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Fri 18 Sep 2009

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

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
  - $R(t) = R_* + O(\sqrt{t})$
  - $a(t) = a_0 + a_1 t + a_2 t^2 + O(t^{5/2})$
existence of the Newtonian regime $\Delta(\phi) = 4 \pi G \rho$
- $|F(R)| \ll R, |F'(R)| \ll 1, R |F''(R)| \ll 1$ for $R_{now} \ll R$ (up to some very large R)
- de Sitter regime stable if
- equivalent to $\omega_{BD} = 0$ in scalar-tensor gravity
use for inflation Starobinsky 1980: $f(R) = R + \frac{R^2}{6 M^2}$
- 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. $N \sim 50, n_s = 1 - 2/N = 0.96, r = 12/N^2 = 4.8 \times 10^{-4} ...$
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???
- $F(R) \propto R^{-n}$ for $R \rightarrow 0$ does not work for many reasons
- viable model - must be regular at $=0
  - Starobinsky 2007, ArXiv:0706.2041 : $f(R) = R + \lambda R_* \left[\frac{1}{ \left( 1 + R^2/R_*^(?) \right)^n} -1 \right]$ * or: $f(R) = R - \lambda R_* \mathrm{tanh}^2 (R/R_*)$ * f(0) = 0
observational constraints
- cosmology - anomalous growth of non-relativistic matter perturbations in the regime $k \gg M(R)$
- lab and Solar System tests $M(R) L \gg 1$ 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 $R \rightarrow \infty$ 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: $f'(R) > 0, f''(R) > 0 \forall R$
  - $|f-R| \ll R, |f'-1| \ll 1, R|f''| \ll 1$ * ...
- unification of primordial DE (i.e. inflation) and present DE is possible for $M = 3\times 10^{-6} M_{(Pl???)}$
- 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

David POLARSKI - DE

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 $F(\phi) = \phi, Z(\phi) = \frac{\omega_{BD}(\phi)}{\phi}$ ...
- $G_{\mathrm{eff}}, G_N, G_*$
effects on structure formation

Roman JUSZKIEWICZ

non-linear perturbation theory for sigma_8

Jerzy KROL

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

Babak VAKILI

Noether approach ...

-- BoudRoukema - 18 Sep 2009

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Topic revision: r2 - 18 Sep 2009, BoudRoukema

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