Exponential Inflation Research Articles

Exact Inflationary Solution to Nonminimally Coupled ScalarField

We present a new exact inflationary solution to nonminimally coupledscalar field. The inflation is driven by the evolution of scalar fieldwith inflation potential V(φ) = (λ/4)φ4−(1/2)m2φ2+V0. This includes the solutionthat behaves exponential inflation for φ0>φ>φend and then develops smoothlytowards radiation-like evolution for φ<φend.The spectral index of the scalar density fluctuations, ns, iscomputed, and the result is consistent with the analysisof the Wilkinson-microwave anisotropy probe data. This model can leadto successful inflation with λ≈10−7, rather than10−13 reported previously.

THE FIRST TURBULENT COMBUSTION

ABSTRACT The first turbulent combustion arises in a hot-big-bang cosmological model (Gibson, 2004) where nonlinear exothermic turbulence permitted by quantum mechanics, general relativity, multidimensional superstring theory, and fluid mechanics cascades from Planck to strong-force freeze-out scales with gravity balancing turbulent inertial-vortex forces. Interactions between Planck scale spinning and non-spinning black holes produce high Reynolds number turbulence and temperature mixing with huge Reynolds stresses driving the rapid inflation of space. Kolmogorovian turbulent temperature patterns are fossilized as strong-force exponential inflation stretches them beyond the scale of causal connection ct where c is light speed and t is time. Fossil temperature turbulence patterns seed nucleosynthesis, and then hydro-gravitational structure formation in the plasma epoch, (Gibson, 1996, 2000). Evidence about formation mechanisms is preserved by cosmic microwave background (CMB) temperature anisotropies. CMB spectra indicate hydro-gravitational fragmentation at supercluster to galaxy masses in the primordial plasma with space stretched by ∼ 1050. Bershadskii and Sreenivasan (2002, 2003) CMB multi-scaling coefficients support a strong turbulence origin for the anisotropies prior to the plasma epoch.

Genericness of Inflation in Isotropic Loop Quantum Cosmology

Nonperturbative corrections from loop quantum cosmology (LQC) to the scalar matter sector are already known to imply inflation. We prove that the LQC modified scalar field generates exponential inflation in the small scale factor regime, for all positive definite potentials, independent of initial conditions and independent of ambiguity parameters. For positive semidefinite potentials it is always possible to choose, without fine-tuning, a value of one of the ambiguity parameters such that exponential inflation results, provided zeros of the potential are approached at most as a power law in the scale factor. In conjunction with the generic occurrence of bounce at small volumes, particle horizon is absent, thus eliminating the horizon problem of the standard big bang model.

Exact Solution in Chaotic Inflation Model with NegativePotential

New exact solution to the Einstein equations that describe theevolution of cosmological chaotic inflation model is derived. Theinflation is driven by the evolution of scalar field with negativepotential V(φ) = -V0 + ½m2φ2. Thisincludes the solution which is exponential inflation for φ0>φ>φf, and then develops smoothly towards theradiation-like evolution for φ<φf. The spectralindices of the scalar density ns and the gravitational wavefluctuations ng are computed. The value of ns lies well insidethe limits set by the cosmic background explorer satellite.

Inflation of Fireballs, the Gluon Wind and the Homogeneity of the HBT Radii at RHIC

We solve analytically the ellipsoidally expanding fireball hydrodynamics with source terms in the momentum and the energy equations, using the non-relativistic approximation. We find that energy transport from high pt jets of gluons to the medium leads to a transient, exponential inflation of the fireballs created in high energy heavy ion collisions. In this transient, inflatory period, the slopes of the single particle spectra increase, while the HBT radius parameters decrease exponentially with time. This effect is shown to be similar to the development of the homogeneity of our Universe due to an inflatory period. Independently of the initial conditions, and the exact value of the freeze-out time and temperature, the meausurables (single particle spectra, the correlation functions, the slope parameters, elliptic flow, HBT radii and cross terms) become time independent during the late, non-inflatory stages of the expansion, and they satisfy new kind of scaling laws. If the expansion starts with a transient inflation caused by the gluon wind, it leads naturally to large transverse flows and the simultaneous equality and scaling behaviour of the HBT radius parameters, R_{side} \approx R_{out} \approx R_{long} \approx t_f \sqrt{T_f/m}. With certain relativistic corrections, the scaling limit is \tau_f \sqrt{T_f/m_t}, where m_t is the mean transverse mass of the pair.

Collapse of topological texture

We study analytically the process of a topological texture collapse in the approximation of a scaling ansatz in the nonlinear sigma-model. In this approximation we show that in flat space-time topological texture eventually collapses while in the case of spatially flat expanding universe its fate depends on the rate of expansion. If the universe is inflationary, then there is a possibility that texture will expand eternally; in the case of exponential inflation the texture may also shrink or expand eternally to a finite limiting size, although this behavior is degenerate. In the case of power law noninflationary expansion topological texture eventually collapses. In a cold matter dominated universe we find that texture which is formed comoving with the universe expansion starts collapsing when its spatial size becomes comparable to the Hubble size, which result is in agreement with the previous considerations. In the nonlinear sigma-model approximation we consider also the final stage of the collapsing ellipsoidal topological texture. We show that during collapse of such a texture at least two of its principal dimensions shrink to zero in a similar way, so that their ratio remains finite. The third dimension may remain finite (collapse of cigar type), or it may also shrink to zero similar to the other two dimensions (collapse of scaling type), or shrink to zero similar to the product of the remaining two dimensions (collapse of pancake type).

Gravitational wave spectra from pole-like inflations based on generalized gravity theories

We present a general and unified formulation which can handle the classical evolution and quantum generation processes of the cosmological gravitational wave in a broad class of generalized gravity theories. Applications are demonstrated in several inflation models based on the scalar-tensor theory, the induced gravity and the low-energy effective action of string theories. The gravitational wave power spectra based on the vacuum expectation value of the quantized fluctuating metric during the pole-like inflation stages are derived in analytic forms. Assuming that the gravity theory transits to an Einstein one while the relevant scales remain in the superhorizon scale, we derive the consequent power spectra and the directional fluctuations of the relic radiation produced by the gravitational wave. The spectra seeded by the vacuum fluctuations in the pole-like inflation models based on the generalized gravity show a distinguished common feature ( spectrum) which differs from the scale-invariant one ( spectrum) generated in an exponential inflation in Einstein gravity which is supported by observations.

The fine tuning problem in pre-big-bang inflation

We examine the effect of spatial curvature in the pre-big-bang inflationary model suggested by string theory. We study $O(\alpha ')$ corrections and we show that, independently of the initial curvature, they lead to a phase of exponential inflation. The amount of inflation in this phase is long enough to solve the horizon and flatness problems if the evolution starts deeply into the weak coupling regime. There is a region of the parameter space of the model where such a long inflationary phase at the string scale is consistent with COBE anisotropies, millisecond pulsar timing and nucleosynthesis constraints. We discuss implications for the spectrum of relic gravitational waves at the frequencies of LIGO and Virgo.

Wavefront speeds in power-law inflation driven by bulk viscosity and matter creation

In the framework of a spatially flat FLRW model, we account for dissipative effects in a simple fluid, namely bulk viscosity and matter creation. For an isentropic evolution, we study the wavefront speeds associated with the characteristics of the fluid. With the assumption of a barotropic equation of state, we investigate the consequences on these speeds of power-law behaviour for the scale factor. Our conclusion is that, in contrast to the exponential inflation, the isentropic power-law inflation is compatible with causality, under conditions linking the generalized `adiabatic' index to the exponent m of the power law.

New exact solutions in standard inflationary models

The exact solutions in the standard inflationary model based on the self-interacting scalar field minimally coupled to gravity are considered. The shape's freedom of the self-interacting potential V( F) is postulated to obtain a new set of the exact solutions in the framework of Friedmann-Robertson-Walker Universes. The general solution was found in the case of power law inflation. We obtained new solutions and compared them with obtained ones earlier for the exponential type inflation.

Inflation in cosmological models with a non-minimally coupled, massless scalar field

A homogeneous, spatially flat cosmological model induced by a massless scalar field is investigated. The parameter ξ of coupling of the field with the curvature can take any value. It is shown that the range of values of ξ is divided into three regions, ξ 1/6, each of which is characterized by the behavior of the scale factor in it. The points ξ=0 and ξ=1/6 are singular. Stages with exponential and power-law inflation are found in the ranges 0 1/6. An exponential inflationary stage with acceptable cosmological consequences can occur for small positive ξ.

Inflationary solutions for anisotropic model in scalar-tensor theory

In this paper we have studied B-D theory and general scalar tensor theory of Gravitation for anisotropic cosmological model in the false vacuum state. The possibility of both exponential inflation and power function inflation are examined for constant or variable coupling parameter ω. Also asymptotic limit of the scalar field and ω are discussed.

Collisional equilibrium, particle production, and the inflationary universe.

Particle production processes in the expanding universe are described within a simple kinetic model. The equilibrium conditions for a Maxwell-Boltzmann gas with variable particle number are investigated. We find that radiation and nonrelativistic matter may be in equilibrium at the same temperature provided the matter particles are created at a rate that is half the expansion rate. Using the fact that the creation of particles is dynamically equivalent to a nonvanishing bulk pressure we calculate the back reaction of this process on the cosmological dynamics. It turns out that the `adiabatic' creation of massive particles with an equilibrium distribution for the latter necessarily implies power-law inflation. Exponential inflation in this context is shown to become inconsistent with the second law of thermodynamics after a time interval of the order of the Hubble time.

Wavefront velocities in a cosmic fluid with bulk viscosity and matter creation

Wavefront velocities are calculated for a dissipative simple fluid. The dissipative effects considered are scalar: bulk viscous stress and matter creation. Relativistic extended irreversible thermodynamics are used and cross-effects are considered. These results are applied to exponential inflation in the spatially flat Friedmann - Lemaître - Robertson - Walker cosmological model, and give infinite wave speeds. We thus conclude that exponential inflation cannot be driven by bulk viscosity.

Evolving Lorentzian wormholes

Evolving Lorentzian wormholes with the required matter satisfying the energy conditions are discussed. Several different scale factors are used and the corresponding consequences derived. The effect of extra, decaying (in time) compact dimensions present in the wormhole metric is also explored and certain interesting conclusions are derived for the cases of exponential and Kaluza-Klein inflation. \textcopyright{} 1996 The American Physical Society.

Inflation in Poincar� gauge gravitation theory

Exponential inflation and power-law inflation are studied in the Poincare gauge gravitation theory for a Robertson-Walker metric.

Exact inflationary cosmologies with exit.

We find exact inflationary solutions with exit, including exact forms of the potential, by specifying the rate of expansion and using the number of e-foldings as the effective dynamical variable. These include solutions in which the potential drives nearly exponential or power-law inflation for ${\mathit{t}}_{\mathit{i}}$\ensuremath{\le}t${\mathit{t}}_{\mathit{e}}$, and then directs the expansion smoothly towards radiationlike evolution for t\ensuremath{\ge}${\mathit{t}}_{\mathit{e}}$.

Signature change induces compactification.

It is shown -- using a FRW model with ${\bf S}^3 \times {\bf S}^6$ as spatial sections and a positive cosmological constant -- that classical signature change implies a new compactification mechanism. The internal scale factor is of the order $\Lambda^{-1/2}$, and the solutions are stable against small perturbatons. In the case of compactified ${\bf S}^6$, it is shown that the effective four-dimensional space-time metric has Lorentzian signature, undergoes exponential inflation in ${\bf S}^3$ and is unique. Speculations concerning relations to quantum cosmology and conceivable modifications are added.

Multidimensional cosmological models in effective string gravitation. II

We carry out an analysis of the exact solution obtained in the first part of this work for a homogeneous and anisotropic flat cosmological model in the general conformal representation of multidimensional low-energy string theory. We show that the singular solutions with power law of variation of the scale factors of maximally symmetric subspaces and scalar field are asymptotes of the general solution in early and late stages of evolution. We study the conditions under which models of exponential, extended, and violent inflation are realized. As an illustration of the general regularities we consider the specific example of an antisymmetric Kalb-Ramond field as a gravitational source. We demonstrate the possibility of dynamic compactification of the extra dimensions.

Matter creation and bulk viscosity in early cosmology

The two distinct irreversible phenomena of matter creation and bulk viscosity are considered as independent, giving cross effects in relativistic extended irreversible thermodynamics, as applied to the primordial Friedman-Lemaître-Robertson-Walker cosmology. Some consequences are developed in the isentropic exponential inflation case.