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K. S. Stelle, “Renormalization of Higher Derivative Quantum Gravity,” Phys. Rev. D 16
1977
Earlier work this paper cites.
A. A. Starobinsky, “A New Type of Isotropic Cosmological Models Without Singularity,” Phys. Lett. 91B
1980
Earlier work this paper cites.
A. H. Guth, “The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems,” Phys. Rev. D 23
1981
Earlier work this paper cites.
A. D. Linde, “A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole Problems,” Phys. Lett. B 108
1982
Earlier work this paper cites.
A. A. Starobinsky, “Dynamics of Phase Transition in the New Inflationary Universe Scenario and Generation of Perturbations,” Phys. Lett. B 117
1982
Earlier work this paper cites.
A. D. Linde, “Chaotic Inflation,” Phys. Lett. 129B
1983
Earlier work this paper cites.
K. i. Maeda, “Inflation as a Transient Attractor in R**2 Cosmology,” Phys. Rev. D 37
1988
Earlier work this paper cites.
J. D. Barrow and S. Cotsakis, “Inflation and the Conformal Structure of Higher Order Gravity Theories,” Phys. Lett. B 214
1988
Earlier work this paper cites.
C. Wetterich, “Exact evolution equation for the effective potential,” Phys. Lett. B 301
1993
Earlier work this paper cites.
M. Niedermaier and M. Reuter, “The Asymptotic Safety Scenario in Quantum Gravity,” Living Rev. Rel. 9
2006
Earlier work this paper cites.
P. F. Machado and F. Saueressig, “On the renormalization group flow of f(R)-gravity,” Phys. Rev. D 77
Original
2008
Earlier work this paper cites.
A. Codello, R. Percacci and C. Rahmede, “Ultraviolet properties of f(R)-gravity,” Int. J. Mod. Phys. A 23
Original
2008
Earlier work this paper cites.
A. Codello, R. Percacci and C. Rahmede, “Investigating the Ultraviolet Properties of Gravity with a Wilsonian Renormalization Group Equation,” Annals Phys. 324
Original
2008
Earlier work this paper cites.
T. P. Sotiriou and V. Faraoni, “f(R) Theories Of Gravity,” Rev. Mod. Phys. 82
Original
2010
Earlier work this paper cites.
A. De Felice and S. Tsujikawa, “f(R) theories,” Living Rev. Rel. 13
Original
2010
Earlier work this paper cites.
A. Bonanno, A. Contillo and R. Percacci, “Inflationary solutions in asymptotically safe f(R) theories,” Class. Quant. Grav. 28
Original
2011
Earlier work this paper cites.

Similar

A. Contillo, “Evolution of cosmological perturbations in an RG-driven inflationary scenario,” Phys. Rev. D 83
Original
2011
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G. Narain and R. Anishetty, “Short Distance Freedom of Quantum Gravity,” Phys. Lett. B 711
Original
2012
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G. Narain and R. Anishetty, “Unitary and Renormalizable Theory of Higher Derivative Gravity,” J. Phys. Conf. Ser. 405
Original
2012
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R. Kallosh and A. Linde, “Superconformal generalization of the chaotic inflation model λ 4 ϕ 4 − ξ 2 ϕ 2 R \frac{\lambda}{4}\phi^{4}-\frac{\xi}{2}\phi^{2}R ,” JCAP 1306
Original
2013
Cited alongside, same era.
R. Kallosh and A. Linde, “Non-minimal Inflationary Attractors,” JCAP 1310

Then

N. Ohta, R. Percacci and G. P. Vacca, “Flow equation for f ⁡ ( R ) f(R) gravity and some of its exact solutions,” Phys. Rev. D 92
Original
2015
Later among the works it cites.
A. Y. Kamenshchik and C. F. Steinwachs, “Question of quantum equivalence between Jordan frame and Einstein frame,” Phys. Rev. D 91
Original
2015
Later among the works it cites.
E. J. Copeland, C. Rahmede and I. D. Saltas, “Asymptotically Safe Starobinsky Inflation,” Phys. Rev. D 91
Original
2015
Later among the works it cites.
R. Kallosh and A. Linde, “Cosmological Attractors and Asymptotic Freedom of the Inflaton Field,” JCAP 1606
Original
2016
Later among the works it cites.
E. Elizalde, S. D. Odintsov, E. O. Pozdeeva and S. Y. Vernov, “Cosmological attractor inflation from the RG-improved Higgs sector of finite gauge theory,” JCAP 1602

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2017

On the Renormalization Group perspective of $\alpha$-attractors

Narain, Gaurav

Understand

In this short paper we outline a recipe for the reconstruction of $F(R)$ gravity starting from single field inflationary potentials in the Einstein frame.

For simple potentials one can compute the explicit form of $F(R)$, whilst for more involved examples one gets a parametric form of $F(R)$.
The $F(R)$ reconstruction algorithm is used to study various examples: power-law $\phi^n$, exponential and $\alpha$-attractors.
In each case it is seen that for large $R$ (corresponding to large value of inflaton field), $F(R) \sim R^2$.

Built on

K. S. Stelle, “Renormalization of Higher Derivative Quantum Gravity,” Phys. Rev. D 16
1977
Earlier work this paper cites.
A. A. Starobinsky, “A New Type of Isotropic Cosmological Models Without Singularity,” Phys. Lett. 91B
1980
Earlier work this paper cites.
A. H. Guth, “The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems,” Phys. Rev. D 23
1981
Earlier work this paper cites.
A. D. Linde, “A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole Problems,” Phys. Lett. B 108
1982
Earlier work this paper cites.
A. A. Starobinsky, “Dynamics of Phase Transition in the New Inflationary Universe Scenario and Generation of Perturbations,” Phys. Lett. B 117
1982
Earlier work this paper cites.
A. D. Linde, “Chaotic Inflation,” Phys. Lett. 129B
1983
Earlier work this paper cites.
K. i. Maeda, “Inflation as a Transient Attractor in R**2 Cosmology,” Phys. Rev. D 37
1988
Earlier work this paper cites.
J. D. Barrow and S. Cotsakis, “Inflation and the Conformal Structure of Higher Order Gravity Theories,” Phys. Lett. B 214
1988
Earlier work this paper cites.
C. Wetterich, “Exact evolution equation for the effective potential,” Phys. Lett. B 301
1993
Earlier work this paper cites.
M. Niedermaier and M. Reuter, “The Asymptotic Safety Scenario in Quantum Gravity,” Living Rev. Rel. 9
2006
Earlier work this paper cites.
P. F. Machado and F. Saueressig, “On the renormalization group flow of f(R)-gravity,” Phys. Rev. D 77
Original
2008
Earlier work this paper cites.
A. Codello, R. Percacci and C. Rahmede, “Ultraviolet properties of f(R)-gravity,” Int. J. Mod. Phys. A 23
Original
2008
Earlier work this paper cites.
A. Codello, R. Percacci and C. Rahmede, “Investigating the Ultraviolet Properties of Gravity with a Wilsonian Renormalization Group Equation,” Annals Phys. 324
Original
2008
Earlier work this paper cites.
T. P. Sotiriou and V. Faraoni, “f(R) Theories Of Gravity,” Rev. Mod. Phys. 82
Original
2010
Earlier work this paper cites.
A. De Felice and S. Tsujikawa, “f(R) theories,” Living Rev. Rel. 13
Original
2010
Earlier work this paper cites.
A. Bonanno, A. Contillo and R. Percacci, “Inflationary solutions in asymptotically safe f(R) theories,” Class. Quant. Grav. 28
Original
2011
Earlier work this paper cites.