Singular inflation from Born–Infeld-f(R) gravity

Abstract

Accelerating dynamics from Born–Infeld-f(R) gravity are studied in a simplified conformal approach without matter. Explicit unification of inflation with late-time acceleration is realized within this singular inflation approach, which is similar to Odintsov–Oikonomou singular f(R) inflation. Our model turns out to be consistent with the latest release of Planck data.

Born–Infeld inspired modifications of gravity

“…A simple extension within this class is to combine the Born-Infeld action with the wellknown f (R) theories in the metric-affine formalism, as considered in [245,244,246,151]. The resulting action adapted to our notation is given by…”

“…The Riemann tensor and the Ricci scalar both depend only on the connection and not on the metric. This idea of combining Born-Infeld and f (R) gravity was further investigated in [246,244,151]. Due to the presence of the Ricci scalar, the model exhibits more freedom for simultaneous applications to early and late time universe cosmology.…”

“…It is worth mentioning that this same model of Born-Infeld-f (R) theories was also used in [151] in order to construct singular inflationary cosmologies. For this purpose, they borrow ideas from singular f (R) inflation [267].…”

“…With this Ansatz of the scale factor, one can establish the required relation between the dynamical and auxiliary metric. For large values of the constant c 1 > 1, singular inflation with a graceful exist can be realised [151].…”

Born-Infeld-$f(R)$ gravity with de Sitter solutions

“…In this model, the BI gravitational action is combined with the well-known f (R) theories in the Palatini formalism. This model attracted a lot of attention and it is used wide variety of fields especially in cosmology [8][9][10][11][12][13][14]. On the other hand there is different generalization of BI-f (R) model which f (R) function directly enters in the determinantal structure [7,13].…”