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Non-Locality and Late-Time Cosmic Acceleration from an Ultraviolet Complete Theory ^{†}

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## Abstract

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## 1. Introduction

## 2. Non-Local Gravity

## 3. Induced Gravity Model

## 4. Local to Non-Local

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Riess, A.G.; Filippenko, A.V.; Challis, P.; Clocchiatti, A.; Diercks, A.; Garnavich, P.M.; Gilliland, R.L.; Hogan, C.J.; Jha, S.; Kirshner, R.P.; et al. Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J.
**1998**, 116, 1009–1083. [Google Scholar] [CrossRef] - Perlmutter, S.; Aldering, G.; Goldhaber, G.; Knop, R.A.; Nugent, P.; Castro, P.G.; Deustua, S.; Fabbro, S.; Goobar, A.; Groom, D.E.; et al. Measurements of Omega and Lambda from 42 high redshift supernovae. Astron. J.
**1999**, 517, 565–586. [Google Scholar] [CrossRef] - Wetterich, C. Cosmology and the Fate of Dilatation Symmetry. Nucl. Phys. B
**1988**, 302, 668–696. [Google Scholar] [CrossRef] - Frieman, J.A.; Hill, C.T.; Stebbins, A.; Waga, I. Cosmology with ultralight pseudo Nambu-Goldstone bosons. Phys. Rev. Lett.
**1995**, 75, 2077–2080. [Google Scholar] [CrossRef] [PubMed] - Zlatev, I.; Wang, L.M.; Steinhardt, P.J. Quintessence, cosmic coincidence, and the cosmological constant. Phys. Rev. Lett.
**1999**, 82, 896–899. [Google Scholar] [CrossRef] - Ferreira, P.G.; Joyce, M. Structure formation with a selftuning scalar field. Phys. Rev. Lett.
**1997**, 79, 4740–4743. [Google Scholar] [CrossRef] - Garriga, J.; Mukhanov, V.F. Perturbations in k-inflation. Phys. Lett. B
**1999**, 458, 219–225. [Google Scholar] [CrossRef][Green Version] - Armendariz-Picon, C.; Damour, T.; Mukhanov, V.F. k-inflation. Phys. Lett. B
**1999**, 458, 209–218. [Google Scholar] [CrossRef] - Armendariz-Picon, C.; Mukhanov, V.F.; Steinhardt, P.J. A Dynamical solution to the problem of a small cosmological constant and late time cosmic acceleration. Phys. Rev. Lett.
**2000**, 85, 4438–4441. [Google Scholar] [CrossRef] [PubMed] - Maggiore, M.; Mancarella, M. Nonlocal gravity and dark energy. Phys. Rev. D
**2014**, 90, 023005. [Google Scholar] [CrossRef] - Cusin, G.; Foffa, S.; Maggiore, M.; Mancarella, M. Conformal symmetry and nonlinear extensions of nonlocal gravity. Phys. Rev. D
**2016**, 93, 083008. [Google Scholar] [CrossRef] - Maggiore, M. Nonlocal Infrared Modifications of Gravity. A Review. Fundam. Theor. Phys.
**2017**, 187, 221–281. [Google Scholar] [CrossRef] - Dirian, Y.; Foffa, S.; Kunz, M.; Maggiore, M.; Pettorino, V. Non-local gravity and comparison with observational datasets. J. Cosmol. Astropart. Phys.
**2015**, 1504, 044. [Google Scholar] [CrossRef] - Dirian, Y.; Foffa, S.; Kunz, M.; Maggiore, M.; Pettorino, V. Non-local gravity and comparison with observational datasets. II. Updated results and Bayesian model comparison with ΛCDM. J. Cosmol. Astropart. Phys.
**2016**, 1605, 068. [Google Scholar] [CrossRef] - Maggiore, M. Dark energy and dimensional transmutation in R
^{2}gravity. arXiv, 2017; arXiv:1506.06217. [Google Scholar] - Maggiore, M. Perturbative loop corrections and nonlocal gravity. Phys. Rev. D
**2016**, 93, 063008. [Google Scholar] [CrossRef][Green Version] - Narain, G.; Li, T. Ultraviolet complete dark energy model. Phys. Rev. D
**2018**, 97, 083523. [Google Scholar] [CrossRef] - Narain, G. Exorcising Ghosts in Induced Gravity. Eur. Phys. J. C
**2017**, 77, 683. [Google Scholar] [CrossRef] - Appelquist, T.; Carazzone, J. Infrared Singularities and Massive Fields. Phys. Rev. D
**1975**, 11, 2856–2861. [Google Scholar] [CrossRef] - Gorbar, E.V.; Shapiro, I.L. Renormalization group and decoupling in curved space. J. High Energy Phys.
**2003**, 0302, 021. [Google Scholar] [CrossRef] - Arkani-Hamed, N.; Dimopoulos, S.; Dvali, G.; Gabadadze, G. Non-local modification of gravity and the cosmological constant problem. arXiv, 2017; arXiv:hep-th/0209227. [Google Scholar]
- Jaccard, M.; Maggiore, M.; Mitsou, E. Nonlocal theory of massive gravity. Phys. Rev. D
**2013**, 88, 044033. [Google Scholar] [CrossRef] - Maggiore, M. Phantom dark energy from nonlocal infrared modifications of general relativity. Phys. Rev. D
**2014**, 89, 043008. [Google Scholar] [CrossRef] - Foffa, S.; Maggiore, M.; Mitsou, E. Cosmological dynamics and dark energy from nonlocal infrared modifications of gravity. Int. J. Mod. Phys. A
**2014**, 29, 1450116. [Google Scholar] [CrossRef][Green Version] - Dirian, Y.; Foffa, S.; Khosravi, N.; Kunz, M.; Maggiore, M. Cosmological perturbations and structure formation in nonlocal infrared modifications of general relativity. J. Cosmol. Astropart. Phys.
**2014**, 1406, 033. [Google Scholar] [CrossRef] - Barreira, A.; Li, B.; Hellwing, W.A.; Baugh, C.M.; Pascoli, S. Nonlinear structure formation in Nonlocal Gravity. J. Cosmol. Astropart. Phys.
**2014**, 1409, 031. [Google Scholar] [CrossRef] - Stelle, K.S. Renormalization of Higher Derivative Quantum Gravity. Phys. Rev. D
**1977**, 16, 953–969. [Google Scholar] [CrossRef] - Narain, G.; Anishetty, R. Short Distance Freedom of Quantum Gravity. Phys. Lett. B
**2012**, 711, 128–131. [Google Scholar] [CrossRef] - Narain, G.; Anishetty, R. Unitary and Renormalizable Theory of Higher Derivative Gravity. J. Phys. Conf. Ser.
**2012**, 405, 012024. [Google Scholar] [CrossRef][Green Version] - Fradkin, E.S.; Tseytlin, A.A. Renormalizable asymptotically free quantum theory of gravity. Nucl. Phys. B
**1982**, 201, 469–491. [Google Scholar] [CrossRef] - Julve, J.; Tonin, M. Quantum Gravity with Higher Derivative Terms. Nuovo Cim. B
**1978**, 46, 137–152. [Google Scholar] [CrossRef] - Barth, N.H.; Christensen, S.M. Quantizing Fourth Order Gravity Theories. 1. The Functional Integral. Phys. Rev. D
**1983**, 28, 1876–1893. [Google Scholar] [CrossRef] - Avramidi, I.G.; Barvinsky, A.O. Asymptotic Freedom in Higher Derivative Quantum Gravity. Phys. Lett. B
**1985**, 159, 269–274. [Google Scholar] [CrossRef] - Salvio, A.; Strumia, A. Agravity. J. High Energy Phys.
**2014**, 1406, 080. [Google Scholar] [CrossRef] - Einhorn, M.B.; Jones, D.R.T. Naturalness and Dimensional Transmutation in Classically Scale-Invariant Gravity. J. High Energy Phys.
**2015**, 1503, 047. [Google Scholar] [CrossRef] - Jones, T.; Einhorn, M. Quantum Gravity and Dimensional Transmutation. PoS PLANCK
**2015**, 2015, 061. [Google Scholar] - Einhorn, M.B.; Jones, D.R.T. Induced Gravity I: Real Scalar Field. J. High Energy Phys.
**2016**, 1601, 019. [Google Scholar] [CrossRef] - Einhorn, M.B.; Jones, D.R.T. Induced Gravity II: Grand Unification. J. High Energy Phys.
**2016**, 1605, 185. [Google Scholar] [CrossRef] - Salvio, A.; Strumia, A. Quantum mechanics of 4-derivative theories. Eur. Phys. J. C
**2016**, 76, 227. [Google Scholar] [CrossRef] [PubMed] - Narain, G. Signs and Stability in Higher-Derivative Gravity. Int. J. Mod. Phys. A
**2018**, 33, 1850031. [Google Scholar] [CrossRef] - Narain, G.; Anishetty, R. Charge Renormalization due to Graviton Loops. J. High Energy Phys.
**2013**, 1307, 106. [Google Scholar] [CrossRef] - Narain, G.; Anishetty, R. Running Couplings in Quantum Theory of Gravity Coupled with Gauge Fields. J. High Energy Phys.
**2013**, 1310, 203. [Google Scholar] [CrossRef] - Salam, A.; Strathdee, J.A. Remarks on High-energy Stability and Renormalizability of Gravity Theory. Phys. Rev. D
**1978**, 18, 4480. [Google Scholar] [CrossRef]

1. | In [39], a quantum mechanical treatment of higher-derivative theories is attempted, whose suitable generalisation is expected to offer a treatment of ghosts in higher-derivative gravity. |

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**MDPI and ACS Style**

Narain, G.; Li, T. Non-Locality and Late-Time Cosmic Acceleration from an Ultraviolet Complete Theory ^{†}. *Universe* **2018**, *4*, 82.
https://doi.org/10.3390/universe4080082

**AMA Style**

Narain G, Li T. Non-Locality and Late-Time Cosmic Acceleration from an Ultraviolet Complete Theory ^{†}. *Universe*. 2018; 4(8):82.
https://doi.org/10.3390/universe4080082

**Chicago/Turabian Style**

Narain, Gaurav, and Tianjun Li. 2018. "Non-Locality and Late-Time Cosmic Acceleration from an Ultraviolet Complete Theory ^{†}" *Universe* 4, no. 8: 82.
https://doi.org/10.3390/universe4080082