### Abstract

Many cosmological models invoke rolling scalar fields to account for the observed acceleration of the expansion of the Universe. These theories generally include a potential V(φ) which is a function of the scalar field φ. Although V(φ) can be represented by a very diverse set of functions, recent work has shown that under some conditions, such as the slow-roll conditions, the equation of state parameter w is either independent of the form of V(φ) or part of family of solutions with only a few parameters. In realistic models of this type the scalar field couples to other sectors of the model leading to possibly observable changes in the fundamental constants such as the fine structure constant α and the proton to electron mass ratio μ. Although the current situation on a possible variance of α is complicated, there are firm limitations on the variance of μ in the early universe. This paper explores the limits this puts on the validity of various cosmologies that invoke rolling scalar fields. We find that the limit on the variation of μ puts significant constraints on the product of a cosmological parameter w + 1 and a new physics parameter ζ ^{2}_{μ}, the coupling constant between μ and the rolling scalar field. Even when the cosmologies are restricted to very slow roll conditions either the value of ζ _{μ} must be at the lower end of or less than its expected values or the value of w + 1 must be restricted to values vanishingly close to 0. This implies that either the rolling scalar field is very weakly coupled to the electromagnetic field, small ζ _{μ}, very weakly coupled to gravity, (w + 1) ≈ 0 or both. These results stress that adherence to the measured invariance in μ is a very significant test of the validity of any proposed cosmology and any new physics it requires. The limits on the variation of μ also produces a significant tension with the reported changes in the value of α.

Original language | English (US) |
---|---|

Pages (from-to) | 2232-2240 |

Number of pages | 9 |

Journal | Monthly Notices of the Royal Astronomical Society |

Volume | 428 |

Issue number | 3 |

DOIs | |

State | Published - Jan 2013 |

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### Keywords

- Cosmological parameters
- Dark energy
- Early Universe

### ASJC Scopus subject areas

- Space and Planetary Science
- Astronomy and Astrophysics

### Cite this

*Monthly Notices of the Royal Astronomical Society*,

*428*(3), 2232-2240. https://doi.org/10.1093/mnras/sts187

**Constraining cosmologies with fundamental constants - I. Quintessence and K-essence.** / Thompson, Rodger I; Martins, C. J A P; Vielzeuf, P. E.

Research output: Contribution to journal › Article

*Monthly Notices of the Royal Astronomical Society*, vol. 428, no. 3, pp. 2232-2240. https://doi.org/10.1093/mnras/sts187

}

TY - JOUR

T1 - Constraining cosmologies with fundamental constants - I. Quintessence and K-essence

AU - Thompson, Rodger I

AU - Martins, C. J A P

AU - Vielzeuf, P. E.

PY - 2013/1

Y1 - 2013/1

N2 - Many cosmological models invoke rolling scalar fields to account for the observed acceleration of the expansion of the Universe. These theories generally include a potential V(φ) which is a function of the scalar field φ. Although V(φ) can be represented by a very diverse set of functions, recent work has shown that under some conditions, such as the slow-roll conditions, the equation of state parameter w is either independent of the form of V(φ) or part of family of solutions with only a few parameters. In realistic models of this type the scalar field couples to other sectors of the model leading to possibly observable changes in the fundamental constants such as the fine structure constant α and the proton to electron mass ratio μ. Although the current situation on a possible variance of α is complicated, there are firm limitations on the variance of μ in the early universe. This paper explores the limits this puts on the validity of various cosmologies that invoke rolling scalar fields. We find that the limit on the variation of μ puts significant constraints on the product of a cosmological parameter w + 1 and a new physics parameter ζ 2μ, the coupling constant between μ and the rolling scalar field. Even when the cosmologies are restricted to very slow roll conditions either the value of ζ μ must be at the lower end of or less than its expected values or the value of w + 1 must be restricted to values vanishingly close to 0. This implies that either the rolling scalar field is very weakly coupled to the electromagnetic field, small ζ μ, very weakly coupled to gravity, (w + 1) ≈ 0 or both. These results stress that adherence to the measured invariance in μ is a very significant test of the validity of any proposed cosmology and any new physics it requires. The limits on the variation of μ also produces a significant tension with the reported changes in the value of α.

AB - Many cosmological models invoke rolling scalar fields to account for the observed acceleration of the expansion of the Universe. These theories generally include a potential V(φ) which is a function of the scalar field φ. Although V(φ) can be represented by a very diverse set of functions, recent work has shown that under some conditions, such as the slow-roll conditions, the equation of state parameter w is either independent of the form of V(φ) or part of family of solutions with only a few parameters. In realistic models of this type the scalar field couples to other sectors of the model leading to possibly observable changes in the fundamental constants such as the fine structure constant α and the proton to electron mass ratio μ. Although the current situation on a possible variance of α is complicated, there are firm limitations on the variance of μ in the early universe. This paper explores the limits this puts on the validity of various cosmologies that invoke rolling scalar fields. We find that the limit on the variation of μ puts significant constraints on the product of a cosmological parameter w + 1 and a new physics parameter ζ 2μ, the coupling constant between μ and the rolling scalar field. Even when the cosmologies are restricted to very slow roll conditions either the value of ζ μ must be at the lower end of or less than its expected values or the value of w + 1 must be restricted to values vanishingly close to 0. This implies that either the rolling scalar field is very weakly coupled to the electromagnetic field, small ζ μ, very weakly coupled to gravity, (w + 1) ≈ 0 or both. These results stress that adherence to the measured invariance in μ is a very significant test of the validity of any proposed cosmology and any new physics it requires. The limits on the variation of μ also produces a significant tension with the reported changes in the value of α.

KW - Cosmological parameters

KW - Dark energy

KW - Early Universe

UR - http://www.scopus.com/inward/record.url?scp=84873448050&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84873448050&partnerID=8YFLogxK

U2 - 10.1093/mnras/sts187

DO - 10.1093/mnras/sts187

M3 - Article

VL - 428

SP - 2232

EP - 2240

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

SN - 0035-8711

IS - 3

ER -