Abstract
Within General Relativity, a minimally coupled scalar field governed by a quadratic potential is able to produce an accelerated expansion of the universe provided its value and excursion are larger than the Planck scale. This is an archetypical example of the so called large field inflation models. We show that by including higher curvature corrections to the gravitational action in the form of the Geometric Inflation models, it is possible to obtain accelerated expansion with a free scalar field whose values are well below the Planck scale, thereby turning a traditional large field model into a small field one. We provide the conditions the theory has to satisfy in order for this mechanism to operate, and we present two explicit models illustrating it. Finally, we present some open questions raised by this scenario in which inflation takes place completely in a higher curvature dominated regime, such as those concerning the study of perturbations.
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References
L. Senatore, Lectures on Inflation, arXiv:1609.00716 [INSPIRE].
D.H. Lyth, What would we learn by detecting a gravitational wave signal in the cosmic microwave background anisotropy?, Phys. Rev. Lett. 78 (1997) 1861 [hep-ph/9606387] [INSPIRE].
L. Boubekeur and D.H. Lyth, Hilltop inflation, JCAP 07 (2005) 010 [hep-ph/0502047] [INSPIRE].
S. Weinberg, Effective Field Theory for Inflation, Phys. Rev. D 77 (2008) 123541 [arXiv:0804.4291] [INSPIRE].
P. Bueno and P.A. Cano, Einsteinian cubic gravity, Phys. Rev. D 94 (2016) 104005 [arXiv:1607.06463] [INSPIRE].
R.A. Hennigar and R.B. Mann, Black holes in Einsteinian cubic gravity, Phys. Rev. D 95 (2017) 064055 [arXiv:1610.06675] [INSPIRE].
P. Bueno, P.A. Cano, V.S. Min and M.R. Visser, Aspects of general higher-order gravities, Phys. Rev. D 95 (2017) 044010 [arXiv:1610.08519] [INSPIRE].
X.O. Camanho and J.D. Edelstein, A Lovelock black hole bestiary, Class. Quant. Grav. 30 (2013) 035009 [arXiv:1103.3669] [INSPIRE].
R.A. Hennigar, D. Kubizňák and R.B. Mann, Generalized quasitopological gravity, Phys. Rev. D 95 (2017) 104042 [arXiv:1703.01631] [INSPIRE].
P. Bueno, P.A. Cano, R.A. Hennigar and R.B. Mann, NUTs and bolts beyond Lovelock, JHEP 10 (2018) 095 [arXiv:1808.01671] [INSPIRE].
G. Arciniega, J.D. Edelstein and L.G. Jaime, Towards geometric inflation: the cubic case, Phys. Lett. B 802 (2020) 135272 [arXiv:1810.08166] [INSPIRE].
G. Arciniega, P. Bueno, P.A. Cano, J.D. Edelstein, R.A. Hennigar and L.G. Jaime, Geometric Inflation, Phys. Lett. B 802 (2020) 135242 [arXiv:1812.11187] [INSPIRE].
G. Arciniega, P. Bueno, P.A. Cano, J.D. Edelstein, R.A. Hennigar and L.G. Jaime, Cosmic inflation without inflaton, Int. J. Mod. Phys. D 28 (2019) 1944008 [INSPIRE].
A. Cisterna, N. Grandi and J. Oliva, On four-dimensional Einsteinian gravity, quasitopological gravity, cosmology and black holes, Phys. Lett. B 805 (2020) 135435 [arXiv:1811.06523] [INSPIRE].
C. Erices, E. Papantonopoulos and E.N. Saridakis, Cosmology in cubic and f (P ) gravity, Phys. Rev. D 99 (2019) 123527 [arXiv:1903.11128] [INSPIRE].
G. Arciniega, L. Jaime and G. Piccinelli, Inflationary predictions of Geometric Inflation, Phys. Lett. B 809 (2020) 135731 [arXiv:2001.11094] [INSPIRE].
M.C. Pookkillath, A. De Felice and A.A. Starobinsky, Anisotropic instability in a higher order gravity theory, JCAP 07 (2020) 041 [arXiv:2004.03912] [INSPIRE].
J.D. Edelstein, D. Vázquez Rodríguez and A. Vilar López, Aspects of Geometric Inflation, JCAP 12 (2020) 040 [arXiv:2006.10007] [INSPIRE].
V.-M. Enckell, K. Enqvist, S. Rasanen and L.-P. Wahlman, Inflation with R2 term in the Palatini formalism, JCAP 02 (2019) 022 [arXiv:1810.05536] [INSPIRE].
I. Antoniadis, A. Karam, A. Lykkas and K. Tamvakis, Palatini inflation in models with an R2 term, JCAP 11 (2018) 028 [arXiv:1810.10418] [INSPIRE].
O. Hohm and B. Zwiebach, Duality invariant cosmology to all orders in α’, Phys. Rev. D 100 (2019) 126011 [arXiv:1905.06963] [INSPIRE].
C. Krishnan, De Sitter, αJ -Corrections & Duality Invariant Cosmology, JCAP 10 (2019) 009 [arXiv:1906.09257] [INSPIRE].
O. Hohm and B. Zwiebach, Non-perturbative de Sitter vacua via α′ corrections, Int. J. Mod. Phys. D 28 (2019) 1943002 [arXiv:1905.06583] [INSPIRE].
J.D. Edelstein, K. Sfetsos, J. Sierra-Garcia and A. Vilar López, T-duality equivalences beyond string theory, JHEP 05 (2019) 082 [arXiv:1903.05554] [INSPIRE].
R.A. Hennigar, M.B.J. Poshteh and R.B. Mann, Shadows, Signals, and Stability in Einsteinian Cubic Gravity, Phys. Rev. D 97 (2018) 064041 [arXiv:1801.03223] [INSPIRE].
H. Khodabakhshi, A. Giaimo and R.B. Mann, Einstein Quartic Gravity: Shadows, Signals, and Stability, Phys. Rev. D 102 (2020) 044038 [arXiv:2006.02237] [INSPIRE].
J.D. Edelstein, S. Paban and A. Vilar López, Cosmological perturbations in Geometric Inflation, in progress.
J. Scholtz and J. Unwin, What if Planet 9 is a Primordial Black Hole?, Phys. Rev. Lett. 125 (2020) 051103 [arXiv:1909.11090] [INSPIRE].
E. Witten, Searching for a Black Hole in the Outer Solar System, arXiv:2004.14192 [INSPIRE].
S. Lawrence and Z. Rogoszinski, The brute-force search for Planet 9, arXiv:2004.14980.
A. Siraj and A. Loeb, Searching for Black Holes in the Outer Solar System with LSST, Astrophys. J. Lett. 898 (2020) L4 [arXiv:2005.12280] [INSPIRE].
A. Arbey and J. Auffinger, Detecting Planet 9 via Hawking radiation, arXiv:2006.02944 [INSPIRE].
X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, Causality Constraints on Corrections to the Graviton Three-Point Coupling, JHEP 02 (2016) 020 [arXiv:1407.5597] [INSPIRE].
S.D. Chowdhury, A. Gadde, T. Gopalka, I. Halder, L. Janagal and S. Minwalla, Classifying and constraining local four photon and four graviton S-matrices, JHEP 02 (2020) 114 [arXiv:1910.14392] [INSPIRE].
C. de Rham and A.J. Tolley, Causality in curved spacetimes: The speed of light and gravity, Phys. Rev. D 102 (2020) 084048 [arXiv:2007.01847] [INSPIRE].
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Edelstein, J.D., Mann, R.B., Rodríguez, D.V. et al. Small free field inflation in higher curvature gravity. J. High Energ. Phys. 2021, 29 (2021). https://doi.org/10.1007/JHEP01(2021)029
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DOI: https://doi.org/10.1007/JHEP01(2021)029