Cosmological evolution and exact solutions in a fourth-order theory of gravity

Abstract

A fourth-order theory of gravity is considered which in terms of dynamics has the same degrees of freedom and number of constraints as those of scalar-tensor theories. In addition it admits a canonical point-like Lagrangian description. We study the critical points of the theory and we show that it can describe the matter epoch of the universe and that two accelerated phases can be recovered one of which describes a de Sitter universe. Finally for some models exact solutions are presented.PACS numbers: 98.80.-k, 95.35.+d, 95.36.+x

De Sitter and scaling solutions in a higher-order modified teleparallel theory

“…Specifically we found that V (φ) = V 0 e −λφ , λ = 3, where the equation of state parameter is γ = −2 1 − λ 3 , and scale factor a (t) = a 0 t 2 3γ . That result is in agreement with that of the analysis in the dimensionless variables [57]. As far as concerns the stability of that solution it was found that for λ > 0 the solution is stable.…”

“…That specific case, f (T, B) = T + Φ (B) , was the main subject of study in [57] in the cosmological scenario of a spatially flat FLRW spacetime. Moreover, with the use of Lagrange Multipliers the extra degrees of freedom have been attributed to annoncanonical scalar field.…”

Minisuperspace Quantization of f(T, B) Cosmology

“…A special case of the f (T, B) theory which has been studied before is that in which f ,TT = 0, f ,TB = 0 , which means that f is a linear function of T, that is, f (T, B) = T + F(B) [36]. In the latter consideration in the case of Friedmann-Lemaître-Robertson-Walker (FLRW) universe, the theory can be written as a scalar field theory, but not a scalar tensor theory, with the same number of dynamical constraints as the f (R)-theory.…”

“…That observation leads to field equations which can be described by a point-like Lagrangian with the same number of constraint equations as f (R)-gravity which means that there is a minisuperspace description for the theory. The general asymptotic behaviour as also the stability of some important cosmological solutions such are the scaling or the de Sitter solutions have been studied before in [36,37]. Moreover, the integrability properties of the field equations for this modified theory of gravity were investigated in [38].…”

New integrable models and analytical solutions in f(R) cosmology with an ideal gas

“…The modification of the Einstein-Hilbert action by introducing other kind of invariants has lead to an entire menagerie of f -theories [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. Some theories are second-order, like general relativity, while others are of at least 4 th order.…”