Energy conditions in Gauss–Bonnet gravity

Abstract We study the Energy Conditions in modified $$f(\mathcal {G})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> gravity, with $$\mathcal {G}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>G</mml:mi> </mml:math> being the topological Gauss–Bonnet term. Then we use the cosmographic parameters to constrain the functional form of the gravitational action and investigate the possibility to have standard inflation in the early time. Specifically, we select models containing symmetries within the modified $$f(\mathcal {G})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> theory and obtain conditions for which (i) the energy conditions can be violated and (ii) the magnitude of the slow-roll parameters is small, thus suggesting that under given limits the analyzed theory can potentially trace the cosmic history both at early and at the late times.