<p>We study a single-field inflationary scenario with a nontrivial coupling to the Gauss–Bonnet term and compute its predictions for the background dynamics and cosmological perturbations. The model is analyzed within the slow-roll regime, and we derive analytic expressions for the inflationary observables, including the scalar spectral index <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$n_s$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>n</mi> <mi>s</mi> </msub> </math></EquationSource> </InlineEquation>, the tensor-to-scalar ratio <i>r</i>, and the running <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\alpha _s$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>α</mi> <mi>s</mi> </msub> </math></EquationSource> </InlineEquation>. Motivated by string-theoretic considerations, we impose the theoretical constraint <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$V(\phi )\xi (\phi ) = \text {constant}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>V</mi> <mo stretchy="false">(</mo> <mi>ϕ</mi> <mo stretchy="false">)</mo> <mi>ξ</mi> <mo stretchy="false">(</mo> <mi>ϕ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mtext>constant</mtext> </mrow> </math></EquationSource> </InlineEquation>, which reduces the parameter space and provides a more predictive framework. The Gauss–Bonnet coupling modifies the standard consistency relations and enables compatibility with current Planck constraints for a broad parameter range (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">$n_s \in [0.955, 0.970]$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>n</mi> <mi>s</mi> </msub> <mo>∈</mo> <mrow> <mo stretchy="false">[</mo> <mn>0.955</mn> <mo>,</mo> <mn>0.970</mn> <mo stretchy="false">]</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$r \in [0.003, 0.09]$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>r</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>0.003</mn> <mo>,</mo> <mn>0.09</mn> <mo stretchy="false">]</mo> </mrow> </math></EquationSource> </InlineEquation>). We perform a comprehensive Markov Chain Monte Carlo (MCMC) analysis using Planck 2018 and BICEP/Keck data, obtaining posterior constraints on model parameters. Additionally, we examine swampland compatibility, reheating predictions, non-Gaussian signatures, and potential implications for primordial black hole formation. Our analysis demonstrates that this framework provides a well-motivated extension of standard single-field inflation while maintaining observational viability and offering distinctive testable predictions for future cosmological surveys.</p>

Constrained Gauss–Bonnet inflation: analytical predictions, MCMC constraints from Planck/BK18, and primordial black hole signatures

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发表日期：

2026年8月3日

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Feyzollah Younesizadeh,
Younes Younesizadeh,
Ahmed E. Ali

摘要

We study a single-field inflationary scenario with a nontrivial coupling to the Gauss–Bonnet term and compute its predictions for the background dynamics and cosmological perturbations. The model is analyzed within the slow-roll regime, and we derive analytic expressions for the inflationary observables, including the scalar spectral index $n_s$ $n_{s}$ , the tensor-to-scalar ratio r, and the running $\alpha _s$ $α_{s}$ . Motivated by string-theoretic considerations, we impose the theoretical constraint $V(\phi )\xi (\phi ) = \text {constant}$ $V (ϕ) ξ (ϕ) = constant$ , which reduces the parameter space and provides a more predictive framework. The Gauss–Bonnet coupling modifies the standard consistency relations and enables compatibility with current Planck constraints for a broad parameter range ( $n_s \in [0.955, 0.970]$ $n_{s} \in [0.955, 0.970]$ , $r \in [0.003, 0.09]$ $r \in [0.003, 0.09]$ ). We perform a comprehensive Markov Chain Monte Carlo (MCMC) analysis using Planck 2018 and BICEP/Keck data, obtaining posterior constraints on model parameters. Additionally, we examine swampland compatibility, reheating predictions, non-Gaussian signatures, and potential implications for primordial black hole formation. Our analysis demonstrates that this framework provides a well-motivated extension of standard single-field inflation while maintaining observational viability and offering distinctive testable predictions for future cosmological surveys.