### Abstract

Original language | English |
---|---|

Article number | 043510 |

Journal | Physical Review D |

Volume | 93 |

ISSN | 2470-0010 |

DOIs | |

Publication status | Published - 2016 |

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### Keywords

- hep-th
- astro-ph.CO
- gr-qc
- hep-ph

### Cite this

*Physical Review D*,

*93*, [043510]. https://doi.org/10.1103/PhysRevD.93.043510

}

*Physical Review D*, vol. 93, 043510. https://doi.org/10.1103/PhysRevD.93.043510

**Large Field Inflation and Gravitational Entropy.** / Kaloper, Nemanja; Kleban, Matthew; Lawrence, Albion; Sloth, Martin S.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - Large Field Inflation and Gravitational Entropy

AU - Kaloper, Nemanja

AU - Kleban, Matthew

AU - Lawrence, Albion

AU - Sloth, Martin S.

N1 - 25 pages including references and title page, 18 pages of text.

PY - 2016

Y1 - 2016

N2 - Large field inflation can be sensitive to perturbative and nonperturbative quantum corrections that spoil slow roll. A large number $N$ of light species in the theory, which occur in many string constructions, can amplify these problems. One might even worry that in a de Sitter background, light species will lead to a violation of the covariant entropy bound at large $N$. If so, requiring the validity of the covariant entropy bound could limit the number of light species and their couplings, which in turn could severely constrain axion-driven inflation. Here we show that there is no such problem when we correctly renormalize models with many light species, taking the {\it physical} Planck scale to be $M^2_{pl} \gtrsim N {\cal M}_{UV}^2$, where ${\cal M}_{UV}$ is the cutoff for the QFT coupled to semiclassical quantum gravity. The number of light species then cancels out of the gravitational entropy of de Sitter or near-de Sitter backgrounds at leading order. Working in detail with $N$ scalar fields in de Sitter space, renormalized to one loop order, we show that the gravitational entropy automatically obeys the covariant entropy bound. Furthermore, while the axion decay constant is a strong coupling scale for the axion dynamics, we show that it is {\it not} in general the cutoff of 4d semiclassical gravity. After renormalizing the two point function of the inflaton, we note that it is also controlled by scales much below the cutoff. We revisit $N$-flation and KKLT-type compactifications in this light, and show that they are perfectly consistent with the covariant entropy bound. Thus, while quantum gravity might yet spoil large field inflation, holographic considerations in the semiclassical theory do not obstruct it.

AB - Large field inflation can be sensitive to perturbative and nonperturbative quantum corrections that spoil slow roll. A large number $N$ of light species in the theory, which occur in many string constructions, can amplify these problems. One might even worry that in a de Sitter background, light species will lead to a violation of the covariant entropy bound at large $N$. If so, requiring the validity of the covariant entropy bound could limit the number of light species and their couplings, which in turn could severely constrain axion-driven inflation. Here we show that there is no such problem when we correctly renormalize models with many light species, taking the {\it physical} Planck scale to be $M^2_{pl} \gtrsim N {\cal M}_{UV}^2$, where ${\cal M}_{UV}$ is the cutoff for the QFT coupled to semiclassical quantum gravity. The number of light species then cancels out of the gravitational entropy of de Sitter or near-de Sitter backgrounds at leading order. Working in detail with $N$ scalar fields in de Sitter space, renormalized to one loop order, we show that the gravitational entropy automatically obeys the covariant entropy bound. Furthermore, while the axion decay constant is a strong coupling scale for the axion dynamics, we show that it is {\it not} in general the cutoff of 4d semiclassical gravity. After renormalizing the two point function of the inflaton, we note that it is also controlled by scales much below the cutoff. We revisit $N$-flation and KKLT-type compactifications in this light, and show that they are perfectly consistent with the covariant entropy bound. Thus, while quantum gravity might yet spoil large field inflation, holographic considerations in the semiclassical theory do not obstruct it.

KW - hep-th

KW - astro-ph.CO

KW - gr-qc

KW - hep-ph

U2 - 10.1103/PhysRevD.93.043510

DO - 10.1103/PhysRevD.93.043510

M3 - Journal article

VL - 93

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

M1 - 043510

ER -