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. 1.Why f(R)? 2.Point-like Lagrangian and the equations of motion. 3.Noether Symmetry Approach. 4.A particular case. 5.Contrast with some observational data. 6.Conclusions and further comments.

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

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

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

6. 3. Noether symmetry One solution is: We ask for the existence of a Noether symmetry 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 Time units such that The dimensionless quantity must be For simplicity, we take A possible choice of the parameters:

9. 4. Contrast with some observational data 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 ! 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. z The concordance between the distance modulus of our model and of the CDM model with,, seems to be perfect.

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.