We investigate the circumstances under which cosmic inflation can arise from very inhomogeneous initial conditions using numerical relativity simulations. Previous studies have not considered cases with non-zero momentum density due to technical challenges with solving the coupled Einstein constraint equations. Here we address these, introducing and comparing several different ways of constructing cosmological initial conditions with inhomogeneous scalar field and time derivative profiles. We evolve such initial conditions with large inhomogeneities in both single- and two-field inflationary models. We study cases where the initial gradient and kinetic energy are much larger than the inflationary energy scale, and black holes can form, as well as cases where the initial scalar potential energy is comparable, as in scenarios where inflation occurs at nearly Planckian densities, finding large-field inflation to be generally robust. We consider examples of initial conditions where a large scalar field velocity towards non-inflationary values would prevent inflation from occurring in the homogeneous case, finding that the addition of large gradients in the scalar field can actually dilute this effect, with the increased expansion and non-vanishing restoring force leading to inflation.
Inhomogeneous fluid models for warm inflation are investigated. The early-time acceleration is supported by inhomogeneous fluid whose coupling with radiation leads to the radiation dominated era after inflation. Several examples are analyzed, strong dissipation regime is discussed, and the viability of the models respect to the last Planck data is verified.
We study how the initial inhomogeneities of the universe affect the onset of inflation in the closed universe. We consider the model of a chaotic inflation which is driven by a massive scalar field. In order to construct an inhomogeneous universe model, we use the long wavelength approximation ( the gradient expansion method ). We show the condition of the inhomogeneities for the universe to enter the inflationary phase.
In this paper, we investigate inhomogeneous viscous fluid cosmology for inflation. Several toy models are presented in the attempt to analyze how inflation can be realized according with cosmological data by making use of an inhomogeneous EoS parameter for the fluid and/or by introducing a viscosity to have a graceful exit from inflation. The results will be compared with the ones of scalar field representation and discussed. We will pay attention on the possibility to recover the reheating and therefore the Friedmann universe.
We study the robustness of single-field inflation against inhomogeneities. We derive a simple analytic criterion on the shape of the potential for successful inflation in the presence of inhomogeneities, and demonstrate its validity using full 3+1 dimensional numerical relativity simulations on several classes of popular models of single-field inflation. We find that models with convex potentials are more robust to inhomogeneities than those with concave potentials, and that concave potentials that vary on super-Planckian scales are significantly more robust than those that vary on sub-Plancki…
We consider spatially averaged inhomogeneous universe models and argue that, already in the absence of sources, an effective scalar field arises through foliating and spatially averaging inhomogeneous geometrical curvature invariants of the Einstein vacuum. This scalar field (the `morphon') acts as an inflaton, if we prescribe a potential of some generic form. We show that, for any initially negative average spatial curvature, the morphon is driven through an inflationary phase and leads - on average - to a spatially flat, homogeneous and isotropic universe model, providing initial conditions …
We analyze the existence of inflationary solutions in an inhomogeneous Kaluza-Klein cosmological model in 4+n dimensions. It is shown that the 5-dimensional case is the exception rather than the rule, in the sense that the system is integrable (under the assumption of the equation of state $ρ= kp$) for any value of k. It is also shown that the cases k=0 and k=1/3 are integrable if and only if n=1.
We consider the effects of inhomogeneous initial conditions in both the scalar field profile and the extrinsic curvature on different inflationary models. In particular, we compare the robustness of small field inflation to that of large field inflation, using numerical simulations with Einstein gravity in 3+1 dimensions. We find that small field inflation can fail in the presence of subdominant gradient energies, suggesting that it is much less robust to inhomogeneities than large field inflation, which withstands dominant gradient energies. However, we also show that small field inflation ca…
We study numerically the inhomogeneous pre-big-bang inflation in a spherically symmetric space-time. We find that a large initial inhomogeneity suppresses the onset of the pre-big-bang inflation. We also find that even if the pre-big-bang inflationary stage is realized, the initial inhomogeneities are not homogenized. Namely, during the pre-big-bang inflation ``hairs''(irregularities) do not fall, in sharp contrast to the usual (potential energy dominated) inflation where initial inhomogeneity and anisotropy are damped and thus the resulting universe is less sensitive to initial conditions.
Using numerical solutions of the full Einstein field equations coupled to a scalar inflaton field in 3+1 dimensions, we study the conditions under which a universe that is initially expanding, highly inhomogeneous and dominated by gradient energy can transition to an inflationary period. If the initial scalar field variations are contained within a sufficiently flat region of the inflaton potential, and the universe is spatially flat or open on average, inflation will occur following the dilution of the gradient and kinetic energy due to expansion. This is the case even when the scale of the i…
We present new exact cosmological inhomogeneous solutions for gravity coupled to a scalar field in a general framework specified by the parameter $λ$. The equations of motion (and consequently the solutions) in this framework correspond either to low-energy string theory or Weyl integrable spacetime according to the sign of $λ$. We show that different inflationary behaviours are possible, as suggested by the study of the violation of the strong energy condition. Finally, by the analysis of certain curvature scalars we found that some of the solutions may be nonsingular.
Using a long wavelength iteration scheme to solve Einstein's equations near the Big-Bang singularity of a universe driven by a massive scalar field, we find how big initial quasi-isotropic inhomogeneities can be before they can prevent inflation to set in.
We use the 3+1 formalism of numerical relativity to investigate the robustness of Starobinsky and Higgs inflation to inhomogeneous initial conditions, in the form of either field gradient or kinetic energy density. Sub-Hubble and Hubble-sized fluctuations generically lead to inflation after an oscillatory phase between gradient and kinetic energies. Hubble-sized inhomogeneities also produce contracting regions that may end up forming primordial black holes, subsequently diluted by inflation. We analyse the dynamics of the preinflation era and the generation of vector and tensor fluctuations. O…
A generalized equation of state corresponding to a model that includes a Chaplygin gas and a viscous term is investigated, in the context of the reconstruction program in scalar field cosmology. The corresponding inflationary model parameters can be conveniently adjusted in order to reproduce the most recent PLANCK data. The influence of the Chaplygin gas term contribution, in relation with previous models, is discussed. Exit from inflation is shown to occur quite naturally in the new model.
We consider the robustness of small-field inflation in the presence of scalar field inhomogeneities. Previous numerical work has shown that if the scalar potential is flat only over a narrow interval, such as in commonly considered inflection-point models, even small-amplitude inhomogeneities present at the would-be onset of inflation at $τ= τ_i$ can disrupt the accelerated expansion. In this paper, we parametrise and evolve the inhomogeneities from an earlier time $τ_{IC}$ at which the initial data were imprinted, and show that for a broad range of inflationary and pre-inflationary models, in…
We study polarized Gowdy cosmologies on the three torus coupled to a massive scalar field. The phase space of the model admits a simple splitting between homogeneous and inhomogeneous sectors after a suitable gauge fixing. The presence of the mass term of the scalar field breaks the linearity of the equations of motion of the inhomogeneous fields. We discuss regimes of physical interest in which we recover a linear dynamics of these nonperturbative inhomogeneities, despite the metric is fully inhomogeneous at early times. We expand the inhomogeneous fields in Fourier modes and express them at …
We derive a ``generic'' inhomogeneous ``bridge'' solution for a cosmological model in the presence of a real self-interacting scalar field. This solution connects a Kasner-like regime to an inflationary stage of evolution and therefore provides a dynamical mechanism for the quasi-isotropization of the universe. In the framework of a standard Arnowitt-Deser-Misner Hamiltonian formulation of the dynamics and by adopting Misner-Chitrè-like variables, we integrate the Einstein-Hamilton-Jacobi equation corresponding to a ``generic'' inhomogeneous cosmological model whose evolution is influenced by …
We briefly review the arising of an inflationary phase in the Universe evolution in order to discuss an inhomogeneous cosmological solution in presence of a real self interacting scalar field minimally coupled to gravity in the region of a slow rolling potential plateau. During the inhomogeneous de Sitter phase the scalar field dominant term is a function of the spatial coordinates only. We apply this generic solution to the Coleman-Weinberg potential and to the Lemaitre-Tolman metric. This framework specialized nearby the FLRW model allows a classical origin for the inhomogeneous perturbation…
We model the large scale late time universe as a Lambda-CDM cosmology driven by cosmological constant and perfect dust fluid. Our aim is to find new solutions in the matter and Lambda epoch consistent with inflationary initial conditions, namely that to the far past in the matter era the cosmology tends to a flat FLRW solution. We identify the moduli degrees of freedom that parametrize the flat Lambda-dust FLRW solution and then promote these moduli to slowly varying functions of the spatial coordinates and show how to solve the Einstein equations in a comoving gradient expansion, controlled b…
Theories with ingredients like the Higgs mechanism, gravitons, and inflaton fields rejuvenate the idea that relativistic kinematics is dynamically emergent. Eternal inflation treats the Hubble constant H as depending on location. Microscopic dynamics implies that H is over much smaller lengths than pocket universes to be understood as a local space reproduction rate. We illustrate this via discussing that even exponential inflation in TeV-gravity is slow on the relevant time scale. In our on small scales inhomogeneous cosmos, a reproduction rate H depends on position. We therefore discuss Eins…
The cosmic no hair conjecture is tested for a large class of inhomogeneous cosmologies with a positive cosmological constant. Firstly, we derive a new class of exact inhomogeneous cosmological solutions whose matter content of the models is formed by a mixture of two interacting simple fluids plus a cosmological Lambda-term. These models generalize the de Sitter spacetime and the inhomogeneous two-fluid Szekeres-type cosmologies derived by Lima and Tiomno. Finally, we show that the late time behaviour of our solutions is in agreement with the "cosmic no hair theorem" of Hawking and Moss.
We obtain exact solutions for the Einstein equations with an exponential-potential scalar field (\(V=Λe^{kϕ}\)) which represent simple inhomogeneous generalizations of Bianchi I cosmologies. Studying these equations numerically we find that in most of the cases there is a certain period of inflationary behaviour for \(k^2<2\). We as well find that for \(k^2>2\) the solutions homogenize generically at late times. Yet, {\em none of the solutions} isotropize. For some particular values of the integration constants we find a multiple inflationary behaviour for which the deceleration and the inflat…
In the framework of a flat FLRW model we derive an inflationary regime in which the scalar field, laying on the plateau of its potential, admits a linear time dependence and remains close to a constant value. The behaviour of inhomogeneous perturbations is determined on the background metric in agreement to the "slow-rolling" approximation. We show that the inhomogeneous scales which before inflation were not much greater then the physical horizon, conserve their spectrum (almost) unaltered after the de Sitter phase.
We consider the effective evolution of a phenomenological model from FLRW supersymmetric quantum cosmology with a scalar field. The scalar field acts as a clock and inflaton. We examine a family of simple superpotentials that produce an inflation whose virtual effect on inhomogeneous fluctuations shows very good agreement with PLANCK observational evidence for the tensor-to-scalar ratio and the scalar spectral index.
A new model of the observed universe, using solutions to the full Einstein equations, is developed from the hypothesis that our observable universe is an underdense bubble, with an internally inhomogeneous fractal bubble distribution of bound matter systems, in a spatially flat bulk universe. It is argued on the basis of primordial inflation and resulting structure formation, that the clocks of the isotropic observers in average galaxies coincide with clocks defined by the true surfaces of matter homogeneity of the bulk universe, rather than the comoving clocks at average spatial positions in …
A new gauge-invariant criterion for stability against inhomogeneous perturbations of de Sitter space is applied to scenarios of dark energy and inflation in scalar-tensor gravity. The results extend previous studies.
Models of inflationary cosmology admit a choice of the metric for which the geometry of homogeneous isotropic solutions becomes flat Minkowski space in the infinite past. In this primordial flat frame all mass scales vanish in the infinite past and quantum scale symmetry is realized. The cosmological evolution is dominantly described by the slow increase of a scalar field which sets the scale of all masses. We construct the primordial flat frame for standard models of inflation as Starobinsky inflation or chaotic inflation. In particular, we discuss the evolution of inhomogeneous solutions in …
We study analytically and numerically the inflationary solutions for various type scalar potentials in the nonminimally coupled scalar field theory. The Hamilton-Jacobi equation is used to deal with nonlinear evolutions of inhomogeneous spacetimes and the long-wavelength approximation is employed. The constraints that lead to a sufficient inflation are found for the nonminimal coupling constant and initial conditions of the scalar field for inflation potentials. In particular, we numerically find an inflationary solution in the new inflation model of a nonminimal scalar field.
We find a simple inflationary solution in an inhomogeneous spacetime with heat flux. The heat flux obeys a causal transport equation, and counteracts the inflationary decrease of energy density. At late times, the heat flux tends to zero and the fluid approaches the equation of state $p=-ρ$.
A non-minimal coupling $η$ has been attracting growing interest particularly in the context of inflation models, though its quantum nature is not clear yet. We study the renormalization of a non-minimal coupling in the scalar quantum electrodynamics (QED). We find ${\it no}$ inhomogeneous term of the renormalization group equation (RGE) at the two-loop level. This is similar to other theories, where an inhomogeneous term of the RGE appears only at a higher-loop order: e.g., four-loop order in $λϕ^{4}$ theory.
In homogeneous and isotropic Friedmann-Robertson-Walker cosmology, the topology of the universe determines its ultimate fate. If the Weak Energy Condition is satisfied, open and flat universes must expand forever, while closed cosmologies can recollapse to a Big Crunch. A similar statement holds for homogeneous but anisotropic (Bianchi) universes. Here, we prove that $arbitrarily$ inhomogeneous and anisotropic cosmologies with "flat" (including toroidal) and "open" (including compact hyperbolic) spatial topology that are initially expanding must continue to expand forever at least in some regi…
In this paper, we have investigated the possibility to have inflation from inhomogeneous viscous fluids by taking into account the brane correction coming from string-inspired five dimensional Einsten's gravity. We have realized several kinds of viable solutions for early-time acceleration. At the end of inflation, the classical Einstein's gravity is recovered and fluids produce decelerated expansion.
We propose a cosmological model that describes isotropic expansion of inhomogeneous universe. The energy-momentum tensor that creates the spatial inhomogeneity may not affect the uniform expansion scaling factor $a(t)$ in the FLRW-like metrics. Such energy-momentum tensor may not be exotic; in fact any linear or non-linear $σ$-model has this feature. We show that the classical spatial inhomogeneity can be embedded in both inflation models and the traditional cosmological expansion by perfect fluid. The spatial inhomogeneity resembles the primordial quantum perturbation that was frozen in the c…
A cosmological scenario is proposed where the dark matter (DM) and dark energy (DE) of the universe are two simultaneous manifestations of an inhomogenous dilaton. The equation of state of the field is scale-dependent and pressureless at galactic and larger scales and it has negative pressure as a DE at very large scales. The dilaton drives an inflationary phase followed by a kinetic energy-dominated one, as in the "quintessential inflation" model introduced by Peebles & Vilenkin, and soon after the end of inflation particle production seeds the first inhomogeneities that lead to galaxy format…
Some exact solutions for the Einstein field equations corresponding to inhomogeneous $G_2$ cosmologies with an exponential-potential scalar field which generalize solutions obtained previously are considered. Several particular cases are studied and the properties related to generalized inflation and asymptotic behaviour of the models are discussed.
In the new-minimal supergravity formulation we present the embedding of the $R+R^2$ Starobinsky model of inflation. Starting from the superspace action we perform the projection to component fields and identify the Starobinsky model in the bosonic sector. Since there exist no other scalar fields, this is by construction a single field model. This higher curvature supergravity also gives rise to a propagating massive vector. Finally we comment on the issues of higher order corrections and initial conditions.
The dynamics of both the preinflationary and the preheating epochs for a model consisting of a Higgs inflaton plus an additional auxiliary field are studied in full General Relativity. The minimally coupled auxiliary field allows for parametric-type resonances that successfully transfer energy from the inflaton condensate to particle excitations in both fields. Depending on the interaction strengths of the fields, the broad resonance periods lead to structure formation consisting of large under/over-densities, and possibly the formation of compact objects. Moreover, when confronting the same m…
In the framework of multidimensional $f(R)$ gravity, we study the metrics of compact extra dimensions assuming that our 4D space has the de Sitter metric. Manifolds described by such metrics could be formed at the inflationary and even higher energy scales. It is shown that in the presence of a scalar field, varying in the extra factor space $\mathbb{M}_2$, it is possible to obtain a variety of inhomogeneous metrics in $\mathbb{M}_2$. Each of these metrics leads to a certain value of the 4D cosmological constant $Λ_4$, and in particular, it is possible to obtain $Λ_4 =0$, as is confirmed by nu…
We study a generality of an inflationary scenario by integrating the Einstein equations numerically in a plane-symmetric spacetime. We consider the inhomogeneous spacetimes due to (i) localized gravitational waves with a positive cosmological constant $Λ$, and (ii) an inhomogeneous inflaton field $Φ$ with a potential $\frac12 m^2 Φ^2$. For the case (i), we find that any initial inhomogeneities are smoothed out even if waves collide, so that we conclude that inhomogeneity due to gravitational waves do not prevent the onset of inflation. As for the case (ii), if the mean value of the inflaton fi…
We present exact non-singular bounce solutions of general relativity in the presence of a positive cosmological constant and an electromagnetic field, without any exotic matter. The solutions are distinguished by being spatially inhomogeneous in one direction, while they can also contain non-trivial electromagnetic field lines. The inhomogeneity may be substantial, for instance, there can be one bounce in one region of the universe and two bounces elsewhere. Since the bounces are followed by a phase of accelerated expansion, the metrics described here also permit the study of (geodesically com…
In this paper, we reconstruct viable inflationary models by starting from spectral index and tensor-to-scalar ratio from Planck observations. We analyze three different kinds of models: scalar field theories, fluid cosmology and f(R)-modified gravity. We recover the well known R^2-inflation in Jodan frame and Einstein frame representation, the massive scalar inflaton models and two models of inhomogeneous fluid. A model of R^2-correction to Einstein's gravity plus a "cosmological constant" with an exact solution for early time acceleration is reconstructed.
Extending our previous work on the robustness of inflation to perturbations in the scalar field, we investigate the effects of perturbations in the transverse traceless part of the extrinsic curvature on the evolution of an inhomogeneous inflaton field. Focusing on small field models, we show that these additional metric inhomogeneities initially reduce the total number of e-folds as the amplitude increases, but that the reduction saturates and even reverses above a certain amplitude. We present an argument that this is due to the presence of a large initial Hubble friction when metric perturb…
We analyse numerically the onset of pre-big bang inflation in an inhomogeneous, spherically symmetric Universe. Adding a small dilatonic perturbation to a trivial (Milne) background, we find that suitable regions of space undergo dilaton-driven inflation and quickly become spatially flat ($Ω\to 1$). Numerical calculations are pushed close enough to the big bang singularity to allow cross checks against previously proposed analytic asymptotic solutions.
We elaborate on the inflationary model starting from multidimensional Lagrangian and gravity with second-order curvature terms. The effective scalar field is related to the Ricci scalar of extra dimensions. It is shown that the Kretschmann and the Ricci tensor square terms dominate during inflation. The observable values of the spectral index and the tensor-to-scalar ratio are obtained for specific values of the model parameters.
It is shown that a large class of higher-order (i.e. non-quadratic) scalar kinetic terms can, without the help of potential terms, drive an inflationary evolution starting from rather generic initial conditions. In many models, this kinetically driven inflation (or "k-inflation" for short) rolls slowly from a high-curvature initial phase, down to a low-curvature phase and can exit inflation to end up being radiation-dominated, in a naturally graceful manner. We hope that this novel inflation mechanism might be useful in suggesting new ways of reconciling the string dilaton with inflation.
We contrast the possibility of inflation starting a) from the universe's inception or b) from an earlier non-inflationary state. Neither case is ideal since a) assumes quantum mechanical reasoning is straightforwardly applicable to the early universe; while case b) requires that a singularity still be present. Further, in agreement with Vachaspati and Trodden [1] case b) can only solve the horizon problem if the non-inflationary phase has equation of state $γ<4/3$.
In this paper, we analyzed inflation from k-essence in the framework of Horndeski gravity. In the specific, we considered models of canonical scalar field and k-essence with quadratic kinetic term. Viable inflationary models can be reconstructed by starting from the cosmological data. Several possibilities are explored in order to correctly reproduce the spectral index and the tensor-to-scalar ratio of primordial cosmological perturbations.
Starting from the inhomogeneous shear--free Nariai metric we show, by solving the Einstein--Klein--Gordon field equations, how a self--interacting scalar field plus a material fluid, a variable cosmological term and a heat flux can drive the universe to its currently observed state of homogeneous accelerated expansion. A quintessence scenario where power-law inflation takes place for a string-motivated potential in the late--time dominated field regime is proposed.
Using ideas of STM theory, but starting from a 6D vacuum state, we propose an inflationary model where the universe emerges from the blast of a white hole. Under this approach, the expansion is affected by a geometrical deformation induced by the gravitational attraction of the hole, which should be responsible for the k_{R}-non invariant spectrum of galaxies (and likewise of the matter density) today observed.
Starting from a gauge invariant treatment of perturbations an analytical expression for the spectrum of long wavelength density perturbations in warm inflation is derived. The adiabatic and entropy modes are exhibited explicitly. As an application of the analytical results, we determined the observational constraint for the dissipation term compatible with COBE observation of the cosmic microwave radiation anisotropy for some specific models. In view of the results the feasibility of warm inflation is discussed.
We investigate a framework aiming to provide a common origin for the large-angle anomalies detected in the Cosmic Microwave Background (CMB), which are hypothesized as the result of the statistical inhomogeneity developed by different isocurvature fields of mass $m\sim H$ present during inflation. The inhomogeneity arises as the combined effect of $(i)$ the initial conditions for isocurvature fields (obtained after a fast-roll stage finishing many $e$-foldings before cosmological scales exit the horizon), $(ii)$ their inflationary fluctuations and $(iii)$ their coupling to other degrees of fre…
It is shown in this letter that in the framework of an inhomogeneous geometry and a massive non self-interacting scalar field with spherical symmetry, one needs a homogeneous patch bigger than a dizaine of horizons in order to start inflation. The results are completly independent of initial conditions on the spatial distribution of the scalar field. The initial condition on the metric parameters are also justified. This is a generalization of the results obtained in Ref.[1], showing that their conclusions are rather robust.
In this contribution we summarize two recent applications of a correspondence between backreaction terms in averaged inhomogeneous cosmologies and an effective scalar field (the `morphon'). Backreaction terms that add to the standard sources of Friedmannian kinematical laws and that emerge from geometrical curvature invariants built from inhomogeneities, can be interpreted in terms of a minimally coupled scalar field in the case of a dust matter source. We consider closure conditions of the averaged equations that lead to different evolution scenarii: a) the standard Chaplygin equation of stat…
We consider the possibility that the universe, viewed as a three-brane, originated in a region of strong external field strength due to a four-form gauge field in the bulk. It is shown that in a scenario of this kind inflation is generic for a wide range of initial conditions. This is true even for small field inflation with a simple quadratic inflaton potential, as well as for Higgs potentials with the initial field well away from the local maximum, not necessarily starting from rest. The power spectrum, spectral index, and $r$ parameter help to constrain parameters in this scenario, and $r<0…
The slow-roll approximation is the usual starting point to study the constraints imposed on the inflaton potential parameters by the observational data. We show that, for a potential exhibiting at least two extrema and giving rise to a limited inflationary period, slow-roll does not have to be taken as an additional hypothesis and is in fact forced by the constraints on the number of e-foldings.
