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
    • 
    • 
• 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
• 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

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 ...
  • 
• 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 ...