Is General Relativity the final theory of gravity?: Modified gravity and new problems.

Ismael Ayuso Marazuela

Faculdade de Ciências da Universidad de Lisboa - Instituto de Astrofísica e Ciências do Espacio

Director: Jose Pedro Mimoso

Codirector: Francisco Lobo

2nd IDPASC Students Workshop Porto 2016

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Outline

1. Present theory of gravity: General Relativity. 2. General Relativity in Cosmology.

• Problems of the Standard Cosmology Model. 3. Alternative proposals to the problems of the

Standard Cosmology Model. • Modifying the theory of gravity. • Back-reaction models: the problem of the

averaging. 4. How is G.R. modified?

• Alternative actions. • Current work.

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Current theory of gravity: General Relativity

Newton’s law was not compatible with Special Relativity.

The General Relativity was born to meet the next three principles:

• The equivalence’s principle. • General covariance. • It is a metric theory of gravitation.

This theory has passed all tests in the scale of the Solar System!

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Problems of the General Relativity

• We can not quantize this theory.

• The problem of the singularities.

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General Relativity in Cosmology: the CDM Model

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• Cosmological principle: homogeneous and isotropic Universe

• Einstein’s equations with a cosmological constant:

Dark Energy1. Radiation 2. Matter

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• Cosmological principle: homogeneous and isotropic Universe

• Einstein’s equations with a cosmological constant:

Dark Energy

• Tiny in the beginning. Problem of the fine tuning. • It becomes the term which domains when the structures appears. Both

phenomena may be related. • Vacuum energy: 120 orders of magnitud of discrepancy! “The worst

theoretical prediction in the history of the physics ”

In Planck’s units

Problems of the Standard Cosmology Model

Is it true? On small scales there are many structures.

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Alternative Proposals to the SCM

• Modified gravity: It is the proposal to modify the gravity in order to obtain a more general theory which resolves the previous problems.

• Back-reaction models: This proposal tries to understand if the large scales are affected by the structures in small scales, i.e. it tries to find out the veracity of the Cosmological Principle. The problem of the average appears in these models since there are different ideas about how this treatment has to be done.

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How is G.R. modified?

Variation with respect to the metric

In order to explain the current acceleration of the Universe, to obtain a theory of gravity which could be quantized and maybe to explain other

phenomena.

Problems: new degrees of freedom, emergence of ghosts and instabilities and difficult to study these models.

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Some examples

Non-local action

It can be transformed in G.R. with two scalar fields coupled

It was one of the first proposal actions and currently it’s the most studied.

This action includes the trace of the energy-momentum tensor like a

generalization of the previous action

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Example of transformation of the previous actions

Conformal transformation Redefinition of the fields

This is the Einstein’s frame

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I. Ayuso, J. A. R. Cembranos,(2014) [arXiv:1411.1653 [gr-qc]]

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An example with instabilities

It depends on the matter we use in the energy-momentum tensor but, in general, this action doesn’t agree with the Horndeski’s theorem. This theorem give us the most general action with an extra scalar field without the Ostrogradski’s instability.

I. Ayuso, J. Beltrán Jiménez, A. Dombriz, Phys.Rev. D91 (2015) no.10, 104003

[arXiv:1411.1636 [hep-th]]

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Example of a proposal action

It could provide a mechanism to connect the onset of the acceleration with the past matter dominated era and remove the

need for unnatural constants in the theory.

We can rewrite this action in a local action with the help of two scalar fields in order to study perturbations, i.e. the

formation of structures in the Universe by fluctuations of the background.

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S. Deser, R. P. Woodard, Phys.Rev.Lett. 99 (2007) 111301

[iv:0706.2151 [astro-ph]]

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A non-local action

Modify the gravitational constant

Local representation

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A non-local action

• Variation with respect to the metric.

• Variation with respect to the fields.

Equations of motion (background)

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A non-local action

• Variation with respect to the metric

• Variation with respect to the fields.

Equations of motion (background)

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A non-local action

Equations of motion (background)

• Variation with respect to the metric

• Variation with respect to the fieldsNew degrees of freedom: it introduces instabilities!

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A non-local action

The absent of instabilities is insured if we impose:

The gravity must be attractive.The kinetic term doesn’t introduce instabilities.

In the quasi-static approximation this model is able to reproduce the General Relativity for the Solar System scale.

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T. S. Koivisto, Phys.Rev. D78 (2008) 123505

[arXiv:0807.3778 [gr-qc]]

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A non-local action

Study of perturbations without the quasi-static approximation:

Work in progress

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Conclusions

• The current theory of gravity is the General Relativity. • However this theory can’t be quantized. • This theory, together the Cosmological Principle, tries to explain

the evolution of the Universe and it is called the CDM. • But, this model has some issues which have to be studied such as

the fine tuning problem. • There are two alternative proposals:

1. To remove the Cosmological Principle: back reaction mechanism.

2. To obtain an alternative theory of gravity. • There are new problems in some new theories like the presence of

instabilities but there are hopeful theories which could explain the current acceleration and allow quantize the gravity.

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