Abstract
We consider the existence of an “inflaton” described by an homogeneous scalar field in the Szekeres cosmological metric. The gravitational field equations are reduced to two families of solutions which describe the homogeneous Kantowski–Sachs spacetime and an inhomogeneous FLRW(-like) spacetime with spatial curvature a constant. The main differences with the original Szekeres spacetimes containing only pressure-free matter are discussed. We investigate the stability of the two families of solution by studying the critical points of the field equations. We find that there exist stable solutions which describe accelerating spatially-flat FLRW geometries.
Highlights
The main mechanism to explain the isotropization of the observable part of the universe today from a general set of initial conditions by means of an early period of accelerated expansion, the so-called inflationary epoch, is often based on the existence of an explicit or effective scalar field dubbed the “inflaton” [1]
As in the case of the Szekeres system, with or without the cosmological constant, we find two sets of solutions which correspond to the (a) Kantowski–Sachs family and to the (b) FLRW family, of spacetimes
2 dt plus the conservation Eq (6). At this point it is interesting that the inhomogeneous spacetime (8) reduces to the homogeneous Kantowski–Sachs element and not to the inhomogeneous Kantowski–Sachs(like) as in the case without the scalar field [13,29,31]
Summary
The main mechanism to explain the isotropization of the observable part of the universe today from a general set of initial conditions by means of an early period of accelerated expansion, the so-called inflationary epoch, is often based on the existence of an explicit or effective scalar field dubbed the “inflaton” [1]. An important family of inhomogeneous analytic spacetimes are the Szekeres spacetimes [13] They belong to the class of ’Silent’ universes where information does not propagate via gravitational or sound waves. Inhomogeneous Szekeres exact solutions with a cosmological constant were derived by Barrow et al [29], and others with a general time-dependent pressure are given in [31,32]. We know that in general the Szekeres diagonal form of the metric requires any diagonal pressure in the energy-momentum tensor to depend on time but not on space. In particular this is why exact solutions are found with dust and with dust and a cosmological constant.
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