Observational constraints on new exact inflationary scalar-field solutions

Abstract

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.PACS numbers: 98.80.-k, 95.35.+d, 95.36.+x

On the Necessity of Phantom Fields for Solving the Horizon Problem in Scalar Cosmologies

“…Incidentally, it should be noticed that Equation (35) grants a(τ) < a(τ + ) for τ ∈ (τ 0 , τ + ); together with the assumption k 0 of Equation (31) and the conditions on w i , λ i stated in Equations (34) and (33), this yields…”

“…Let us recall that λ i is the constant coefficient introduced in Equation (12), while w i is the parameter in the equation of state (9). The condition (33) means that all fluids have positive densities; assuming this, the conditions in Equation (34) mean that all the n fluids fulfill the weak energy condition and at least one of them fulfills (as a strict inequality) the strong energy condition (compare with Equations (23) and (24)). Let us also remark that w i > (2/d) − 1 > −1 if the ith fluid is a radiation (w i = 1/d) in spatial dimension d 2, or a dust (w i = 0) in spatial dimension d 3.…”

“…Exact solutions of the Einstein equations for these models are obtained in [12,18,[22][23][24][25][26][27][28][29][30][31][32][33]. Again, in the area of exact solutions, we would mention a peculiar, "inverse" approach to the evolution equations of scalar cosmologies: here the time dependence of the scale factor (or of some other physically relevant quantity) is prescribed, and the Einstein equations are used to determine the other observables of the model, including the self-interaction potential of the scalar field [5,10,34,35].…”

A new approach to exact solutions construction in scalar cosmology with a Gauss–Bonnet term

“…In the present work we generalize the proposed method to the case of an open and closed Friedmann universe, besides new solutions for a spatially-flat universe are presented as well. It should be noted here, that we used the presentation of open and closed universes as a spatiallyflat one filled by a perfect fluid [25].…”

Superpotential method for chiral cosmological models connected with modified gravity

“…It is difficult to consider such solutions as exact ones without involving the dynamic equations of the chiral fields 2. Other methods allowing to find exact solutions in inflationary models were presented in[26,31,32,34,[51][52][53][54][55][56][57][58] (for recent review, see[33]). …”