In the present paper, we use the holographic approach to describe the early-time acceleration and the late-time acceleration eras of our Universe in a unified manner. Such "holographic unification" is found to have a correspondence with various higher curvature cosmological models with or without matter fields. The corresponding holographic cutoffs are determined in terms of the particle horizon and its derivatives, or the future horizon and its derivatives. As a result, the holographic energy density we propose is able to merge various cosmological epochs of the Universe from a holographic point of view. We find the holographic correspondence of several FðRÞ gravity models, including axion-FðRÞ gravity models, of several Gauss-Bonnet FðGÞ models and finally of FðTÞ models, and in each case we demonstrate that it is possible to describe in a unified way inflation and late-time acceleration in the context of the same holographic model.

We have explicitly demonstrated that scalar coupled Gauss-Bonnet gravity in four dimension can have non-trivial effects on the early inflationary stage of our universe. In particular, we have shown that the scalar coupled Gauss-Bonnet term alone is capable of driving the inflationary stages of the universe without incorporating slow roll approximation, while remaining compatible with the current observations. Subsequently, to avoid the instability of the tensor perturbation modes we have introduced a self-interacting potential for the inflaton field and have shown that in this context as well it is possible to have inflationary scenario. Moreover it turns out that presence of the Gauss-Bonnet term is incompatible with the slow roll approximation and hence one must work with the field equations in the most general context. Finally, we have shown that the scalar coupled Gauss-Bonnet term attains smaller and smaller values as the universe exits from inflation. Thus at the end of the inflation the universe makes a smooth transition to Einstein Therefore most of the inflationary paradigms are driven by a scalar field with a non-trivial self-interacting potential in Einstein gravity.A natural pathway through which such a scalar field can enter the gravitational dynamics at the early universe is through the coupling of the field with the Gauss-Bonnet term. The Gauss-Bonnet term is the first non-trivial higher curvature correction to the Einstein-Hilbert action [27][28][29][30], leading to second order field equations and hence avoiding the Ostrogradsky instability [31]. Even though the Gauss-Bonnet term alone, in the context of four dimensional physics, does not contribute to the gravitational field equations, the scalar coupling makes the Gauss-Bonnet term (and hence the field equations) non-trivial. Some aspects of this scalar coupled Gauss-Bonnet gravity in the context of early universe physics has been explored in [32][33][34][35][36][37][38][39][40][41][42][43] (for a set of earlier works in other alternative theories in the similar spirit, see ). Below we provide a brief discussion on the results obtained in these works.The inflationary paradigm has been explored in [36,37] only in the context of scalar coupled Gauss-Bonnet gravity, excluding the Einstein term. While in [39,43], even though the Einstein term was essential, the self-interacting potential itself governs the inflation, having no effect of the Gauss-Bonnet term. On the other hand, in [32][33][34][35] both the self-interacting potential as well as the Gauss-Bonnet coupling for the inflaton field has been considered, but in the context of slow-roll approximation (see also [35,[40][41][42]98,99]). Thus non-trivial effects of the scalar coupled Gauss-Bonnet term in the Einstein-Hilbert action, in absence of self-interacting scalar potential in the context of inflationary paradigm has not been explored before. Besides, even when the self-interacting potential is added to the action, the relevant consequences of not incorporating the slow-roll approximation...

The intriguing question, why the present scale of the universe is free from any perceptible footprints of rank-2 antisymmetric tensor fields? (generally known as Kalb-Ramond fields) is addressed. A quite natural explanation of this issue is given from the angle of higher-curvature gravity, both in four-and in five-dimensional spacetime. The results here obtained reveal that the amplitude of the Kalb-Ramond field may be actually large and play a significant role during the early universe, while the presence of higher-order gravity suppresses this field during the cosmological evolution, so that it eventually becomes negligible in the current universe. Besides the suppression of the Kalb-Ramond field, the extra degree of freedom in F (R) gravity, usually known as scalaron, also turns out to be responsible for inflation. Such F(R) gravity with Kalb-Ramond fields may govern the early universe to undergo an inflationary stage at early times (with the subsequent graceful exit) for wider range of F(R) gravity than without antisymmetric fields.. Furthermore, the models-in fourand five-dimensional spacetimes-are linked to observational constraints, with the conclusion that the corresponding values of the spectral index and tensor-to-scalar ratio closely match the values provided by the Planck survey 2018 data.

In this paper we shall study the inflationary aspects of a logarithmic corrected R 2 Starobinsky inflation model, in the presence of a Kalb-Ramond field in the gravitational action of F (R) gravity. Our main interest is to pin down the effect of this rank two antisymmetric tensor field on the inflationary phenomenology of the F (R) gravity theory at hand. The effects of the Kalb-Ramond field are expected to be strong during the inflationary era, however as the Universe expands, the energy density of the Kalb-Ramond field scales as ∼ a −6 so dark matter and radiation dominate over the Kalb-Ramond field effects. In general, antisymmetric fields constitute the field content of superstring theories, and thus their effect at the low-energy limit of the theory is expected to be significant. As we will show, for a flat Friedmann-Robertson-Walker metric, the Kalb-Ramond field actually reduces to a scalar field, so it is feasible to calculate the observational indices of inflation. We shall calculate the spectral index and the tensor-to-scalar ratio for the model at hand, by assuming two conditions for the resulting Kalb-Ramond scalar field, the slow-roll and the constant-roll condition. As we shall demonstrate, in both the slow-roll and constantroll cases, compatibility with the latest observational data can be achieved. Also the effect of the Kalb-Ramond field on the inflationary phenomenology is to increase the amount of the predicted primordial gravitational radiation, in comparison to the corresponding f (R) gravities, however the results are still compatible with the observational data.

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