formulated with Lorentz, de Sitter and anti-de Sitter tangent groups, which determine the fermionic representations. We show that besides of the Lorentz group only anti-de Sitter tangent group is consistent with all physical requirements., Comment: 6 pages

I consider the generic model independent predictions of the theory of quantum cosmological perturbations. To describe the stage of cosmic inflation, where these perturbations are amplified, the hydrodynamical approch is used. The inflationary stage is completely characterized by the deviation of the equation of state from cosmological constant which is a smooth function of the number of e-folds until the end of inflation. It is shown that in this case the spectral index should deviate from the flat one at least by 3 percent irrespective of any particular scenario. Given the value of the spectral index the lower bound on the amount of the gravitational waves produced is derived. Finally the relation between effective hydrodynamical description of inflation and inflationary scenarios is discussed.

The Hessian's determinant for a version of massive gravity given by an infinite expansion of a square root function of the induced metric, vanishes. We show that it allows us to eliminate one of four scalar fields used to generate the graviton mass. This, however, gives rise to the appearance of extra terms in the action with the squared time derivative of the metric, thus signaling that a nonlinear ghost survives.We demonstrate this phenomenon considering a simple system with constraint, which is supposed to reduces the number of physical degrees of freedom, however, we explicitly show how the constraint forces the metric to propagate an extra tachyonic state., Comment: 17 pages

Recent progress in observational cosmology, and especially the forthcoming PLANCK mission data, open new directions in so-called precision cosmology. In this paper we illustrate this statement considering the accuracy of cosmological determination of the two-quanta decay rate of 2s hydrogen atom state. We show that the PLANCK data will allow us to measure this decay rate significantly better than in the laboratory experiments., Comment: v2: matched with the version accepted in JCAP (minor changes)

Einstein-Strauss Hermitian gravity was recently formulated as a gauge theory where the tangent group is taken to be the pseudo-unitary group instead of the orthogonal group. A Higgs mechanism for massive gravity was also formulated. We generalize this construction to obtain massive Hermitian gravity with the use of a complex Higgs multiplet. We show that both the graviton and antisymmetric tensor acquire the same mass. At the linearized level, the theory is ghost free around Minkowski background and describes a massive graviton with five degrees of freedom and an antisymmetric field with three degrees of of freedom. We determine the strong coupling scales for these degrees of freedom and argue that the potential nonlinear ghosts, if they exist, have to decouple from the gravitational degrees of freedom in strong coupling regime., Comment: 10 pages

We present a simplified formulation of massive gravity where the Higgs fields have quadratic kinetic term. This new formulation allows us to prove in a very explicit way that all massive gravity theories considered so far inevitably have Boulware-Deser ghost in non-trivial fluctuations of background metric., Comment: 8 pages, paragraph added proving that Bianchi identity does not imply vanishing of linearized curvature

We discuss observational consequences of the curvaton scenario, which naturally appears in the context of the simplest model of chaotic inflation in supergravity. The non-gaussianity parameter f_NL in this scenario can take values in the observationally interesting range from O(10) to O(100). These values may be different in different parts of the universe. The regions where f_NL is particularly large form a curvaton web resembling a net of thick domain walls, strings, or global monopoles., Comment: 17 pages, 1 figure. Non-perturbative effects related to non-gaussianity in the curvaton scenario are discussed, some references are added. This is the version accepted in JCAP

We consider Higgs massive gravity [1,2] and investigate whether a nonlinear ghost in this theory can be avoided. We show that although the theory considered in [10,11] is ghost free in the decoupling limit, the ghost nevertheless reappears in the fourth order away from the decoupling limit. We also demonstrate that there is no direct relation between the value of the Vainshtein scale and the existence of nonlinear ghost. We discuss how massive gravity should be modified to avoid the appearance of the ghost., Comment: 16 pages

We consider the massless limit of Higgs gravity, where the graviton becomes massive when the scalar fields acquire expectation values. We determine the Vainshtein scale and prove that massive gravity smoothly goes to General Relativity below this scale. We find that the Vainshtein scale depends on the particular action of scalar fields used to give mass to the graviton., Comment: 21 pages,references added

A Higgs mechanism for gravity is presented, where four scalars with global Lorentz symmetry are employed. We show that in the broken symmetry phase a graviton absorbs all scalars and become massive spin 2 particle with five degrees of freedom. The resulting theory is unitary and free of ghosts., Comment: 8 pages, References added. The decoupling of ghost state is analyzed in detail.

Einstein Gravity can be formulated as a gauge theory with the tangent space respecting the Lorentz symmetry. In this paper we show that the dimension of the tangent space can be larger than the dimension of the manifold and by requiring the invariance of the theory with respect to 5d Lorentz group (de Sitter group) Einstein theory is reproduced unambiguously. The other possibility is to have unitary symmetry on a complex tangent space of the same dimension as the manifold. In this case the resultant theory is Einstein-Strauss Hermitian gravity. The tangent group is important for matter couplings. We show that in the de Sitter case the 4 dimensional space time vector and scalar are naturally unified by a hidden symmetry being components of a 5d vector in the tangent space. With a de Sitter tangent group spinors can exist only when they are made complex or taken in doublets in a way similar to N=2 supersymmetry., Comment: 23 pages, one reference added.To be published in JHEP

We consider the possibility of generation of the seeds of primordial magnetic field on inflation and show that the effect of the back reaction of this field can be very important. Assuming that back reaction does not spoil inflation we find a rather strong restriction on the amplitude of the primordial seeds which could be generated on inflation. Namely, this amplitude recalculated to the present epoch cannot exceed $10^{-32}G$ in $Mpc$ scales. This field seems to be too small to be amplified to the observable values by galactic dynamo mechanism., Comment: 10 pages

We discuss the gravitational waves (GW) in the context of vector inflation. We derive the action for tensor perturbations and find that tachyonic instabilities are present in most (but not all) of the inflationary models with large fields. In contrast, the stability of the small field inflation ($A_{\mu}A^{\mu}\ll\frac{1}{N}$) is ensured by the usual slow-roll conditions, where $N$ is the total number of fields. For example, the Coleman-Weinberg potential and the power-law inflation are always stable in the small fields limit with an approximately flat spectrum of GW. We also provide some examples which lead to a rapid decay of GW and predict the absence of tensor modes in the CMB., Comment: 6 pages

We propose a scenario where inflation is driven by non-minimally coupled massive vector fields. In an isotropic homogeneous universe these fields behave in presicely the same way as a massive minimally coupled scalar field. Therefore our model is very similar to the model of chaotic inflation with scalar field. For vector fields the isotropy of expansion is achived either by considering a triplet of orthogonal vector fields or for the expense of $N$ randomly oriented vector fields. In the last case the substantial anisotropy of the expansion of order $1/\sqrt{N}$ survives until the end of inflation. The lightest vector fields might also force the late time acceleration of the Universe., Comment: 6 pages; minor changes

The new ekpyrotic scenario attempts to solve the singularity problem by involving violation of the null energy condition in a model which combines the ekpyrotic/cyclic scenario with the ghost condensate theory and the curvaton mechanism of production of adiabatic perturbations of metric. The Lagrangian of this theory, as well as of the ghost condensate model, contains a term with higher derivatives, which was added to the theory to stabilize its vacuum state. We found that this term may affect the dynamics of the cosmological evolution. Moreover, after a proper quantization, this term results in the existence of a new ghost field with negative energy, which leads to a catastrophic vacuum instability. We explain why one cannot treat this dangerous term as a correction valid only at small energies and momenta below some UV cut-off, and demonstrate the problems arising when one attempts to construct a UV completion of this theory., Comment: 24 pages, 5 figs

The k-essence theories admit in general the superluminal propagation of the perturbations on classical backgrounds. We show that in spite of the superluminal propagation the causal paradoxes do not arise in these theories and in this respect they are not less safe than General Relativity., Comment: 34 pages, 5 figures

In this short talk we review our results from the paper hep-th/0604075 with the main stress on the issues of causality and acoustic metric in eikonal approximation. In addition we correct the formula for the redshift of sound signals from our original work. We show that, if there exists a special kind of Born-Infeld type scalar field, then one can send information from inside a black hole. This information is encoded in perturbations of the field propagating in non-trivial scalar field backgrounds, which serve as a "new ether". Although the action of the theory is manifestly Lorentz-invariant the non-trivial solutions break this symmetry spontaneously, allowing, the superluminal propagation of perturbations with respect to this "new ether". We found the stationary solution for background, which describes the accretion of the scalar field onto a black hole. Examining the propagation of small perturbations around this solution we show that the signals emitted inside the Schwarzschild horizon can reach an observer located outside the black hole. Thus the accreting field forms a hydrodynamical analog of a black hole whose horizon is inside of the gravitational black hole drawing in the scalar field., Comment: To appear in the proceedings of 11th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation, and Relativistic Field Theories, Berlin, Germany, 23-29 Jul 2006

Recently a non-inflationary mechanism of generation of scale-free cosmological perturbations of metric was proposed by Brandenberger, Nayeri, and Vafa in the context of the string gas cosmology. We discuss various problems of their model and argue that the cosmological perturbations of metric produced in this model have blue spectrum with a spectral index n = 5, which strongly disagrees with observations. We conclude that this model in its present form is not a viable alternative to inflationary cosmology., Comment: 11 pages, 1 figure

We discuss nontrivial features of the large scale structure of the universe in the simplest curvaton model proposed in our paper astro-ph/9610219. The amplitude of metric perturbations in this model takes different values in different parts of the universe. The spatial distribution of the amplitude looks like a web consisting of exponentially large cells. Depending on the relation between the cell size l_0 and the scale of the horizon l_H, one may either live in a part of the universe dominated by gaussian perturbations (inside a cell with l_0 >> l_H), or in the universe dominated by nongaussian perturbations (for l_0 << l_H). We show that the curvaton contribution to the total amplitude of adiabatic density perturbations can be strongly suppressed if the energy density of the universe prior to the curvaton decay was dominated not by the classical curvaton field but by the curvaton particles produced during reheating. We describe the curvaton-inflaton transmutation effect: The same field in different parts of the universe may play either the role of the curvaton or the role of the inflaton. Finally, we discuss an interplay between the curvaton web and anthropic considerations in the string theory landscape., Comment: 15 pages, 3 figures, references added, discussion of long-wavelenth perturbations expanded

We explain why it is so difficult and perhaps even impossible to increase the cosmological tensor-to-scalar perturbation ratio during the post-inflationary evolution of the universe. Nevertheless, contrary to some recent claims, tensor perturbations can be relatively large in the simplest inflationary models which do not violate any rules of modern quantum field theory., Comment: 9 pages; references added

We consider a cosmological model with non-Gaussian initial perturbations, which in principle could be generated in non-standard inflationary scenarios with two or more scalar fields. In particular we focus our attention on the model proposed by Linde & Mukhanov (1997) perturbations are quadratic in a Gaussian field. These perturbations, if they exist, have to be observable as a non-Gaussian distribution of the CMB signal on the sky. In order to efficiently pick up the non-Gaussian signal in CMB maps of degree resolution, one can use Minkowski Functionals and peak statistics. Our paper contains the theoretical predictions of the properties for Minkowski Functionals and distributions of peaks of the CMB anisotropy in the model with "squared" Gaussian statistics. Likelihood comparison of the four-year COBE DMR data to this non-Gaussian model and the standard Gaussian model does not select any of them as most likely. We also suggest an efficient algorithm for fast simulation of CMB maps on the whole sky. Using a cylindrical partition of the sphere, we rewrite the spherical harmonics analysis as a Fourier transform in flat space, which makes the problem accessible to numerically advantageous FFT methods., Comment: 10 pages, 7 figures, accepted for publication in Astronomy and Astrophysics

We draw attention to the possibility that inflation (i.e. accelerated expansion) might continue after the end of slow roll, during a period of fast oscillations of the inflaton field \phi . This phenomenon takes place when a mild non-convexity inequality is satisfied by the potential V(\phi). The presence of such a period of \phi-oscillation-driven inflation can substantially modify reheating scenarios. In some models the effect of these fast oscillations might be imprinted on the primordial perturbation spectrum at cosmological scales., Comment: 9 pages, Revtex, psfig, 1 figure, minor modifications, references added