1. Do consistent modified gravity models mimic General Relativity? S. Appleby, R. Battye. Talk based on arXiv:0705.3199

2. Introduction  Modified gravity covers a wide range of models,,,,,,, We consider F(R) gravity, in particular the metric formalism.We consider F(R) gravity, in particular the metric formalism.   Different functions F(R) can be used to model, InflationInflation Late time accelerationLate time acceleration  Can we constrain the form that F(R) can take?

3. What form can F(R) take?  Consistency conditions, Absence of ghosts:Absence of ghosts: Stability at large R underStability at large R under metric perturbations: metric perturbations: CMB, constraints, large R:CMB, constraints, large R: Minkowski space a solution:Minkowski space a solution:  If we demand that these constraints hold for all R, then we find that the form of the function must be;  An obvious choice is the tanh function.

4. A trial F(R)  We consider the function  Integrating this function gives,  The integration constant A is chosen such that   Two free parameters, a and b, to be constrained.

5. Constraints  We choose the parameters a and b such that,  Expansions:  We require a late time accelerating solution to the vacuum field equations, This givesThis gives  Newton’s Law:

6. Constraints (cont.)  Local gravity constraints,  Cosmological constraint; We require that the model has a late time accelerating solution to the field equationsWe require that the model has a late time accelerating solution to the field equations For any particular R throughout the cosmic history of the model, the corrections remain small.For any particular R throughout the cosmic history of the model, the corrections remain small.  An acceptable matter era?  Other constraints; black hole entropy, power spectrum, gravitational wave spectrum.

7. General F(R) models  So far, we have considered a particular F(R) which satisfies the conditions required to be consistent model,  However, this model is an example of a general class of models which have recently appeared in the literature, Another example isAnother example is  These models can be expanded as where for  They share the important property that for, and for large R. The F(R) considered here asymptotes exponentially towards GR for large R,The F(R) considered here asymptotes exponentially towards GR for large R, Hu’s model asymptotes to GR as a power law.Hu’s model asymptotes to GR as a power law. arXiv:0795.1158

8. Matter instability  This model contains an instability,  Look for a solution around a known stable matter source,  Field equation,  By perturbing, with

9. Matter Instability (cont.)  Can we save this F(R)? Introduce new terms, e.g.Introduce new terms, e.g. Introduce a scalar field,Introduce a scalar field, Couple R explicitly to matter.Couple R explicitly to matter.  Is this instability generic to F(R) models that can be expanded as ?  Field equation for If, then we find violent instabilities.If, then we find violent instabilities.

10. Conclusion  We have considered models which have for all Such models can, Satisfy the consistency conditions that we impose (e.g. absence of ghosts and singularities)Satisfy the consistency conditions that we impose (e.g. absence of ghosts and singularities) Mimic General Relativity with matter and late time accelerating eras,Mimic General Relativity with matter and late time accelerating eras, Satisfy the stringent constraints imposed by local gravity constraints,Satisfy the stringent constraints imposed by local gravity constraints,  However, such models can potentially be susceptible to violent instabilities, Can such instabilities be avoided?Can such instabilities be avoided?