A refined Einstein–Gauss–Bonnet inflationary theoretical framework
V K Oikonomou
Abstract
Abstract We provide a refined and much more simplified Einstein–Gauss–Bonnet inflationary theoretical framework, which is compatible with the GW170817 observational constraints on the gravitational wave speed. As in previous works, the constraint that the gravitational wave speed is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> <mml:mrow> <mml:mtext>T</mml:mtext> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:math> in natural units, results to a constraint differential equation that relates the coupling function of the scalar field to the Gauss–Bonnet invariant ξ ( ϕ ) and the scalar potential V ( ϕ ). Adopting the slow-roll conditions for the scalar field and the Hubble rate, and in contrast to previous works, by further assuming that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>κ</mml:mi> <mml:mfrac> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>ξ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>′</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>ξ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>″</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:mfrac> <mml:mo>≪</mml:mo> <mml:mn>1</mml:mn> </mml:math> , which is motivated by slow-roll arguments, we succeed in providing much more simpler expressions for the slow-roll indices and for the tensor and scalar spectral indices and for the tensor-to-scalar ratio. We exemplify our refined theoretical framework by using an illustrative example with a simple power-law scalar coupling function ξ ( ϕ ) ∼ ϕ ν and as we demonstrate the resulting inflationary phenomenology is compatible with the latest Planck data. Moreover, this particular model produces a blue-tilted tensor spectral index, so we discuss in brief the perspective of describing the NANOGrav result with this model as is indicated in the recent literature.