Cosmology in the mimetic higher-curvature $$f(R,R_{\mu \nu }R^{\mu \nu })$$ gravity

In the framework of the mimetic approach, we study the $$f(R,R_{\mu \nu }R^{\mu \nu })$$ f ( R , R μ ν R μ ν ) gravity with the Lagrange multiplier constraint and the scalar potential. We introduce field equations for the discussed theory and overview their properties. By using the general reconstruction scheme we obtain the power law cosmology model for the $$f(R,R_{\mu \nu }R^{\mu \nu })=R+d(R_{\mu \nu }R^{\mu \nu })^p$$ f ( R , R μ ν R μ ν ) = R + d ( R μ ν R μ ν ) p case as well as the model that describes symmetric bounce. Moreover, we reconstruct model, unifying both matter dominated and accelerated phases, where ordinary matter is neglected. Using inverted reconstruction scheme we recover specific $$f(R,R_{\mu \nu }R^{\mu \nu })$$ f ( R , R μ ν R μ ν ) function which give rise to the de-Sitter evolution. Finally, by employing the perfect fluid approach, we demonstrate that this model can realize inflation consistent with the bounds coming from the BICEP2/Keck array and the Planck data. We also discuss the holographic dark energy density in terms of the presented $$f(R,R_{\mu \nu }R^{\mu \nu })$$ f ( R , R μ ν R μ ν ) theory. Thus, it is suggested that the introduced extension of the mimetic regime may describe any given cosmological model.

Reconstructing inflation in scalar-torsion $$f(T,\phi )$$ gravity

It is investigated the reconstruction during the slow-roll inflation in the most general class of scalar-torsion theories whose Lagrangian density is an arbitrary function $$f(T,\phi )$$ f ( T , ϕ ) of the torsion scalar T of teleparallel gravity and the inflaton $$\phi $$ ϕ . For the class of theories with Lagrangian density $$f(T,\phi )=-M_{pl}^{2} T/2 - G(T) F(\phi ) - V(\phi )$$ f ( T , ϕ ) = - M pl 2 T / 2 - G ( T ) F ( ϕ ) - V ( ϕ ) , with $$G(T)\sim T^{s+1}$$ G ( T ) ∼ T s + 1 and the power s as constant, we consider a reconstruction scheme for determining both the non-minimal coupling function $$F(\phi )$$ F ( ϕ ) and the scalar potential $$V(\phi )$$ V ( ϕ ) through the parametrization (or attractor) of the scalar spectral index $$n_{s}(N)$$ n s ( N ) and the tensor-to-scalar ratio r(N) as functions of the number of $$e-$$ e - folds N. As specific examples, we analyze the attractors $$n_{s}-1 \propto 1/N$$ n s - 1 ∝ 1 / N and $$r\propto 1/N$$ r ∝ 1 / N , as well as the case $$r\propto 1/N (N+\gamma )$$ r ∝ 1 / N ( N + γ ) with $$\gamma $$ γ a dimensionless constant. In this sense and depending on the attractors considered, we obtain different expressions for the function $$F(\phi )$$ F ( ϕ ) and the potential $$V(\phi )$$ V ( ϕ ) , as also the constraints on the parameters present in our model and its reconstruction.

The barrow holographic dark energy-based reconstruction of f(R) gravity and cosmology with Nojiri–Odintsov cutoff

In the work reported here we have considered Barrow holographic dark energy (BHDE) proposed in E. N. Saridakis, Barrow holographic dark energy, Phys. Rev. D 102 (2020) 123525 as a special case of more generalized version of Nojiri–Odintsov holographic dark energy (NOHDE) proposed in S. I. Nojiri and S. D. Odintsov, Unifying phantom inflation with late-time acceleration: Scalar phantom–non-phantom transition model and generalized holographic dark energy, Gen. Relativ. Gravit. 38 (2006) 1285–1304 and also reconstructed [Formula: see text] gravity with BHDE as the form of background evolution. It has been observed that in the case of BHDE reconstructed [Formula: see text] gravity the equation of state can have a transition from quintessence to phantom. In a particular case of reconstruction, possibility of Little Rip singularity has been observed. Finally, the generalized second law of thermodynamics has been found to be valid under this reconstruction scheme.

Thermodynamics of Barrow Holographic Dark Energy with Specific Cut-Off

Motivated by the work of Saridakis (Phys. Rev. D102, 123525 (2020)), the present study reports the cosmological consequences of Barrow holographic dark energy (HDE) and its thermodynamics. The literature demonstrates that dark energy (DE) may result from electroweak symmetry breaking that triggers a phase transition from early inflation to late-time acceleration. In the present study, we incorporated viscosity in the Barrow HDE. A reconstruction scheme is presented for the parameters associated with Barrow holographic dark energy under the purview of viscous cosmology. The equation of state (EoS) parameter is reconstructed in this scenario and quintessence behaviour is observed. Considering Barrow HDE as a specific case of Nojiri–Odintsov (NO) HDE, we have observed quintom behaviour of the EoS parameter and for some values of n the EoS has been observed to be very close to −1 for the current universe. The generalised second law of thermodynamics has come out to be valid in all the scenarios under consideration. Physical viability of considering Barrow HDE as a specific case of NO HDE is demonstrated in this study. Finally, it has been observed that the model under consideration is very close to ΛCDM and cannot go beyond it.

A survey on deep learning-based Monte Carlo denoising

Monte Carlo (MC) integration is used ubiquitously in realistic image synthesis because of its flexibility and generality. However, the integration has to balance estimator bias and variance, which causes visually distracting noise with low sample counts. Existing solutions fall into two categories, in-process sampling schemes and post-processing reconstruction schemes. This report summarizes recent trends in the post-processing reconstruction scheme. Recent years have seen increasing attention and significant progress in denoising MC rendering with deep learning, by training neural networks to reconstruct denoised rendering results from sparse MC samples. Many of these techniques show promising results in real-world applications, and this report aims to provide an assessment of these approaches for practitioners and researchers.

Cosmology of Barrow Holographic Dark Energy as Nojiri-Odintsov Holographic Dark Energy with Specific Cut-off and the Thermodynamics

Motivated by the work of Saridakis (Phys. Rev. D 102, 123525 (2020)), the present study reports the cosmological consequences of Barrow holographic dark energy (HDE) and its thermodynamics. Literatures demonstrate that Dark Energy (DE) may result from electroweak symmetry breaking that triggers a phase transition from early inflation to late time acceleration. In the present study, we incorporated viscosity in the Barrow HDE. A reconstruction scheme is presented for the parameters associated with Barrow holographic dark energy under the purview of viscous cosmology. Equation of state (EoS) parameter is reconstructed in this scenario and quintessence behaviour is observed. Considering BarrowHDE as a specific case ofNojiri-Odintsov (NO) HDE, we have observed quintom behaviour of the EoS parameter and for some values of n the EoS has been observed to be very close to −1 for the current universe. The generalised second law of thermodynamics has come out to be valid in all the scenarios under consideration. Physical viability of considering Barrow HDE as a specific case of NO HDE is demonstrated in this study.