Exact Inflationary Solutions Research Articles

New method of exponential potentials reconstruction based on given scale factor in phantonical two-field models

We investigate two-field cosmological model with phantom and canonical fields (phantonical model as a generalisation of the quintom model for global universe evolution, including early inflationary stage). The model is represented as the chiral cosmological model with the target space conformal to 2D pseudo-Euclidean space. We found three sorts of exact solutions for a constant potential by direct integration of dynamic equations and proposed new method of exact solution construction also extended for e-folds N-formalism for the case of non-constant exponential potential. We show that the exact solutions of cosmological dynamic equations can be obtained in explicit form for any type of scale factor evolution a(t) which implies the explicit inverse dependence t = t(a), considering the quasi de Sitter expansion of the universe with non-negligible kinetic energies of scalar fields and showing that the appeared effective cosmological constant can be considered as the source of second accelerated expansion of the universe. Further we analyze cosmological perturbations in the two-field model under consideration reducing it to the single field one. Such transition give us the way of cosmological parameters calculation and comparison them to observational data. We find that in proposed two-field cosmological model the isocurvature perturbations are negligible, and observable curvature perturbations are induced by adiabatic modes only. The series of phantonical models based on exact inflationary solutions are represented, and it is shown the correspondence to observational data for these models.

Dirac–Born–Infeld inflation under constant-roll conditions

In this paper, we aim to generalize the constant-roll inflation in the noncanonical set-up, in the context of scalar Dirac–Born–Infeld (DBI) theory. Assuming the simplest case, when the speed of sound of scalar fluctuations is constant, we obtain exact inflationary solutions under constant-roll conditions. We finally provide an observational bound to constrain the DBI constant-roll parameter by using the values of scalar spectral index and speed of sound provided by Planck and WMAP data.

Anisotropic constant-roll inflation for the Dirac\u2013Born\u2013Infeld model

In this paper, we study a non-canonical extension of a supergravity-motivated model acting as a vivid counterexample to the cosmic no-hair conjecture due to its unusual coupling between scalar and electromagnetic fields. In particular, a canonical scalar field is replaced by the string-inspired Dirac–Born–Infeld one in this extension. As a result, exact anisotropic inflationary solutions for this Dirac–Born–Infeld model are figured out under a constant-roll condition. Furthermore, numerical calculations are performed to verify that these anisotropic constant-roll solutions are indeed attractive during their inflationary phase.

Exact inflationary solutions in exponential gravity

We consider a modified gravity model of the form $ f(R,\phi)=R e^{h(\phi)R} $, where the strong gravity corrections are taken to all orders and $\phi$ is a self-interacting massless scalar field. We show that the conformal transformation of this model to Einstein frame leads to non-canonical kinetic term and negates the advantage of the Einstein frame. We obtain exact solutions for the background in the Jordan frame without performing conformal transformations and show that the model leads to inflation with exit. We obtain scalar and tensor power-spectrum in Jordan frame and show that the model leads to red-tilt. We discuss the implications of the same in the light of cosmological observations.

On the initial conditions of scalar and tensor fluctuations in f(R,phi ) gravity

We have considered the perturbation equations governing the growth of fluctuations during inflation in generalized scalar tensor theory f(R,phi ). We have found that the scalar metric perturbations at very early times are negligible compared to the scalar field perturbation, just like general relativity. At sufficiently early times, when the physical momentum of perturbation mode, q / a is much larger than the Hubble parameter H, i.e. q/agg H, we have obtained the metric and scalar field perturbation in the form of WKB solutions up to an undetermined coefficient. Then we have quantized the scalar fluctuations and expanded the metric and the scalar field perturbations with the help of annihilation and creation operators of the scalar field perturbation. The standard commutation relations of annihilation and creation operators fix the unknown coefficient. Going over to the gauge invariant quantities which are conserved beyond the horizon, we have obtained the initial condition of the generalized Mukhanov–Sasaki equation. Then a similar procedure is performed for the case of tensor metric perturbation. As an example of the generalized Mukhanov–Sasaki equation and its initial condition, we have proposed a power-law functional form as f(R,phi )=f_0 R^m phi ^n and obtained an exact inflationary solution. In this background, then we have discussed how the scalar and tensor fluctuations grow.

Anisotropic constant-roll Inflation

We study constant-roll inflation in the presence of a gauge field coupled to an inflaton. By imposing the constant anisotropy condition, we find new exact anisotropic constant-roll inflationary solutions which include anisotropic power-law inflation as a special case. We also numerically show that the new anisotropic solutions are attractors in the phase space.

Exact inflation in Einstein–Gauss–Bonnet gravity

We study cosmological inflation in the Einstein gravity model, where additionally the Gauss-Bonnet term non-minimally coupled to a scalar field is included. We prove that inflationary solutions of exponential and power-law types are allowable and we found few examples of them. We also proposed the method of the exact inflationary solutions construction for a single scalar field with given scale factor and Gauss-Bonnet coupling term in the spatially flat Friedmann-Robertson-Walker Universe on the basis of connection with standard inflation and using special anzatses. With one special anzats we presented the system of equations in the form which allowed generation of exact solutions (at least in quadratures) of wide class by setting the scale factor.

The high-frequency gravitational waves in exact inflationary models with Gauss-Bonnet term

We consider the exact inflationary solutions for a single scalar field with an arbitrary potential and an arbitrary nonminimal coupling to the Gauss-Bonnet term in the flat Friedmann-Robertson-Walker universe on the basis of connection with standard inflation. The possibility of the registration of relic gravitational waves by using the phenomenon of a low-frequency optical resonance in Fabri-Perot interferometers are also received.

Observational constraints on new exact inflationary scalar-field solutions

An algorithm is used to generate new solutions of the scalar field equations in homogeneous and isotropic universes. Solutions can be found for pure scalar fields with various potentials in the absence and presence of spatial curvature and other perfect fluids. A series of generalisations of the Chaplygin gas and bulk viscous cosmological solutions for inflationary universes are found. Furthermore other closed-form solutions which provide inflationary universes are presented. We also show how the Hubble slow-roll parameters can be calculated using the solution algorithm and we compare these inflationary solutions with the observational data provided by the Planck 2015 collaboration in order to constraint and rule out some of these models.

Exact Inflationary Solutions Inspired by the Emergent Universe Scenario

We present new classes of exact inflationary solutions for a two-component chiral cosmological model with phantom and canonical scalar fields. These solutions are obtained by use of the scale factor in the form corresponding to that exploited in the emergent universe scenario. We outline in detail the method of deriving exact solutions and discuss the potential and kinetic interaction for the model.

Exact inflationary solution in the chaotic inflation model to non-minimally coupled scalar field

We present a new exact inflationary solution for the chaotic inflation model with non-minimal coupling, by taking the Hubble parameter directly as a function of a scalar field. We then prove that the spectral index of the scalar density fluctuation (and other parameters), which derived from the exact inflationary solution, is exactly consistent with recent astronomical observations.

Tachyon – dilaton driven inflation as an α' – non-perturbative solution in first quantized string cosmology

Applying a novel non-perturbative functional method framework to a two-dimensional bosonic sigma model with tachyon, dilaton and graviton backgrounds we construct exact (non perturbative in the Regge slope α') inflationary solutions, consistent with world-sheet Weyl Invariance. The mechanism for inflation entails a (partial) ‘alignment’ between tachyon and dilaton backgrounds in the solution space. Some cosmological solutions which contain inflationary eras for a short period and interpolate between flat universes in the far past and far future are also discussed. These solutions are characterized by the absence of cosmological horizons, and therefore have well-defined scattering amplitudes. This makes them compatible with a perturbative string framework, and therefore it is these solutions that we consider as self-consistent in our approach. Within the context of the interpolating solutions, string production at the end of inflation (preheating) may also be studied. The advantage of our method is that the solutions are valid directly in four target-space-time dimensions, as a result of the non trivial dilaton configurations. Whether the model is phenomenologically realistic, with respect to its particle physics aspects, remains an open issue. This talk was based on work recently done with J. Alexandre and N. E. Mavromatos [1].

An exact inflationary solution in the chaotic model with non-minimal coupling

This paper presents a new exact inflationary solution to the non-minimally coupled scalar field. The inflation is driven by the evolution of a scalar field with inflation potential V(φ) = (λ/4)φ4 + b1φ2 + b2 + b3φ−2 + b4φ−4. The spectral index of the scalar density fluctuations ns is consistent with the result of WMAP3 (Wilkinson Microwave Anisotropy Probe 3) for ΛCDM (Lambda–Cold Dark Matter). This model relaxes the constraint to the quartic coupling constant. And it can enter smoothly into a radiation-dominated stage when inflation ends.

A Model with Exact Inflationary Solution in Finsler Universe

In this paper, using the Gravity’s Rainbow theory, we introduce rainbow metric into rainbow Robertson-Walker metric, and obtain a model which depends on the energy of probe particles. Furthermore, we research on an exact inflationary solution of the model, and it can be consistent with the conclusions of observation. The results of our research show that some details in inflation depend on the energy of particles which are observed by observers.

An Exact Inflationary Solution to Non-Minimally Coupling

We find a new exact inflationary solution to non-minimally coupled scalar field from a specific H(φ). The inflation is driven by the evolution of the scalar field with a new inflation potential. The spectral index of the scalar density fluctuations ns is consistent with the result of WMAP3 for the power-law flat ΛCDM model. Our solution relaxes the constraint to the quartic coupling constant, e.g. when ξ=103, λ≤8.9×10−11.

A Kind of Exact Inflationary Solution in the Chaotic Inflation Model to Non-minimally Coupled Scalar Field

We present a kind of exact inflationary solution in the chaotic inflation scenario to non-minimal coupled scalar field, taking the Hubble parameter directly as a function of the scalar field φ, H(φ) = αφn. Using the analysis of the WMAP3 data, we give the range of power index n.

ON THE QUARTIC CURVATURE GRAVITY IN THE CONTEXT OF FRW COSMOLOGY

We consider the purely gravitational fourth-order (in the spacetime curvature) quantum corrections to the Einstein-Hilbert gravity action, coming from superstrings in the leading order with respect to the Regge slope parameter, and study their impact on the evolution of the Hubble scale in the context of the FRW cosmology, in four spacetime dimensions. We propose the generalized Friedmann equations, and rule out the most naive (Bel-Robinson tensor squared) gravity. Our new cosmological equations have exact inflationary solutions without a spacetime singularity.

Exact Scalar Field Inflationary Solution in Rainbow Universe

Using the Friedmann equation in rainbow Universe, we obtain an exact scalar field Inflationary Solution, which is a modification of the exact scalar field with negative potential −V0+m2φ2/2. Because the rainbow metric is Finsler metric, the result in this paper implies that the research of Finsler geometry in Cosmology should lead to several new physics theories.

On the Superstrings‐Induced Four‐Dimensional Gravity and Its Applications to Cosmology

We review the status of the fourth‐order (quartic in the spacetime curvature) terms induced by superstrings/M‐theory (compactified on a warped torus) in the leading order with respect to the Regge slope parameter, and study their (nonperturbative) impact on the evolution of the Hubble scale in the context of the four‐dimensional FRW cosmology. After taking into account the quantum ambiguities in the definition of the off‐shell superstring effective action, we propose the generalized Friedmann equations, find the existence of their (de Sitter) exact inflationary solutions without a spacetime singularity, and constrain the ambiguities by demanding stability and the scale factor duality invariance of our solutions. The most naive (Bel‐Robinson tensor squared) quartic terms are ruled out, thus giving the evidence for the necessity of extra quartic (Ricci tensor‐dependent) terms in the off‐shell gravitational effective action for superstrings. Our methods are generalizable to the higher orders in the spacetime curvature.

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.