Abstract
In this paper, we extend a recent proposed model of two scalar and two vector fields to a hyperbolic inflation scenario, in which the field space of two scalar fields is a hyperbolic space instead of a flat space. In this model, one of the scalar fields is assumed to be a radial field, while the other is set as an angular field. Furthermore, both scalar fields will be coupled to two different vector fields, respectively. As a result, we are able to obtain a set of exact Bianchi type I solutions to this model. Stability analysis is also performed to show that this set of anisotropic solutions is indeed stable and attractive during the inflationary phase. This result indicates that the cosmic no-hair conjecture is extensively violated in this anisotropic hyperbolic inflation model.
Highlights
Cosmic inflation [1–4] has been regarded as a leading paradigm in modern cosmology
This result is due to the fact that many of its theoretical predictions have been shown to be highly consistent with the leading cosmic microwave background radiation (CMB) probes such as the Wilkinson Microwave Anisotropy Probe (WMAP) [5] and the Planck [6–8]
It is worth noting that the backbone of all standard inflationary models [9] has been the cosmological principle [10–13], whose statement is that our universe is just homogeneous and isotropic on large scales as described by the Friedmann–Lemaitre–Robertson–Walker (FLRW) spacetime [14]
Summary
Cosmic inflation [1–4] has been regarded as a leading paradigm in modern cosmology. This result is due to the fact that many of its theoretical predictions have been shown to be highly consistent with the leading cosmic microwave background radiation (CMB) probes such as the Wilkinson Microwave Anisotropy Probe (WMAP) [5] and the Planck [6–8]. A recent study has revealed an interesting smoking gun evidence that the current universe might be anisotropic, i.e., might violate the cosmological principle [23] This is contrast to the statement of the so-called cosmic no-hair conjecture proposed by Hawking and his colleagues long ago [24,25]. The first vivid counterexample to the cosmic no-hair conjecture has been constructed successfully by Kanno, Soda, and Watanabe (KSW) [53,54] As a result, this counterexample is nothing but a stable and attractive Bianchi type I inflationary solution of a supergravitymotivated model, which involves a special coupling between scalar and vector fields of the form f 2(φ)Fμν Fμν [54]. Two scalar fields are allowed to non-minimally couple to two vector fields, respectively This model has been shown to admit an exact Bianchi type I power-law solution, which turns out to be stable and attractive during its inflationary phase.
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