Probing reheating in a holographic induced gravity tachyon model with latest ACT constraints

Abstract In this study, we explore the reheating phase that follows tachyon inflation within the framework of holographic induced gravity (H-IG). Analytical relations for the reheating temperature $$T_{re}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi>re</mml:mi> </mml:mrow> </mml:msub> </mml:math> and the reheating number of e-folds $$N_{re}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>N</mml:mi> <mml:mrow> <mml:mi>re</mml:mi> </mml:mrow> </mml:msub> </mml:math> are derived under the assumption of a constant effective equation of state $$\omega _{re}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ω</mml:mi> <mml:mrow> <mml:mi>re</mml:mi> </mml:mrow> </mml:msub> </mml:math> . A numerical analysis is then performed over a broad range of model parameters namely c (holographic parameter), $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> (potential parameter), and $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> (IG parameter). Incorporating the most recent observational constraints from the Atacama Cosmology Telescope (ACT), which indicate a moderate upward shift in the scalar spectral index, $$n_s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> , relative to the Planck 2018 results, we reassess the viability of tachyon inflation with an exponential potential within this framework. Our analysis shows that when $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> is large ( $$\alpha \sim 2.5\times 10^{-5})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>∼</mml:mo> <mml:mn>2.5</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> <mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , the majority of parameter combinations are consistent with observational constraints, though the best fit for the reheating duration $$N_{re}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>N</mml:mi> <mml:mrow> <mml:mi>re</mml:mi> </mml:mrow> </mml:msub> </mml:math> to the data occurs for smaller c ( $$c\sim 1\times 10^{7}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>c</mml:mi> <mml:mo>∼</mml:mo> <mml:mn>1</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>7</mml:mn> </mml:msup> </mml:mrow> </mml:math> ) and higher $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> ( $$\gamma \sim 0.9$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>γ</mml:mi> <mml:mo>∼</mml:mo> <mml:mn>0.9</mml:mn> </mml:mrow> </mml:math> ) while also satisfying the lower bound on the reheating temperature $$T_{re}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi>re</mml:mi> </mml:mrow> </mml:msub> </mml:math> .