Predictions of quantum gravity in inflationary cosmology: effects of the Weyl-squared term
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Springer
Received: May 25, 2020 Accepted: July 1, 2020 Published: July 29, 2020
Damiano Anselmi,a,b Eugenio Bianchic,d and Marco Pivae a
Dipartimento di Fisica “Enrico Fermi”, Universit` a di Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy b INFN, Sezione di Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy c Institute for Gravitation and the Cosmos, The Pennsylvania State University, University Park, PA 16802, U.S.A. d Department of Physics, The Pennsylvania State University, University Park, PA 16802, U.S.A. e National Institute of Chemical Physics and Biophysics, R¨ avala 10, Tallinn 10143, Estonia
E-mail: [email protected], [email protected], [email protected] Abstract: We derive the predictions of quantum gravity with fakeons on the amplitudes and spectral indices of the scalar and tensor fluctuations in inflationary cosmology. The action is R + R2 plus the Weyl-squared term. The ghost is eliminated by turning it into a fakeon, that is to say a purely virtual particle. We work to the next-to-leading order of the expansion around the de Sitter background. The consistency of the approach puts a lower bound (mχ > mφ /4) on the mass mχ of the fakeon with respect to the mass mφ of the inflaton. The tensor-to-scalar ratio r is predicted within less than an order of magnitude (4/3 < N 2 r < 12 to the leading order in the number of e-foldings N ). Moreover, the relation r ≃ −8nT is not affected by the Weyl-squared term. No vector and no other scalar/tensor degree of freedom is present. Keywords: Beyond Standard Model, Cosmology of Theories beyond the SM, Models of Quantum Gravity ArXiv ePrint: 2005.10293
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)211
JHEP07(2020)211
Predictions of quantum gravity in inflationary cosmology: effects of the Weyl-squared term
Contents 1 Introduction
1
2 Quantum gravity with fakeons
4 7 7 12
4 The fakeon projection 4.1 Consistency condition
14 15
5 Geometric framework (R + R2 + C 2 ) 5.1 mχ ∼ H: tensor fluctuations 5.2 mχ ∼ H: scalar fluctuations 5.3 mχ ∼ mφ : tensor fluctuations 5.4 mχ ∼ mφ : scalar fluctuations
17 18 19 21 22
6 Vector fluctuations
23
7 Summary of predictions and connection with observations
24
8 Conclusions
26
A Map relating the inflaton framework to the geometric framework
27
B Superhorizon evolution
29
1
Introduction
Inflation is a theory of accelerated expansion of the early universe [1–8], which accounts for the origin of the present large-scale structure. It explains the approximate isotropy of the cosmic microwave background radiation and allows us to study the quantum fluctuations as sources of the cosmological perturbations that seed the formation of the structures of the cosmos [9–15]. It also provides a rich environment where we can develop knowledge that might allow us to establish a nontrivial connection between high-energy physics and the physics of large scales. Inflationary cosmology is often studied with the help of a matter field that drives the expansion by rolling
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