New exact solutions in standard inflationary models

Chervon, S. V.; Zhuravlev, V. M.; Shchigolev, V. K.

doi:10.1016/s0370-2693(97)00238-4

Cited by 48 publications

(55 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is an analogue of fine tuning of the potential method applied to a single scalar field [5]. Let us start with a simplification for the chiral metric components…”

Section: The Methods Of Exact Solutions Construction Two Classes Of Ementioning

confidence: 99%

See 1 more Smart Citation

Exact Inflationary Solutions Inspired by the Emergent Universe Scenario

et al. 2014

View full text Add to dashboard Cite

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.

show abstract

“…This is an analogue of fine tuning of the potential method applied to a single scalar field [5]. Let us start with a simplification for the chiral metric components…”

Section: The Methods Of Exact Solutions Construction Two Classes Of Ementioning

confidence: 99%

“…To solve these equations, we specify the scale factor of the universe a = a(t) (see also [5]). This is in contrast to the traditional way of solving such problems where the metric of the target space is specified.…”

Section: Basic Equations Of 2-ccmmentioning

confidence: 99%

Exact Inflationary Solutions Inspired by the Emergent Universe Scenario

et al. 2014

View full text Add to dashboard Cite

show abstract

“…Since they lead to different inflationary scenarios, particularly in respect of the density fluctuations produced, they have different observational consequences for the cosmic microwave background radiation, and this permits them to be finely constrained by observational data. Various inflaton potentials in general relativistic scalar field cosmology have been proposed in [5][6][7][8][9][10][11][12][13][14][15][16][17][18] , while for inflationary models in other gravity theories, where there are more possibilities, see [1,[19][20][21][22][23][24][25][26][27][28][29][30] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Reconstructions of the dark-energy equation of state and the inflationary potential

Barrow

Paliathanasis

2018

Gen Relativ Gravit

View full text Add to dashboard Cite

We use a mathematical approach based on the constraints systems in order to reconstruct the equation of state and the inflationary potential for the inflaton field from the observed spectral indices for the density perturbations n s and the tensor to scalar ratio r . From the astronomical data, we can observe that the measured values of these two indices lie on a two-dimensional surface. We express these indices in terms of the Hubble slow-roll parameters and we assume that n s − 1 = h (r ). For the function h (r ), we consider three cases, where h (r ) is constant, linear and quadratic, respectively. From this, we derive second-order equations whose solutions provide us with the explicit forms for the expansion scale-factor, the scalar-field potential, and the effective equation of state for the scalar field. Finally, we show that for there exist mappings which transform one cosmological solution to another and allow new solutions to be generated from existing ones.

show abstract

“…There one can see that an increase in x 0 leads to a decrease of a minimal y 0 necessary for inflation to occur. Up to x 0 = 2.7 there are no finite solutions of the equation (17) which are more than √ 3 in the range of x on the left of x 0 , therefore, x 0 < 2.7 should be excluded from the further search for those initial conditions that would be sufficient for the inflation's occurrence. (17), and for which this solutions are more than √ 3 on some range of the x axis, for corresponding x 0…”

Section: The Initial Conditions Leading To Inflationmentioning

confidence: 99%

Application of the Abel equation of the 1st kind to inflation analysis of non-exactly solvable cosmological models

2014

View full text Add to dashboard Cite

Application of the Abel Equation of the 1st kindto an inflation analysis of non-exactly solvable cosmological modelsIn this paper we revisit the relationship between the Einstein-Friedman and the Abel equations to demonstrate how it might be applied to the inflationary analysis in a flat Friedman universe filled with a real-valued scalar field. The analysis is performed for three distinct cases of polynomial potentials. As a result of a numeric integration of Abel equation, the necessary and sufficient conditions for both slow-rolling and inflation proper are estimated with respect to the initial value of the field. In addition, the relationship between the slow-rolling condition and the inflation is ascertained.

show abstract

New exact solutions in standard inflationary models

Cited by 48 publications

References 17 publications

Exact Inflationary Solutions Inspired by the Emergent Universe Scenario

Exact Inflationary Solutions Inspired by the Emergent Universe Scenario

Reconstructions of the dark-energy equation of state and the inflationary potential

Application of the Abel equation of the 1st kind to inflation analysis of non-exactly solvable cosmological models

Contact Info

Product

Resources

About