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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 R f' = 2f stable if f'(R_*) > R_1 f''(R_*)
    • 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
  • 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_*

-- BoudRoukema - 18 Sep 2009
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