Loop corrections in the bispectrum in ultraslow-roll inflation with PBHs formation

Firouzjahi, Hassan

doi:10.1103/physrevd.110.043519

Phys. Rev. D

2024

DOI: 10.1103/physrevd.110.043519

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Loop corrections in the bispectrum in ultraslow-roll inflation with PBHs formation

Hassan Firouzjahi

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2024

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Cited by 3 publications

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Proving the absence of large one-loop corrections to the power spectrum of curvature perturbations in transient ultra-slow-roll inflation within the path-integral approach

Kawaguchi,

Tsujikawa,

Yamada

2024

J. High Energ. Phys.

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We revisit one-loop corrections to the power spectrum of curvature perturbations ζ in an inflationary scenario containing a transient ultra-slow-roll (USR) period. In ref. [1], it was argued that one-loop corrections to the power spectrum of ζ can be larger than the tree-level one within the parameter region generating the seeds of primordial black holes during the USR epoch, which implies the breakdown of perturbation theory. We prove that this is not the case by using a master formula for one-loop corrections to the power spectrum obtained in ref. [2]. We derive the same formula within the path-integral formalism, which is simpler than the original derivation in [2]. To show the smallness of one-loop corrections, the consistency relations and the effective constancy of tree-level mode functions of ζ for super-Hubble modes play essential roles, with which the master formula gives a simple expression for one-loop corrections. For concreteness, we provide a reduced set of interactions including the leading-order one, while establishing the consistency relations in a self-consistent manner. We also show how the consistency relations of various operators hold explicitly, which plays a key role in proving the absence of large one-loop corrections.

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Proving the absence of large one-loop corrections to the power spectrum of curvature perturbations in transient ultra-slow-roll inflation within the path-integral approach

Kawaguchi,

Tsujikawa,

Yamada

2024

J. High Energ. Phys.

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Comparing sharp and smooth transitions of the second slow-roll parameter in single-field inflation

Kristiano,

Yokoyama

2024

J. Cosmol. Astropart. Phys.

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In single-field inflation, violation of the slow-roll approximation can lead to growth of curvature perturbation outside the horizon. This violation is characterized by a period with a large negative value of the second slow-roll parameter. At an early time, inflation must satisfy the slow-roll approximation, so the large-scale curvature perturbation can explain the cosmic microwave background fluctuations. At intermediate time, it is viable to have a theory that violates the slow-roll approximation, which implies amplification of the curvature perturbation on small scales. Specifically, we consider ultraslow-roll inflation as the intermediate period. At late time, inflation should go back to the slow roll period so that it can end. This means that there are two transitions of the second slow-roll parameter. In this paper, we compare two different possibilities for the second transition: sharp and smooth transitions. Focusing on effects generated by the relevant cubic self-interaction of the curvature perturbation, we find that the bispectrum and one-loop correction to the power spectrum due to the change of the second slow-roll parameter vanish if and only if the Mukhanov-Sasaki equation for perturbation satisfies a specific condition called Wands duality. We also find in the case of sharp transition that, even though this duality is satisfied in the ultraslow-roll and slow-roll phases, it is severely violated at the transition so that the resultant one-loop correction is extremely large inversely proportional to the duration of the transition.

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Two-Loop Corrections in Power Spectrum in Models of Inflation with Primordial Black Hole Formation

Firouzjahi

2024

Universe

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We calculated the two-loop corrections in the primordial power spectrum in models of single-field inflation incorporating an intermediate USR phase employed for PBH formation. Among the overall eleven one-particle irreducible Feynman diagrams, we calculated the corrections from the “double scoop” two-loop diagram involving two vertices of quartic Hamiltonians. We demonstrate herein the fractional two-loop correction in power spectrum scales, like the square of the fractional one-loop correction. We confirm our previous findings that the loop corrections become arbitrarily large in the setup where the transition from the intermediate USR to the final slow-roll phase is very sharp. This suggests that in order for the analysis to be under perturbative control against loop corrections, one requires a mild transition with a long enough relaxation period towards the final attractor phase.

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Loop corrections in the bispectrum in ultraslow-roll inflation with PBHs formation

Cited by 3 publications

References 73 publications

Proving the absence of large one-loop corrections to the power spectrum of curvature perturbations in transient ultra-slow-roll inflation within the path-integral approach

Proving the absence of large one-loop corrections to the power spectrum of curvature perturbations in transient ultra-slow-roll inflation within the path-integral approach

Comparing sharp and smooth transitions of the second slow-roll parameter in single-field inflation

Two-Loop Corrections in Power Spectrum in Models of Inflation with Primordial Black Hole Formation

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