## Mini courses

**Introduction to Modified Gravity theories**

Fulvio Sbisá (UFES)

Starts : August 11, 2017

Every Friday, from 14:00 to 15:00.

1) Motivations, problems of GR.

2) Ghosts, Ostrogradsky theorem.

3) Constrained Hamiltonian systems, degrees of freedom.

4) The DGP model: weak gravity.

5) The DGP model: Vainshtein mechanism.

6) The DGP model: cosmology and problems.

7) Codimension-2 braneworlds and the cosmological constant.

8) Massive Gravity: the Fierz-Pauli action, the vDVZ discontinuity.

9) Massive Gravity: Stuckelberg fields, the Vainshtein mechanism, the BD ghost.

10) Massive Gravity: dRGT Massive Gravity, cosmology, problems and extensions.

11) f(R) gravity: classification of theories, equivalence with Brans-Dicke.

12) f(R) gravity: the weak field limit, the Chameleon effect.

13) f(R) gravity: cosmology.

14) Galileons.

15) Scalar-tensor theories, Hordenski and beyond.

**Minicurso sobre programação em Python**

Tiago Castro (UFRJ)

1ª Aula: Básico de python (Incluindo numpy, scipy, matplotlib...)

2ª Aula: POO em python (Criação de um pacote para cosmologia)

3ª Aula: Paralelização em Python

4ª Aula: Estatística Bayesiana em Python (Básico de estatística Bayesiana, MCMC, emcee, analisando JLA)

5ª Aula: Análisando Simulações Cosmológicas em Python

Extra: github, Gadget.

Dias: 15 a 19 de maio de 2017. Prédio do PPGFis.

2a: 12:00-14:00, sala 2 -

**aula 1**

3a: 13:00-15:00, sala 1 -

**aula 2, material auxiliar**

4a: 15:30-17:30, sala 1 -

**aula 3, material auxiliar**

5a: 13:00-15:00, sala 1 -

**aula 4 (nb jupyter)**

6a: 15:00-17:00, sala 2 -

**aula 5 (nb jupyter)**

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**Formalismo ADM, Gravitação e Cosmologia Quânticas - Segunda parte do curso Tópicos em Cosmologia do PPGCosmo**

Nelson Pinto-Neto (CBPF)

Dia 08/05/2017, das 18:00 às 19:30.

Tópico: "Cosmologia quântica: o problema da interpretação."

De 09 a 11/05/2017, das 13:30 às 15:00.

Tópicos:

"Equação de Wheeler-De Witt para geometrias homogêneas e isotrópicas e um campo escalar canônico e suas soluções."

"Equação de Wheeler-De Witt para geometrias homogêneas e isotrópicas e um campo escalar tipo quintessência e suas soluções: o caso de fluidos hidrodinâmicos."

"As soluções com ricochete e suas propriedades."

Dia 12/05/2017, das 10:30 às 12:00.

Tópico: "Perturbações de origem quântica em modelos de cosmologia quântica: equações fundamentais e soluções para modelos com ricochete."

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**Separação 3+1 da Teoria da Relatividade Geral - Primeira parte do curso Tópicos em Cosmologia do PPGCosmo**

Nelson Pinto-Neto (CBPF)

1) Formalismo hamiltoniano e quantização de sistemas vinculados

2) Hamiltoniana da TRG e sua quantização

3) Modelos de minisuperespaco e cosmologia quântica

Dias: 21 a 25 de novembro de 2016 (todos os dias).

Horário: Todos os dias das 17 às 19 horas.

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**Dark Matter a short review: history, candidates and detection**

Antonino del Popolo (Universita di Catania, Italy)

This minicourse is a review of the current status of non-baryonic dark matter (DM) research, starting from a historical overview of the evidences of existence of DM, then discussing the main DM candidates, and concluding with the direct and indirect detection methods, and the results of the quoted search.

Lecture 1:

**(**ppt, 29.7 MB

**)**

September 15 (thursday), from 11:00 to 12:00

Lecture 2:

**(**ppt, 21.7 MB

**)**

September 19 (monday), from 11:00 to 12:00

Lecture 3:

**(**ppt, 78.6 MB

**)**

September 21 (wednesday) , from 9:45 to 10:45

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**Emergent Gravity - an exposition**

Raju Roychowdhury (USP, Brasil)

Abstract:

An elucidation on the geometrization of electromagnetic force further leads to a proposal for a gravity theory (which we call emergent gravity) with non-symmetric metric. It will be shown why we believe that in non-commutative (NC) spacetime there always exists a coordinate transformation that locally eliminates electromagnetic force which is nothing but an upshot of Darboux theorem (precisely an analogue of equivalence principle) in symplectic geometry. The consequence is that electromagnetism can be realized as a geometrical property of spacetime like gravity. It will be discussed how emergent gravity reveals a beautiful generalized geometrical structure which is an artifact of the famous Seiberg-Witten equivalence between commutative and NC DBI actions and is reminiscent of the homological mirror symmetry. In emergent gravity the topology of spacetime is determined by the topology of NC U(1) gauge fields. We will show that the topology change of spacetime is ample in emergent gravity and the subsequent resolution of spacetime singularity is possible in NC spacetime. Using ADHM construction we will show why emergent gravity provides a well-defined mechanism for the topology change of spacetime which does not suffer from any spacetime singularity in sharp contrast to general relativity.

Lecture 1 . Fundamentals and Motivations with Mathematical Foundations - Lie Bracket, Courant Bracket, Generalized Geometry etc.

(31/08 - from 11 to 12)

Lecture 2. Tools for future - ADHM construction - a rapid introduction (01/09 - from 11 to 12)

Lecture 3. Physical application - Topology Change in emergent gravity and resolution of singularity (02/09 - from 11 to 12)

______________________________________________________________________

**Some recent developments in gravitation theory**

Dmitry Galtsov (Moscow State University)

Schedule:

June 27 (monday): from 11:00 to 12:00

June 28 (tuesday): from 09:30 to 12:00 (with 30 minutes break)

July 08 (friday): from 09:30 to 10:30

This mini lecture course introduces some recent ideas in the theory of gravitation beyond Einstein gravity. The first is the idea that at small distances gravity becomes multidimensional and strong, with Planck's mass of the order of TeV. This predicts possibility of black hole creation at LHC which is currently under experimental search. Two follwing lectures are devoted to gravity models with massive graviton within the Minkowski space linear theory and the non-linear ghost-free gravity suggested in 2010. The last lecture intriduces non-minimal couplings of matter fields to gravity containing higher derivatives, but without ghosts.

1. TeV-scale gravity with extra dimensions

2. Massive graviton in linearized gravity

3. Non-linear massive gravity and bigravity

4. Horndeski couplings

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**Variational Methods in Differential Equations and Applications**

Júlio César do Espírito Santo (UFOP) --- No, he is not Júlio César Fabris.

June 29 and July 1st. From 11:00 to 12:15

The main objective of this minicourse is to illustrate the direct method in the

Calculus of variations, used to treat problems involving Elliptical Operators.

In general, the method seeks to derive and analyze an equivalent variational

problem, in a certain sense, to the problem in differential equations.

This minicourse, divided in two parts: in the first meeting we wish to show the

Method details, applying it to a linear boundary problem, highlighting the

difficulties that arise and what motivates the concepts that are necessary for

its application. In the last meeting, we shall show what difficulties arise in

applying the Method to a non-linear problems, highlighting how it works to a

problem involving the p-Laplacian operator: known as the prototype and a mascot

to non-linear elliptical differential operators.

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**To be or not to be modified... gravity**

Radouane Gannouji (UCV, Chile)

December 14 -18, 2015.

__First lecture, Monday (Dec 14) from 11:00 to 12:30: The road to modified gravity.__

I will introduce the current problems in cosmology and a possible road of investigation dubbed modified gravity.

__Second lecture, Wednesday (Dec 16) from 11:00 to 12:30: Chameleon mechanism.__

If a modification of gravity can be considered as welcomed at large scales, we need to hide the additional field locally. I will discuss the chameleon mechanism, its strengths and the weaknesses, from the lab to the Universe.

__Third lecture, Friday (Dec 18) from 11:00 to 12:30: Vainshtein mechanism.__

From massive gravity to galileons, various models propose an other screening mechanism. If the chameleon mechanism uses the non-linearities coming from matter couplings, the Vainshtein mechanism uses the self-coupling of a scalar-field degree of freedom as a source for the non-linear effect. We will see also various aspects of this mechanism

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**Introduction to cosmological perturbation theory**

Jai-chan Hwang (Kyungpook National University, Republic of Korea)

November 10, 12 and 16 - 11 a.m. - PPGFis, room 3.

We introduce cosmological perturbation theory which is at the foundation of modern physical cosmology connecting observations with theories. Basics of relativistic linear and nonlinear cosmological perturbation theory will be explained. As it is convenient to have the covariant (1 + 3) and the ADM (3 + 1) formulation of Einstein's gravity, we will introduce these two formulations in the first couple of lectures. The gauge (coordinate degrees of freedom) issue and a way to use it for our convenience will be explained.

Here you can find the pdf file of the lectures.

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**The small scale problems of the LCDM model**

Antonino del Popolo (Universita' di Catania -Italy )

October 05 -09, 2015.

Monday (Oct 05): from 11:00 to 12:30.

Wednesday (Oct 07): from 11:00 to 12:30.

Friday (Oct. 09): from 11:00 to 12:30.

Slides: 1, 2, 3, 4.

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**Horizons for surface waves in fluids**

Alberto Saa (Unicamp)

August 12 -14, 2015.

Wednesday: from 17:00 to 18:15. (pdf)

Thursday: from 11:00 to 12:15. (pdf)

Friday: from 11:00 to 12:15. (pdf)

Surface waves on stationary flows will be revisited. We will focus on the linear regime for the waves, where an effective geometrical formulation is available and the notion of horizon for surface waves makes sense. We will show also that such fluid configurations can be studied experimentally in rather simple hydrodynamics setups which could be considered as simplified analogs of real spacetime phenomena.

**Cosmic inflation and the origin of structure**

David Wands (Institute of Cosmology and Gravitation, University of Portsmouth)

May 7 (Thursday), 8 (Friday), 11 (Monday), 12 (Tuesday) 2015. From 11.00 to 12.30.

Venue: Room 3, ground floor of PPGFIS building.

Lecture 1: Inflationary dynamics

Lecture 2: Gauge-invariant perturbations

Lecture 3: Primordial perturbations from inflation

Lecture 4: Multiple field inflation (entropy perturbations and non-Gaussianity)

**Self-adjoint extensions in Physics**

Giuseppe Dito (Université de Bourgogne)

March 02 - 06, 2015, one lecture per day from 11.00 to 12.00.

Lecture 1: Hilbert spaces and operators

Lecture 2: Symmetric and self-adjoint operators

Lecture 3: Deficiency indices and Von Neumann theory

Lecture 4: Stone and Nelson theorems

Lecture 5: Applications to quantum physics

**Canonical Gravity**

Yaser Tavakoli (UFES)

Program:

*December 15 (monday), from 11:00 to 12:15:*Constrained

*Hamiltonian systems*

*December 16 (tuesday), from 11:00 to 12:15:*

*Hamiltonian formulation of general relativity*

*December 18 (thursday), from 13:30 to 15:00: Ashtekar's variables for canonical gravity*

**Effective field theory methods in gravity and cosmology**

Riccardo Sturani (UNESP)

Três aulas nos dias 18, 20 e 21/11/2014, das 11:00 às 12:30.

In a short series of lectures (3x1h30') I will outline the basis of the applications of effective field theory methods to classical theory of gravity.Effective field theory methods represent a powerful tool to perturbatively solve equations of motions.

In particular I will review the recent proposal to compute cosmological observables taking into account gravity non-linearities by mapping the cosmological equations into those of a viscous fluid coupled to gravity.

These lectures were based on these lecture notes. See also this page.

**Sistemas vinculados: introdução aos formalismos Hamiltonianos de Dirac e Simplético**

Davi Rodrigues (UFES)

Dias: 08/08/2014 e 15/08/2014. Das 11 às 12 horas.

Este minicurso é uma continuação do minicurso "

*Formulação Hamiltoniana da Relatividade Geral*". O principal objetivo deste breve minicurso é apresentar uma introdução ao formalismo simplético, que é um formalismo alternativo ao formalismo Hamiltoniano de Dirac de tratamento de vínculos e simetrias, no qual se baseia o formalismo Hamiltoniano da Relatividade Geral.

**Anti-de Sitter Space-Time**

Betti Hartmann (UFES & Jacobs University Bremen)

Schedule:

16/7 (wednesday) Anti-de Sitter (generalities).

17/7 (thursday): Black holes in Anti-de Sitter

23/7 (wednesday): AdS/CFT in a nutshell

01/8 (friday): Stability of Anti-de Sitter

All the days from 11:00 to 12:15.

**Astrofísica de aglomerado de galáxias com raios-X**

Gastão B. Lima Neto (IAG-USP)

Days: 21, 22 and 23/05/2014. From 11:00 to 12:30. --- Lecture notes.

RESUMO: O objetivo deste mini-curso é dar uma visão geral de aglomerados de

galáxias e suas propriedades físicas. Será dada ênfase aos aspectos

observacionais, particularmente na banda de raios-X (0.1-10.0 keV).

PROGRAMA: Definição de aglomerado de galáxias e suas características.

Componentes de aglomerados: galáxias/estrelas, plasma intra-aglomerado,

matéria escura. Determinação de massa. Emissão de raios-X: descoberta e

processos de emissão. Espectroscopia e imageamento em raios-X e propriedades

astrofísicas associadas. Cooling-flow no centro de aglomerados e aquecimento

do gás intra-aglomerado. Aglomerados em alto redshift. Observação em raios-X

por satélites. Obtenção dos dados em raios-X, redução e análise.

**Métodos Mathematicos**- Minicurso sobre o Mathematica

Davi C. Rodrigues (UFES)

Às quartas-feiras, 11:00-12:00.

Dias em que houve aulas:

09/04/2014, 30/04/2014, 07/05/2014, 11/06/2014

Arquivos utilizados no curso: arquivo principal v4, UGC.txt, SetOptions2a.m.

Caso deseje receber emails de aviso sobre o curso, escreva para site@cosmo-ufes.org .

**Geometric theories of gravity**

Bertrand Chauvineau (Université de Nice-Sophia Antipolis,Observatoire de la Côte d’Azur - France)

Days: 5, 7, 12 and 14/02/2014. Always at 11:00.

Lecture Notes

__Program:__

Geometry & basic tools

I - Gravity & geometrical concepts

II - What can a geometric gravity lagrangian look like?

III – Symmetries, conservation laws, laws of conservation

Geometric gravity : General Relativity & sisters

IV - General Relativity & ways to alternatives

V - f(R) theories

VI - Other purely metric alternatives vs Ostrogradsky theorem

VII - Scalar-tensor theories

VIII - f(R) vs scalar-tensor

IX - Non-dynamical scalar-tensor

**Formulação Hamiltoniana da Relatividade Geral**José André Lourenço (UFES - São Mateus)

Fridays from 14:00 to 15:00.

Starts: 24/01/2014.

Program.

Bibliografia da introdução à formulação Hamiltoniana com vínculos

**Cusps and Cores in galaxies, problems and solutions**

Antonino del Popolo (Universita' di Catania -Italy)

October 22 - 24, 2013.

From 14:00 to 15:00

Abstract & Program

First day, Second day, Third day

This mini course was canceled due to urgent personal reasons.

**Dinâmica de sistemas gravitacionais**José de Freitas Pacheco (OCA-France)

Thursdays from 11:00 to 12:30

Oct, 2013 - Dez, 2013

Program.

Slides of the 2nd day

Lecture notes

**A Física da Radiação Cósmica de Fundo**Hermano Velten (UFES, pdf), Wiliam Hipólito (UFES São Mateus, pdf), Daniel Boriero (Unicamp, pdf)

September 23 - 26, 2013. UFES, Vítória

Program and schedule