# Weyl current, scale-invariant inflation, and Planck scale generation

## Abstract

Scalar fields, $$\phi$$ _{i}, can be coupled nonminimally to curvature and satisfy the general criteria: (i) the theory has no mass input parameters, including M _{P}=0; (ii) the $$\phi$$ _{i} have arbitrary values and gradients, but undergo a general expansion and relaxation to constant values that satisfy a nontrivial constraint, K($$\phi$$ _{i})=constant; (iii) this constraint breaks scale symmetry spontaneously, and the Planck mass is dynamically generated; (iv) there can be adequate inflation associated with slow roll in a scale-invariant potential subject to the constraint; (v) the final vacuum can have a small to vanishing cosmological constant; (vi) large hierarchies in vacuum expectation values can naturally form; (vii) there is a harmless dilaton which naturally eludes the usual constraints on massless scalars. Finally, these models are governed by a global Weyl scale symmetry and its conserved current, K _{μ}. At the quantum level the Weyl scale symmetry can be maintained by an invariant specification of renormalized quantities.

- Authors:

- Univ. of Oxford (United Kingdom). Dept. of Physics
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
- Univ. of Oxford (United Kingdom). Rudolf Peierls Centre for Theoretical Physics

- Publication Date:

- Research Org.:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1345633

- Alternate Identifier(s):
- OSTI ID: 1343347

- Report Number(s):
- FERMILAB-PUB-16-458-T; arXiv:1610.09243

Journal ID: ISSN 2470-0010; PRVDAQ; 1495005

- Grant/Contract Number:
- AC02-07CH11359

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 95; Journal Issue: 4; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Ferreira, Pedro G., Hill, Christopher T., and Ross, Graham G.
```*Weyl current, scale-invariant inflation, and Planck scale generation*. United States: N. p., 2017.
Web. doi:10.1103/PhysRevD.95.043507.

```
Ferreira, Pedro G., Hill, Christopher T., & Ross, Graham G.
```*Weyl current, scale-invariant inflation, and Planck scale generation*. United States. doi:10.1103/PhysRevD.95.043507.

```
Ferreira, Pedro G., Hill, Christopher T., and Ross, Graham G. Wed .
"Weyl current, scale-invariant inflation, and Planck scale generation". United States.
doi:10.1103/PhysRevD.95.043507. https://www.osti.gov/servlets/purl/1345633.
```

```
@article{osti_1345633,
```

title = {Weyl current, scale-invariant inflation, and Planck scale generation},

author = {Ferreira, Pedro G. and Hill, Christopher T. and Ross, Graham G.},

abstractNote = {Scalar fields, $\phi$i, can be coupled nonminimally to curvature and satisfy the general criteria: (i) the theory has no mass input parameters, including MP=0; (ii) the $\phi$i have arbitrary values and gradients, but undergo a general expansion and relaxation to constant values that satisfy a nontrivial constraint, K($\phi$i)=constant; (iii) this constraint breaks scale symmetry spontaneously, and the Planck mass is dynamically generated; (iv) there can be adequate inflation associated with slow roll in a scale-invariant potential subject to the constraint; (v) the final vacuum can have a small to vanishing cosmological constant; (vi) large hierarchies in vacuum expectation values can naturally form; (vii) there is a harmless dilaton which naturally eludes the usual constraints on massless scalars. Finally, these models are governed by a global Weyl scale symmetry and its conserved current, Kμ. At the quantum level the Weyl scale symmetry can be maintained by an invariant specification of renormalized quantities.},

doi = {10.1103/PhysRevD.95.043507},

journal = {Physical Review D},

number = 4,

volume = 95,

place = {United States},

year = {Wed Feb 08 00:00:00 EST 2017},

month = {Wed Feb 08 00:00:00 EST 2017}

}

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