2nd IDPASC Students Workshop
Porto 2016
Is General Relativity the final theory of gravity?:
Modified gravity and new problems.
Ismael Ayuso Marazuela
Director: Jose Pedro Mimoso
Codirector: Francisco Lobo
Faculdade de Ciências da Universidad de Lisboa - Instituto de Astrofísica e Ciências do Espacio
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:
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•
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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
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We can not quantize this theory.
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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 Energy
1. Radiation
2. Matter
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Problems of the Standard Cosmology Model
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Cosmological principle: homogeneous and isotropic
Universe
Is it true? On small scales there are many structures.
Einstein’s equations with a cosmological constant:
In Planck’s units
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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 ”
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Alternative Proposals to the SCM
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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
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
It can be transformed in G.R. with
two scalar fields coupled
Non-local action
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Example of transformation of the previous actions
Conformal transformation
Redefinition of the fields
This is the Einstein’s frame
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
S. Deser, R. P. Woodard,
Phys.Rev.Lett. 99 (2007) 111301
[iv:0706.2151 [astro-ph]]
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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A non-local action
Local representation
Modify the gravitational constant
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A non-local action
Equations of motion (background)
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Variation with respect to the metric.
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Variation with respect to the fields.
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A non-local action
Equations of motion (background)
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Variation with respect to the metric
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Variation with respect to the fields.
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A non-local action
Equations of motion (background)
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Variation with respect to the metric
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New
degrees
Variation with respect to
the
fieldsof freedom: it introduces
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instabilities!
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A non-local action
The absent of instabilities is insured if we impose:
The kinetic term doesn’t
introduce instabilities.
The gravity must be attractive.
In the quasi-static approximation this model is able to reproduce the General
Relativity for the Solar System scale.
T. S. Koivisto,
Phys.Rev. D78 (2008) 123505
[arXiv:0807.3778 [gr-qc]]
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A non-local action
s
s
e
r
g
o
r
p
Study of perturbations without the quasi-static approximation:
r
o
W
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k
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Conclusions
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•
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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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