Power-law Inflation Research Articles

Vacuum Fluctuations as a Source of Adiabatic Perturbations in Power-Law Inflationary Cosmology

An analysis of the decoherence of quantum fluctuations shows that production of classical adiabatic density perturbations may not take place in models of power-law inflation, a(t)~tp, with 1<p≤ 3. Some consequences for models of extended inflation are pointed out. In general, the condition for decoherence places new constraint on inflationary models, which does not depend on often complicated subsequent evolution.

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.

Second-order reconstruction of inflationary dynamics compatible with recent COBE data

A new method is applied to reconstruct the inflationary potential from a more phenomenological point of view. By using the more stringent nonlinear second order slow-roll approximation, we found, besides the power law inflation for n s < 1, an exact solution for which the spectral index is necessarily determined as n s ⋍ 1.5 . Part of these continuous and discrete spectra of the index fits within the 1σ range of recent COBE and CAT data. In the conformal frame, the inflation can be absorbed in a specific nonlinear curvature scalar Lagrangian parametrized by n s which is related to effective string models.

Accurate determination of inflationary perturbations.

We use a numerical code for accurate computation of the amplitude of linear density perturbations and gravitational waves generated by single-field inflation models to study the accuracy of existing analytic results based on the slow-roll approximation. We use our code to calculate the coefficient of an expansion about the exact analytic result for power-law inflation; this generates a fitting function which can be applied to all inflationary models to obtain extremely accurate results. In the appropriate limit our results confirm the Stewart--Lyth analytic second-order calculation, and we find that their results are very accurate for inflationary models favoured by current observational constraints.

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.

Nonlinear lagrangians and the isotropy of the universe

We analyse the question of whether, in higher derivative gravity theories, the present isotropic state of the universe could have been obtained by starting from “arbitrary” initial conditions. We show that the Collins-Hawking conclusion holds in this extended case, that is, the set of spatially homogeneous cosmologies which can approach isotropy at late times is of measure zero in the space of all spatially homogeneous universe models. This involves an examination of a generalized form of the Raychaudhuri equation valid in a general higher-order theory of gravity in four spacetime dimensions. We show that this equation is conformally equivalent to what we call a Raychaudhuri system, that is, to the usual Raychaudhuri equation in general relativity coupled to a scalar-wave equation satisfied by the scalar field generated by the conformal transformation with the usual effective potential. This result is also used to prove directly in higher-order gravity the known forms of cosmic no-hair theorems in the Sitter and power-law inflation in general relativity. Generalizations to arbitrary dimensionality and also the addition of other curvature invariants are discussed.

Anisotropic inflation from extra dimensions

Vacuum multidimensional cosmological models with internal spaces being compact n-dimensional Lie group manifolds are considered. Products of 3-spheres and SU(3) manifold (a novelty in cosmology) are studied. It turns out that the dynamical evolution of the internal space drives (power-law) inflation in the external world. This inflationary solution brings two extra bonuses: 1) it is an attractor in phase space (no fine-tuning required); 2) it is determined by the Lie group space solely and not by any arbitrary inflaton potentials. Only scalar fields representing the anisotropic scale factors of the internal space appears in the four dimensions. The size of the volume of the internal space at the end of inflation is compatible with observational constraints. This simple and natural model can be completed by some extended-inflation-like mechanism that ends the inflationary evolution.

Inflation in multidimensional quantum cosmology.

We extend to multidimensional cosmology Vilenkin's prescription of tunnelling from nothing for the quantum origin of the observable Universe. Our model consists of a $D+4$-dimensional spacetime of topology ${\cal R}\times {\cal S}^3 \times{\cal S}^D$, with a scalar field (``chaotic inflaton'') for the matter component. Einstein gravity and Casimir compactification are assumed. The resulting minisuperspace is 3--dimensional. Patchwise we find an approximate analytic solution of the Wheeler--DeWitt equation through which we discuss the tunnelling picture and the probability of nucleation of the classical Universe with compactifying extra dimensions. Our conclusion is that the most likely initial conditions, although they do not lead to the compactification of the internal space, still yield (power-law) inflation for the outer space. The scenario is physically acceptable because the inner space growth is limited to $\sim 10^{11}$ in 100 e-foldings of inflation, starting from the Planck scale.

Pure Geometrical Evolution of the Multidimensional Universe

An exhaustive qualitative analysis of cosmological evolution for some multidimensional universes is given. The internal space is taken to be a compact Lie group Riemannian manifold. The space is generically anisotropic; i.e., its cosmological evolution is described by its (time-dependent) volume, the dilaton, and by relative anisotropic deformation factors representing the shear of the internal dimensions during the evolution. Neither the internal space nor its subspaces need to be Einstein spaces. The total spacetime is empty, and the cosmic evolution of the external, four-dimensional world is driven by the geometric “matter” consisting of the dilaton and of the deformation factors. Since little is known about any form of matter in the extra dimensions, we do not introduce anyad hocmatter content of the Universe. We derive the four-dimensional Einstein field equations (with a cosmological term) for these geometric sources in full generality, i.e., for any compact Lie group. A detailed analysis is done for some specific internal geometries: products of 3-spheres, andSU(3) space. Asymptotic solutions exhibit power law inflation along with a process of full or partial isotropization. For theSU(3) space all the deformation factors tend to a common value, whereas in the case ofS3's each sphere isotropizes separately.

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}${\mathit{t}}_{\mathit{e}}$.

Stable and unstable circular strings in inflationary universes.

It was shown by Garriga and Vilenkin that the circular shape of nucleated cosmic strings, of zero loop-energy in de Sitter space, is stable in the sense that the ratio of the mean fluctuation amplitude to the loop radius is constant. This result can be generalized to all expanding strings (of non-zero loop-energy) in de Sitter space. In other curved spacetimes the situation, however, may be different. In this paper we develop a general formalism treating fluctuations around circular strings embedded in arbitrary spatially flat FRW spacetimes. As examples we consider Minkowski space, de Sitter space and power law expanding universes. In the special case of power law inflation we find that in certain cases the fluctuations grow much slower that the radius of the underlying unperturbed circular string. The inflation of the universe thus tends to wash out the fluctuations and to stabilize these strings.

Hypersurface-invariant approach to cosmological perturbations.

Using Hamilton-Jacobi theory, we develop a formalism for solving semi-classical cosmological perturbations which does not require an explicit choice of time-hypersurface. The Hamilton-Jacobi equation for gravity interacting with matter (either a scalar or dust field) is solved by making an Ansatz which includes all terms quadratic in the spatial curvature. Gravitational radiation and scalar perturbations are treated on an equal footing. Our technique encompasses linear perturbation theory and it also describes some mild nonlinear effects. As a concrete example of the method, we compute the galaxy-galaxy correlation function as well as large-angle microwave background fluctuations for power-law inflation, and we compare with recent observations.

Detection of cosmic microwave background anisotropy at 1.8 deg: Theoretical implications on inflationary models

Theoretical scenarios for the formation of large-scale structure in the universe are strongly constrained by ARGO (a balloon borne experiment reporting detection of cosmic microwave background (CMB) anisotropy at 1.8 deg) and Cosmic Background Explorer/Differential Microwave Radiometer (COBE/DMR). Here we consider flat hybrid models with either scale invariant or tilted (n not equal to 1) initial conditions. For n less than 1, we take into account the effect of a primordial background of gravitational waves, predicted by power-law inflation scenarios. The main result of our analysis is that the ARGO and COBE/DMR data select a range of values for the primordial spectral index: n = 0.95$^{+0.25$$_-0.15$ (values of n outside this range can be rejected at more than 95\% confidence level). These bounds are basically independent of the cosmological abundance of baryons (at least in the range allowed from primordial nucleosynthesis) and of the ratio of cold to hot dark matter. So, flat, cold, or mixed dark matter models, with scale-invariant initial conditions and a standard recombination history, successfully take into account the CMB anisotropy detected at intermediate and large angular scales. }

Power-law inflation and conformal transformations

We present a discussion of power-law inflation in higher-order gravity theories. Using the conformal equivalence theorem, we find power-law solutions in the context of pure higher-order gravity theories in arbitrary dimension. We also find a family of polar inflationary solutions. We give a perturbation analysis which establishes that the power-law solutions are stable against homogeneous and isotropic perturbations but that the polar solutions are not.

The three-point correlation function of the cosmic microwave background in inflationary models

We analyze the temperature three–point correlation function and the skewness of the Cosmic Microwave Background (CMB), providing general relations in terms of multipole coefficients. We then focus on applications to large angular s anisotropies, such as those measured by the COBE DMR, calculating the contribution to these quantities from primordial, inflation generated, scalar perturbations, via the Sachs–Wolfe effect. Using the techniques of stochastic inflation we are able to provide a universal expression for the ensemble averaged three–point function and for the corresponding skewness, which accounts for all primordial second–order effects. These general expressions would moreover apply to any situation where the bispectrum of the primordial gravitational potential has a hierarchical form. Our results are then specialized to a number of relevant models: power–law inflation driven by an exponential potential, chaotic inflation with a quartic and quadratic potential and a particular case of hybrid inflation. In all these cases non–Gaussian effects are small: as an example, the mean skewness is much smaller than the cosmic rms skewness implied by a Gaussian temperature fluctuation field.

Gravity's rainbow (microwave anisotropy and gravitational waves)

Could COBE DMR be detecting the imprint from a spectrum of gravitational waves generated during inflation? The conventional inflationary prediction had been that the cosmic microwave anisotropy is dominated by energy density fluctuations generated during inflation and that the gravitational waves contribute negligibly. The authors report on recent work that has shown that the conventional wisdom may be wrong; specifically, gravitational waves may dominate the anisotropy in inflationary models where the spectrum of perturbations deviates significantly from scale invariance (e.g., extended and power-law inflation models and extreme versions of chaotic inflation). If gravitational waves do dominate at the large-angular scales measured by COBE DMR, the expectation and interpretation of anisotropies on small-angular scales is profoundly altered.

Exact superstring motivated cosmological models

We present a number of new, exact scalar field cosmologies where the potential consists of two or more exponential terms. Such potentials are motivated by supergravity or superstring models formulated in higher-dimensional spacetimes that have been compactified to 3+1 dimensions. We have found solutions in both curved and flat Robertson-Walker spacetimes. These models have a diverse range of properties and often possess several distinct phases, with a smooth transition between ordinary and inflationary expansion. While exponential potentials typically produce power-law inflation, we find models where the inflationary period contains eras of both power-law and exponential growth.

Evolution of multidimensional flat anisotropic cosmological models.

We study the dynamics of a flat multidimensional anisotropic cosmological model filled with an anisotropic fluidlike medium. By an appropriate choice of variables, the dynamical equations reduce to a two-dimensional dynamical system. We present a detailed analysis of the time evolution of this system and the conditions of the existence of spacetime singularities. We investigate the conditions under which violent, exponential, and power-law inflation is possible. We show that dimensional reduction cannot proceed by anti-inflation (rapid contraction of internal space). Our model indicates that it is very difficult to achieve dimensional reduction by classical means.

Qualitative analysis of soft inflation.

In this paper we perform a qualitative analysis of the dynamical system resulting from the soft inflation scenario. This allows us to examine the various types of asymptotic behavior displayed by the system; we pay particular attention to the inflationary solutions given by Berkin, Maeda, and Yokoyama [Phys. Rev. Lett. 65, 141 (1990)]. We find that as $\ensuremath{\varphi}\ensuremath{\rightarrow}\ensuremath{\infty}$, no unique attracting critical point exists, but rather there exists a higher-dimensional set of critical points. It is shown that the solution given by Berkin, Maeda, and Yokoyama is representative of a class of solutions which asymptotically undergoes power-law inflation. Under the assumption that new inflation occurs, we show that, asymptotically, there exists a global attractor. Under the assumption that chaotic inflation occurs, we show that there exists an attractor for finite values of the field $\ensuremath{\varphi}$ and that solutions which inflate will experience infinitely many inflationary eras.