Bianchi V I I A solutions of effective quadratic gravity

Abstract

It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. Numerical solutions for the anisotropic generalization of the Friedmann "open" model H 3 for this effective gravity are given. It must be emphasized that although numeric, these solutions are exact in the sense that they depend only on the precision of the machine. The solutions are identified asymptotically in a certain way. It is found solutions which asymptote de Sitter space, Riemann flat space and a singularity. The question of isotropisation of an initially anisotropic Universe is of great importance in the context of cosmology. Although isotropisation is not directly discussed in this present work, we show that sufficiently small anisotropies, do not increase indefinitely according to particular quadratic gravity theories. It can be understood as weak isotropisation, and we stress that this result is strongly dependent on initial conditions.

Anisotropic cosmological solutions in $$R + R^2$$ R + R 2 gravity

“…The investigations of this type of models began with [11][12][13][14]. After them, many authors have analyzed the cosmological evolutions of such a model [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. Particular attention is given to the asymptotic behavior in [30][31][32][33][34].…”

On stability of the Kasner solution in quadratic gravity

“…Since then it has been investigated by many authors [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. It is worth to note that cubic and higher order curvature corrections often lead to Big Rip singularity even in the framework of f (R) theory [32][33][34][35] or at least make important cosmological solutions unstable (for an example beyond the f (R) theory see, for example [36]), so our restriction with only quadratic curvature corrections is justified from phenomenological reasons also.…”

Anisotropic cosmological solutions in $R + R^2$ gravity

“…The investigations of this type of models began with [11,12,13,14]. After them, many authors have been analyzed the cosmological evolutions of such a model [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]. A particular attention is given to the asymptotic behavior in [30,31,32,33].…”