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Dark energy and dust matter phases form an exact f(R)-cosmology model

Dark energy and dust matter phases form an exact f(R)-cosmology model. Prado Martín Moruno IFF (CSIC) ERE2008. S. Capozziello, P. Martín-Moruno and C. Rubano Phys. Lett. B664:12-15,2008. Why f(R)? Point-like Lagrangian and the equations of motion. Noether Symmetry Approach.

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Dark energy and dust matter phases form an exact f(R)-cosmology model

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  1. Dark energy and dust matter phases form an exact f(R)-cosmology model Prado Martín Moruno IFF (CSIC) ERE2008 S. Capozziello, P. Martín-Moruno and C. Rubano Phys. Lett. B664:12-15,2008

  2. Why f(R)? • Point-like Lagrangian and the equations of motion. • Noether Symmetry Approach. • A particular case. • Contrast with some observational data. • Conclusions and further comments.

  3. Cosmic acceleration and dark matter could be nothing else but signals of a breakdown of GR. The simpler extension is f(R) 1. Why f(R)? • The validity of GR on large astrophysical and cosmological scales has never been tested • Higher order theories Of course, a new theory of gravitation must reproduce the low energy limits where GR has been tested.

  4. +Lagrange multiplier 2. Point-like Lagrangian (Metric formalism) 4th order differential equations • Homogenity and isotropy FRW metric

  5. Point-like Lagrangian: Energy function: Vacuum Matter D: standard amount of dust fluid

  6. 3. Noether symmetry • We ask for the existence of a Noether symmetry One solution is: Noether symmetry Constant of the motion • Change of variables:

  7. It is possible to solve the equations of motion Integration constants

  8. 4. A particular case A possible choice of the parameters: • Time units such that The dimensionless quantity must be • For simplicity, we take

  9. If an observer living in this universe is unaware of the fact that the function which appears in the Lagrangian is and not , he would then perform the calculations taking into account , obtaining ! 4. Contrast with some observational data In this model, it seems that the consideration of dark matter is only a consequence of the assumption of GR as the physical theory.

  10. The percentage difference of the two scale factors is less than 3% for the range

  11. The concordance between the distance modulus of our model and of the CDM model with, , seems to be perfect. z

  12. 5. Conclusions and further comments • The Noether symmetry approach allows us to obtain an analytic solution. • Our solution interpolates between the qualitative behaviour of a Friedman radiation-like universe, at small t, and an accelerated expansion, at large t. It must be an intermediate Friedman dust-like behaviour. • A first attempt in the selection of the values of the parameters allows us to fulfill some observational prescription. • A more accurate study and selection of the parameters is required.

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