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Theoretical arguments and cosmological observations suggest that Einstein's theory of general relativity needs to be modified at high energies. One of the best motivated higher-curvature extensions of general relativity is…
In a class of generalized Einstein's gravity theories we derive the equations and general asymptotic solutions describing the evolution of the perturbed universe in unified forms. Our gravity theory considers general couplings between the…
We make the cosmological constant, {\Lambda}, into a field and restrict the variations of the action with respect to it by causality. This creates an additional Einstein constraint equation. It restricts the solutions of the standard…
We provide a new extension of general relativity (GR) which has the remarkable property of being more constrained than GR plus a cosmological constant, having one less free parameter. This is implemented by allowing the cosmological…
Some models within the framework of Gauss-Bonnet gravities are considered in the presence of a non-minimally coupled scalar field. By imposing a particular constraint on the scalar field coupling, an extension of the called…
In standard general relativity the universe cannot be started with arbitrary initial conditions, because four of the ten components of the Einstein's field equations (EFE) are constraints on initial conditions. In the previous work it was…
We propose to reinterpret Einstein's field equations as a nonlinear eigenvalue problem, where the cosmological constant $\Lambda$ plays the role of the (smallest) eigenvalue. This interpretation is fully worked out for a simple model of…
A broad class of generalized Einstein's gravity can be cast into Einstein's gravity with a minimally coupled scalar field using suitable conformal rescaling of the metric. Using this conformal equivalence between the theories, we derive the…
We have shown that the varying physical constant model is consistent with the recently published variational approach wherein Einstein equations are modified to include the variation of the speed of light c, gravitational constant G and…
We find exact cosmological solutions when the Newton parameter and the cosmological term are dynamically evolving in a renormalization-group improved Hamiltonian approach. In our derivation we use the Noether symmetry approach, leading to…
A scale--dependent effective action for gravity is introduced and an exact nonperturbative evolution equation is derived which governs its renormalization group flow. It is invariant under general coordinate transformations and satisfies…
We study the behavior of a general gravitational action, including quadratic terms in the curvature, supplemented by a compact scalar field in 4+1 dimensions. The generalized Einstein equation for this system admits solutions which are…
A special class of conformal gravity theories is proposed to solve the long standing problem of the fine-tuned cosmological constant. In the proposed model time evolution of the inflaton field leaves behind a nearly vanishing, but finite…
We present a class of scalar field cosmologies with a dynamically evolving Newton parameter $G$ and cosmological term $\Lambda$. In particular, we discuss a class of solutions which are consistent with a renormalization group scaling for…
The cosmological viability of varying $G\left( t\right) $ and $\Lambda \left( t\right) $ cosmology is discussed by determining the cosmological eras provided by the theory. Such a study is performed with the determination of the critical…
The asymptotic structure of the gravitational field of isolated systems has been analyzed in great detail in the case when the cosmological constant $\Lambda$ is zero. The resulting framework lies at the foundation of research in diverse…
On the basis of qualitative analysis of the system of differential equations of the standard cosmological model it is shown that in the case of zero cosmological constant this system has a stable center corresponding to zero values of…
A D-dimensional gravitational model with a Gauss-Bonnet term and the cosmological term Lambda is considered. Assuming diagonal cosmological metrics, we find, for certain non-zero Lambda new examples of solutions with an exponential time…
In this paper, in an FLRW background and a perfect fluid equation of state, we explore the possibility of the realization of an emergent scenario in a 4D regularized extension of Einstein-Gauss-Bonnet gravity, with the field equations…
In this paper we provide both a diagnosis and resolution of the cosmological constant problem, one in which a large (as opposed to a small) cosmological constant $\Lambda$ can be made compatible with observation. We trace the origin of the…