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main page: GrassmannCosmoFun2009**These are just rough notes - feel free to correct them, add links, etc.** from the Grassmann ian Conference in Fundamental Cosmology (Grasscosmofun'09). These are **not** official proceedings. The speakers might even disagree that they said anything even vaguely related to what are in these online notes! Don't say you weren't warned.
# Fri 18 Sep 2009

## STAROBINSKY - f(R) models

## David POLARSKI - DE

## Roman JUSZKIEWICZ

## Jerzy KROL

## Babak VAKILI

main page: GrassmannCosmoFun2009

- particle content: graviton +
- massive scalar particle ( M^2 = 1/{3 f''(R)} ) (called "scalaron" in Starobinsky 1980)

- stability conditions:
- f' > 0 graviton is not a ghost * f'' > 0 scalaron is not a tachyon

- imposed for R \ge R_{now} at least (i.e. during the whole evolution of the Universe)
- possible microscopic origin of f(R) gravity
- vacuum polarisation in curved space-time
- reduction to 4D from curved (4+n)-D space-time
- limiting case of scalar-tensor gravity
- emergent gravity Klinkhamer & Volovik (2008) ArXiv:0807.3896

- violation of these conditions is undesirable also from the classical point of view
- f'(R_*) = 0 instant loss of homogeneity and isotropy
- f''(R_*) = 0 weak singularity

- existence of the Newtonian regime
- for (up to some very large R)
- de Sitter regime stable if
- equivalent to in scalar-tensor gravity

- use for inflation Starobinsky 1980:
- internally consistent infolationary model with slow-roll decay, a graceful exit to the subsequent RD (radiation-dominated) FRW stage ... and sufficiently effective reheating
- model remains viable, e.g.

- oher viable f(R) inflationary models
- 1. chaotic type - inflation over a large range of R
- 2. new inflationary type - inflation around R =R_0
- both cases: f(R) close to R^2/{6M^2}

- viable for DE???
- for does
**not**work for many reasons - viable model - must be regular at $=0
- Starobinsky 2007, ArXiv:0706.2041 : * or: * f(0) = 0

- for does
- observational constraints
- cosmology - anomalous growth of non-relativistic matter perturbations in the regime
- lab and Solar System tests with R = 8 pi G T_m = 8 \pi G \rho_m; otherwise, \gamma_{(?)} = 1/2 and 'fifth' force appears
- both OK if n \ge 2

- ... "scalaron production" problems
- "big boost" singularity with and its elimination
- elimination: add R^2/{6M^2} to F(R)

- conclusions:
- viable models of DE, distinguishable from LambdaCDM, exist, given certain conditions:
- with a regular f(R) satisfying:
- * ...

- unification of primordial DE (i.e. inflation) and present DE is possible for
- anomalous growth of scalar perturbations at recent times ( z about 1-3 for L = 8 /h Mpc ) would be the most critical test of the f(R) DE models satisfying these conditions

- viable models of DE, distinguishable from LambdaCDM, exist, given certain conditions:

- scalar-tensor theories AstroPh:0701650, AstroPh:0507290
- LambdaCDM problems?
- nbDM halo density profile - no cups seen?
- large scale peculiar flows
- unexpected brightness of SNe Ia at z > 1 (??)
- void problem
- w = -1 constant is an Achilles' heel

- quintessence
- Lagrangian L = fn(F(phi), R, Z U(phi), g_munu
- Brans-Dicke parametrisation ...
- effects on structure formation

- non-linear perturbation theory for sigma_8

- exotic R^4, QG and QFT - ArXiv:0904.1276 and references therein
- R^n with n=4 case is particularly difficult

- Noether approach ...

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Topic revision: r2 - 18 Sep 2009, BoudRoukema

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