We demonstrate that there appear finite-time future singularities in $f(T)$ gravity with $T$ being the torsion scalar. reconstruct a model of realizing singularities. In addition, it is explicitly shown power-low type correction term $T^\beta$ ($\beta>1$) such as $T^2$ can remove gravity. Moreover, we study models inflation early universe, $\Lambda$CDM model, Little Rip cosmology and Pseudo-Rip cosmology. It demonstrated disintegration bound structures for cosmologies occurs same way...

In order to apply holography and entropy relations the whole universe, which is a gravitational thus nonextensive system, for consistency one should use generalized definition universe horizon entropy, namely Tsallis entropy. We formulate holographic dark energy, generalization of standard energy quantified by new dimensionless parameter δ, possessing latter as particular sub-case. provide simple differential equation density parameter, well an analytical expression its equation-of-state...

In this paper, the main motive is to mathematical explore Kuralay equation, which find applications in various fields such as ferromagnetic materials, nonlinear optics, and optical fibers. The objective of study investigate different types soliton solutions analyze integrable motion induced space curves. This article appropriates traveling wave transformation allowing partial differential equation be changed into an ordinary equation. To establish these solutions, employs new auxiliary...

Abstract By considering the concept of modified Chaplygin gas (MCG) as a single fluid model unifying dark energy and matter, we construct static, spherically charged black hole (BH) solution in framework General Relativity. The P – V criticality anti-de Sitter (AdS) BH with surrounding MCG is explored context extended phase space, where negative cosmological constant operates thermodynamical pressure. This critical behavior shows that small/large transition analogous to van der Waals...

Dark energy cosmology is considered in a modified Gauss–Bonnet model of gravity with and without scalar field. It shown that these generalizations general relativity endow it very rich cosmological structure: may naturally lead to an effective constant, quintessence or phantom cosmic acceleration, the possibility describing transition from decelerating accelerating phase explicitly. demonstrated here GB scalar-GB theories are perfectly viable as models. They can describe ΛCDM era any need...

We investigate inflation within $$f(R,\phi )$$ -theories, where a dynamical scalar field is coupled to gravity. A class of models which can support early-time acceleration with the emerging an effective cosmological constant at high curvature studied. The dynamics allow for exit from leading correct amount in agreement data. Furthermore, spectral index and tensor-to-scalar ratio are carefully analyzed. generalization theory incorporate dark matter context mimetic gravity, further extensions...

In this paper, we consider a simple form of expansion history Universe referred to as the hybrid law - product power-law and exponential type functions. The ansatz by construction mimics de Sitter cosmologies special cases but also provides an elegant description transition from deceleration cosmic acceleration. We point out Brans-Dicke realization under consideration. construct potentials for quintessence, phantom tachyon fields, which can give rise in general relativity. investigate...

In this work, we analyse static spherically symmetric solutions in the framework of mimetic gravity, an extension general relativity where conformal degree freedom gravity is isolated a covariant fashion. Here extend previous works by considering addition potential for field. An appropriate choice such allows reconstruction number interesting cosmological and astrophysical scenarios. We explicitly show how to reconstruct space-time. A applications scenarios are then explored, among which...

We study inflation induced by (power-low) scalar curvature corrections to General Relativity. The class of inflationary potentials $V(\sigma)\sim\exp[n\,\sigma]$, $n$ general parameter, is investigated in the Einsein frame and corresponding actions Jordan are derived. found conditions for which these able reproduce viable according with last cosmological data lead large emerge only at a mass scale larger than Planck mass. Cosmological constant may appear or be set equal zero action without...

In this Letter, we derived the first law of thermodynamics using method proposed by Wald. Treating entropy as Noether charge and comparing with usual thermodynamics, obtained expression explicitly which contains infinitely many non-local terms (i.e. integral terms). We have proved, in general, that black bole is violated for $f(R,T)$ gravity. But there might exist some special cases gravity recovered.

A toy model of Einstein gravity with a Gauss-Bonnet classically "entropic" term mimicking quantum correction is considered. The static black hole solution due to Tomozawa found and generalized the inclusion non trivial horizon topology, its entropy evaluated deriving first law by equations motion. As result Bekenstein-Hawking area turns be corrected logarithmic term. Misner-Sharp expression for mass found. Within Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmological setting, used in...

In this paper, we investigate a scenario of variable gravity and apply it to the unified description inflation late-time cosmic acceleration dubbed quintessential inflation. The scalar field called ``cosmon,'' which in model unifies both concepts, reduces inflaton at early epochs. We calculate slow-roll parameters, Hubble parameter end inflation, reheating temperature, tensor-to-scalar ratio, demonstrate agreement with observations Planck data. As for postinflationary dynamics, cosmon tracks...

This pedagogical review is devoted to quintessential inflation, which refers unification of inflation and dark energy using a single scalar field. We present brief but concise description the concepts needed join two ends, include discussion on field dynamic, conformal coupling, instant preheating relic gravitational waves. Models broadly fall into classes, depending upon early late time behavior potential. In first type we models in potential steep for most history universe turn shallow at...

In this work, we shall exhaustively study the effects of modified gravity on energy spectrum primordial gravitational waves background. S. Weinberg has also produced significant works related to waves, with most important one being neutrinos waves. With short review, our main aim is gather all necessary information for studying in a concrete and quantitative way single paper. After reviewing techniques extracting general relativistic spectrum, how obtain, WKB way, damping or amplifying...

In this paper, we study the Kuralay equations, namely Kuralay-I equation (K-IE) and Kuralay-II (K-IIE). The integrable motion of space curves induced by these equations is investigated. gauge equivalence between two established. With help Hirota bilinear method, simplest soliton solutions are also presented. nonlocal dispersionless versions considered. Some generalizations other related nonlinear differential

The solution of partial differential equations has generally been one the most-vital mathematical tools for describing physical phenomena in different scientific disciplines. previous studies performed with classical derivative on this model cannot express propagating behavior at heavy infinite tails. In order to address problem, study addressed fractional regularized long-wave Burgers problem by using two operators, Beta and M-truncated, which are capable predicting where is unable show...