Course

19S1 D. Anselmi
Theories of gravitation

Program

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Book

D. Anselmi
From Physics To Life

A journey to the infinitesimally small and back

In English and Italian

Available on Amazon:
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Recent Papers

Inflation

We compute the inflationary perturbation spectra and the quantity $r+8n_{T}$ to the next-to-next-to-leading log order in quantum gravity with purely virtual particles (which means the theory $R+R^{2}+C^{2}$ with the fakeon prescription/projection for $C^{2}$). The spectra are functions of the inflationary running coupling $\alpha (1/k)$ and satisfy the cosmic renormalization-group flow equations, which determine the tilts and the running coefficients. The tensor fluctuations receive contributions from the spin-2 fakeon $\chi _{\mu \nu }$ at every order of the expansion in powers of $\alpha \sim 1/115$. The dependence of the scalar spectrum on the $\chi
_{\mu \nu }$ mass $m_{\chi }$, on the other hand, starts from the $\alpha^{2}$ corrections, which are handled perturbatively in the ratio $m_{\phi}/m_{\chi }$, where $m_{\phi }$ is the inflaton mass. The predictions have theoretical errors ranging from $\alpha ^{4}\sim 10^{-8}$ to $\alpha^{3}\sim 10^{-6}$. Nontrivial issues concerning the fakeon projection at higher orders are addressed.

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arXiv: 2010.04739 [hep-th]

We study the running of power spectra in inflationary cosmology as a renormalization-group flow from the de Sitter fixed point. The beta function is provided by the equations of the background metric. The spectra of the scalar and tensor fluctuations obey RG evolution equations with vanishing anomalous dimensions. By organizing the perturbative expansion in terms of leading and subleading logs, we calculate the spectral indices, their runnings, the runnings of the runnings, etc., to the next-to-leading log order in quantum gravity with fakeons (i.e., the theory $R+R^2+C^2$ with the fakeon prescription/projection for $C^2$). We show that these quantities are related to the spectra in a universal way. We also compute the first correction to the relation $r=−8n_T$ and provide a number of quantum gravity predictions that can be hopefully tested in the forthcoming future.

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To appear in J. Cosmol. Astropart. Phys.

arXiv: 2007.15023 [hep-th]

Testable predictions of quantum gravity with fakeons on the spectra of the CMB radiation

Based on the paper 20A3 Renorm (arXiv: 2006.01163 [hep-th])

Talk given online by M. Piva for the Tokyo Institute of Technology, on Jun 16th, 2020

Talk given online by Marco Piva for the University of Sussex, on July 20th, 2020

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Testable predictions of quantum gravity with fakeons on the spectra of the CMB radiation

Talk given by M. Piva at the National Institute of Chemical Physics and Biophysics, Tallinn, Estonia, on Jun 9th, 2020

Based on the paper 20A3 Renorm (arXiv: 2006.01163 [hep-th])

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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 $R+R^{2}$ 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 ($m_{\chi }>m_{\phi }/4$) on the mass $m_{\chi }$ of the fakeon with respect to the mass $m_{\phi }$ 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 $r\simeq -8n_{T}$ is not affected by the Weyl-squared term. No vector and no other scalar/tensor degree of freedom is present.

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J. High Energy Phys. 07 (2020) 211 | DOI: 10.1007/JHEP07(2020)211

arXiv: 2005.10293 [hep-th]

Book

14B1 D. Anselmi
Renormalization

Course on renormalization, taught in Pisa in 2015. (More chapters will be added later.)

Last update: May 9th 2015, 230 pages

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Contents:
Preface
1. Functional integral
2. Renormalization
3. Renormalization group
4. Gauge symmetry
5. Canonical formalism
6. Quantum electrodynamics
7. Non-Abelian gauge field theories
Notation and useful formulas
References


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