Abstract
In this paper, we extend our investigation of the validity of the cosmic no-hair conjecture within non-canonical anisotropic inflation. As a result, we are able to figure out an exact Bianchi type I solution to a power-law k-inflation model in the presence of unusual coupling between scalar and electromagnetic fields as -f^2(phi )F_{mu nu }F^{mu nu }/4. Furthermore, stability analysis based on the dynamical system method indicates that the obtained solution does admit stable and attractive hairs during an inflationary phase and therefore violates the cosmic no-hair conjecture. Finally, we show that the corresponding tensor-to-scalar ratio of this model turns out to be highly consistent with the observational data of the Planck 2018.
Highlights
Cosmological principle, which states that our universe is just homogeneous and isotropic on large scales as described the Friedmann–Lemaitre–Robertson–Walker (FLRW) spacetime, has played a central role in cosmology it is not straightforward to observationally confirm this principle [1,2,3]
Many theoretical predictions of the so-called cosmic inflation theory [4,5,6,7], which is basically based on the cosmological principle, have been well confirmed by the cosmic microwave background radiations (CMB) observations such as the Wilkinson Microwave Anisotropy Probe satellite (WMAP) [8] as well as the Planck one [9,10,11]
If the early universe was slightly anisotropic, an important question would be naturally addressed: what would the current state of our universe be ? In other words, would it be slightly anisotropic or completely isotropic ? It is worth noting that some observational evidences have claimed that the current universe might not be isotropic but anisotropic [17]
Summary
Cosmological principle, which states that our universe is just homogeneous and isotropic on large scales as described the Friedmann–Lemaitre–Robertson–Walker (FLRW) spacetime, has played a central role in cosmology it is not straightforward to observationally confirm this principle [1,2,3]. It is worth noting that Starobinsky showed in his seminal paper that the Einstein gravity in the presence of cosmological constant admits an inflationary solution, which will approach globally to an isotropic but inhomogeneous state at late time, regarding the hairs as primordial scalar and tensor perturbations [21]. This model has been shown to admit a Bianchi type I metric, which is homogeneous but anisotropic, as its stable and attractive solution during an inflationary phase, due to the existence of unusual coupling between scalar and electromagnetic (vector) fields − f 2(φ)Fμν Fμν/4 This result indicates that the cosmic nohair conjecture is really broken down in the KSW model. If the cosmic no-hair conjecture was valid within the KSW model as well as in its extensions, the corresponding anisotropic solutions should be unstable against field perturbations during an inflationary phase, meaning that they should decay to an isotropic state at late time. The Einstein field equation can be written explicitly as follows (see the Appendix 1 for a detailed derivation)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
