### Abstract

Just because the propagator of some field obeys a de Sitter invariant equation does not mean it possesses a de Sitter invariant solution. The classic example is the propagator of a massless, minimally coupled scalar. We show that the same thing happens for massive scalars with M _{S} ^{2}<0 and for massive transverse vectors with M _{V} ^{2}≤-2(D-1)H ^{2}, where D is the dimension of space-time and H is the Hubble parameter. Although all masses in these ranges give infrared divergent mode sums, using dimensional regularization (or any other analytic continuation technique) to define the mode sums leads to the incorrect conclusion that de Sitter invariant solutions exist except at discrete values of the masses.

Original language | English |
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Article number | 038006JMP |

Journal | Journal of Mathematical Physics |

Volume | 51 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2010 Jul 1 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*51*(7), [038006JMP]. https://doi.org/10.1063/1.3448926

}

*Journal of Mathematical Physics*, vol. 51, no. 7, 038006JMP. https://doi.org/10.1063/1.3448926

**De Sitter breaking through infrared divergences.** / Miao, Shun-Pei; Tsamis, N. C.; Woodard, R. P.

Research output: Contribution to journal › Article

TY - JOUR

T1 - De Sitter breaking through infrared divergences

AU - Miao, Shun-Pei

AU - Tsamis, N. C.

AU - Woodard, R. P.

PY - 2010/7/1

Y1 - 2010/7/1

N2 - Just because the propagator of some field obeys a de Sitter invariant equation does not mean it possesses a de Sitter invariant solution. The classic example is the propagator of a massless, minimally coupled scalar. We show that the same thing happens for massive scalars with M S 2<0 and for massive transverse vectors with M V 2≤-2(D-1)H 2, where D is the dimension of space-time and H is the Hubble parameter. Although all masses in these ranges give infrared divergent mode sums, using dimensional regularization (or any other analytic continuation technique) to define the mode sums leads to the incorrect conclusion that de Sitter invariant solutions exist except at discrete values of the masses.

AB - Just because the propagator of some field obeys a de Sitter invariant equation does not mean it possesses a de Sitter invariant solution. The classic example is the propagator of a massless, minimally coupled scalar. We show that the same thing happens for massive scalars with M S 2<0 and for massive transverse vectors with M V 2≤-2(D-1)H 2, where D is the dimension of space-time and H is the Hubble parameter. Although all masses in these ranges give infrared divergent mode sums, using dimensional regularization (or any other analytic continuation technique) to define the mode sums leads to the incorrect conclusion that de Sitter invariant solutions exist except at discrete values of the masses.

UR - http://www.scopus.com/inward/record.url?scp=77955574188&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955574188&partnerID=8YFLogxK

U2 - 10.1063/1.3448926

DO - 10.1063/1.3448926

M3 - Article

VL - 51

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 7

M1 - 038006JMP

ER -