The massive scalar field in a closed Friedmann universe model — new rigorous results

For the minimally coupled scalar field in Einstein's theory of gravitation we look for the space of solutions within the class of closed Friedmann universe models. We prove D ≥ 1, where D ≥ is the dimension of the set of solutions which can be integrated up to t → ∞ (D > 0 was conjectured by PAGE (1984)). We discuss concepts like “the probability of the appearance of a sufficiently long inflationary phase” and argue that it is primarily a probability measure μ in the space V of solutions (and not in the space of initial conditions) which has to be applied. μ is naturally defined for Bianchi-type I cosmological models because V is a compact cube. The problems with the closed Friedmann model (which led to controversial claims in the literature) will be shown to originate from the fact that V has a complicated non-compact non-Hausdorff Geroch topology: no natural definition of μ can be given. We conclude: the present state of our universe can be explained by models of the type discussed, but thereby the anthropic principle cannot be fully circumvented.     

Isotropization by scalar field driven inflation and the cosmological quantum boundary

We derive the Wheeler-de Witt equation for the scalar field of mass m > 0 in a Bianchi-type I universe. We argue that classical trajectories become possible at h² ⩽ αt_p^-2, h being the mean Hubble value and t_p the Planck time. We feel justified to set the numerical constant α ≈︁ 1. We discuss this condition in geometrically invariant quantities and compare it with ⩽t_p^-4. The proposed quantum boundary of classical trajectories represents a 3-dimensional sphere in the 4-space of the dynamical system. Equipartition of the initial energy over field (m < m_p) and shear variables at the quantum boundary will cause inflation with a probability p of the order p = 1 - m/m_p thus, p = 1 - 10^-4 for m taken from GUT. In the course of the inflationary stage the initially arbitrarily large shear-anisotropy exponentially decays.     

The branch-cut quantum gravity with a self-coupling inflation scalar field: Dynamical equations

This article focuses on the implications of the recently developed commutative formulation based on branch-cutting cosmology, the Wheeler–DeWitt equation, and Hořava–Lifshitz quantum gravity. Assuming a mini-superspace of variables, we explore the impact of an inflaton-type scalar field $\varphi (t)$ on the dynamical equations that describe the trajectories evolution of the scale factor of the Universe, characterized by the dimensionless helix-like function ${\ln }^{-1}[\beta (t)]$. This scale factor characterizes a Riemannian foliated spacetime that topologically overcomes the big bang and big crunch singularities. Taking the Hořava–Lifshitz action as our starting point, which depends on the scalar curvature of the branched Universe and its derivatives, with running coupling constants denoted as $g_i$, the commutative quantum gravity approach preserves the diffeomorphism property of General Relativity, maintaining compatibility with the Arnowitt–Deser–Misner formalism. We investigate both chaotic and nonchaotic inflationary scenarios, demonstrating the sensitivity of the branch-cut Universe's dynamics to initial conditions and parameterizations of primordial matter content. The results suggest a continuous connection of Riemann surfaces, overcoming primordial singularities and exhibiting diverse evolutionary behaviors, from big crunch to moderate acceleration.     

The branch-cut quantum gravity with a self-coupling inflation scalar field: The wave function of the Universe

This paper focuses on the implications of a commutative formulation that integrates branch-cutting cosmology, the Wheeler–DeWitt equation, and Hořava–Lifshitz quantum gravity. Building on a mini-superspace structure, we explore the impact of an inflaton-type scalar field on the wave function of the Universe. Specifically analyzing the dynamical solutions of branch-cut gravity within a mini-superspace framework, we emphasize the scalar field's influence on the evolution of the evolution of the wave function of the Universe. Our research unveils a helix-like function that characterizes a topologically foliated spacetime structure. The starting point is the Hořava–Lifshitz action, which depends on the scalar curvature of the branched Universe and its derivatives, with running coupling constants denoted as $g_i$. The corresponding wave equations are derived and are resolved. The commutative quantum gravity approach preserves the diffeomorphism property of General Relativity, maintaining compatibility with the Arnowitt–Deser–Misner formalism. Additionally, we delve into a mini-superspace of variables, incorporating scalar-inflaton fields and exploring inflationary models, particularly chaotic and nonchaotic scenarios. We obtained solutions for the wave equations without recurring to numerical approximations.     

Quintessential inflation models with a nonminimally coupled scalar field

The evolution of a homogeneous, isotropic cosmological model driven by a nonminimally coupled scalar field is studied. The potential for the quintessential inflation model proposed by Peebles and Vilenkin is selected as a scalar potential. Possible scenarios for the cosmological dynamics are described in the conformal Einstein and Jordan representations. It is shown that, unlike in models with a minimal scalar field, here a class of solutions exists for which the scalar field is fixed at finite values during cosmological expansion. __________ Translated from Astrofizika, Vol. 49, No. 3, pp. 487–498 (August 2006).     

Inhomogeneous imperfect fluid spherical models without big-bang singularity

So far all known singularity-free cosmological models are cylindrically symmetric. Here we present a new family of spherically symmetric non-singular models filled with imperfect fluid and radial heat flow, and satisfying all the energy conditions. For larget anisotropy in pressure and heat flux tend to vanish leading to a perfect fluid. There is a free function of time in the model, which can be suitably chosen for non-singular behaviour and there exist multiplicity of such choices.     

Comparing selfinteracting scalar fields and R + R3 cosmological models

We generalize the well-known analogies between m²φ² and R + R² theories to include the selfinteraction λφ⁴-term for the scalar field. It turns out to be the R + R³ Lagrangian which gives an appropiate model for it. Considering a spatially flat Friedman cosmological model, common and different properties of these models are discussed, e. g., by linearizing around a ground state the masses of the resp. spin 0-parts concide. Finally, we prove a general conformal equivalence theorem between a Lagrangian L = L(R), L′L″ ≠ 0, and a minimally coupled scalar field in a general potential.     

Exact solutions to Kaluza-Klein cosmologies

We consider general methods to find exact solutions of Kaluza-Klein cosmologies with phenomenological matter and show some general conclusions about factorwise homogeneous and isotropic models.     

Cosmic acceleration and extra dimensions: constraints on modifications of the Friedmann equation

An alternative to dark energy as an explanation for the present phase of accelerated expansion of the Universe is that the Friedmann equation is modified, e.g. by extra dimensional gravity, on large scales. We explore a natural parametrization of a general modified Friedmann equation, and find that the present supernova Type Ia and cosmic microwave background data prefer a correction of the form 1/ H to the Friedmann equation over a cosmological constant.     

New properties of scalar-field dynamics in an isotropic cosmological model on the brane

We investigate some aspects of the scalar-field dynamics on the brane that differ from the corresponding regimes in standard cosmology. We consider asymptotic solutions near singularity, inflation and rebound conditions, and some features of chaos in the model on the brane. Our results are compared with their analogs in classical cosmology.     

Tilted bianchi type v bulk viscous cosmological models in general relativity

Conformally flat tilted Bianchi type V cosmological models in presence of a bulk viscous fluid and heat flow are investigated. The coefficient of bulk viscosity is assumed to be a power function of mass density. Some physical andgeometric aspects of the models are also discussed.     

Tilted Bianchi type I cosmological models filled with disordered radiation in general relativity revisitedD

Tilted Bianchi type I cosmological models filled with disordered radiation in presence of a bulk viscous fluid and heat flow are investigated. The coefficient of bulk viscosity is assumed to be a power function of mass density. Some physical and geometric properties of the models are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Horizon problem and inflation

We show that, the part of the universe that is observable today (in principle), could not have evolved out of a domain which was causally connected in the past. This and other issues related to horizon problem in inflationary models are discussed.     

Global stability analysis for scalar-tensor models

The phase space of a cosmological model with a scalar field coupled to curvature is discussed in detail for any value of the coupling constant ξ and any power law (ϕ²ⁿ) potential. The results obtained generalize previous studies with minimal coupling (ξ = 0) and quadratic or quartic potentials to the entire parameter space (ξ, n). In many cases one finds global attractors and inflationary trajectories, with or without the correct Friedmannian limit. If the coupling constant is positive, a forbidden region cuts out a large part of the phase space, while, if it is negative, escaping regions may occur. Semi-classical instability of vacuum states and singularity-free trajectories are also discussed.     

Noncommutative branch-cut quantum gravity with a self-coupling inflaton scalar field: The wave function of the Universe

This article focuses on the implications of a noncommutative formulation of branch-cut quantum gravity. Based on a mini-superspace structure that obeys the noncommutative Poisson algebra, combined with the Wheeler–DeWitt equation and Hořava–Lifshitz quantum gravity, we explore the impact of a scalar field of the inflaton-type in the evolution of the Universe's wave function. Taking as a starting point the Hořava–Lifshitz action, which depends on the scalar curvature of the branched Universe and its derivatives, the corresponding wave equations are derived and solved. The noncommutative quantum gravity approach adopted preserves the diffeomorphism property of General Relativity, maintaining compatibility with the Arnowitt–Deser–Misner Formalism. In this work we delve deeper into a mini-superspace of noncommutative variables, incorporating scalar inflaton fields and exploring inflationary models, particularly chaotic and nonchaotic scenarios. We obtained solutions to the wave equations without resorting to numerical approximations. The results indicate that the noncommutative algebraic space captures low and high spacetime scales, driving the exponential acceleration of the Universe.     

Warm anisotropic inflation with bulk viscous pressure in intermediate era

The aim of this paper is to study the warm inflation during intermediate era in the framework of locally rotationally symmetric Bianchi type I universe model. We assume that the universe is composed of inflaton and imperfect fluid having radiation and bulk viscous pressure. To this end, dynamical equations (first model field equation and energy conservation equations) under slow-roll approximation and in high dissipative regime are constructed. A necessary condition is developed for the realization of this anisotropic model. We assume both dissipation and bulk viscous coefficients variable as well as constant. We evaluate entropy density, scalar (tensor) power spectra, their corresponding spectral indices, tensor–scalar ratio and running of spectral index in terms of inflaton. These cosmological parameters are constrained using recent Planck and WMAP7 probe.     

Spherical galaxy models with power-law logarithmic slope

We present a new family of spherically symmetric models for the luminous components of elliptical and spiral galaxies and their dark matter haloes. Our starting point is a general expression for the logarithmic slope  α( r ) = d log ρ/d log  r   from which most of the cuspy models yet available in literature may be derived. We then dedicate our attention to a particular set of models where the logarithmic slope is a power-law function of the radius r investigating in detail their dynamics assuming isotropy in the velocity space. While the basic properties (such as the density profile and the gravitational potential) may be expressed analytically, both the distribution function and the observable quantities (the surface brightness and the line-of-sight velocity dispersion) have to be evaluated numerically. We also consider the extension to anisotropic models, trying two different parametrization. As the model recently proposed by Navarro et al. as the best fit to their sample of numerically simulated haloes belongs to the family we present here, analytical approximations are given for the most useful quantities.     

Mini-inflation prior to the cosmic confinement transition?

The onset of the confinement transition in the early universe is studied within the Friedmann model. Exploiting a bag model equation of state for the deconfined matter, which is generalized to include also metastable states, the possibility of a mini-inflationary epoch is demonstrated. A criterion of metastability is derived to estimate parameters of this mini-inflation.