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Register a new userHolographic dark energy in curved spacetime and thermodynamics for interacting fluids
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In this work we explore some aspects of two holographic models for dark energy within the interacting scenario for the dark sector with the inclusion of spatial curvature. A statistical analysis for each holographic model is performed together with their corresponding extensions given by the consideration of massive neutrinos. The first holographic approach considers the usual formula proposed by Li for the dark energy density with a constant parameter $c$ and for the second model we have a function $c(z)$ instead a constant parameter, this latter model is inspired in the apparent horizon. By considering the best fit values of the cosmological parameters we show that the interaction term for each holographic model, $Q$, keeps positive along the cosmic evolution and exhibits a future singularity for a finite value of the redshift, this is inherited from the Hubble parameter. The temperatures for the components of the dark sector are computed and have a growing behavior in both models. The cosmic evolution in this context it is not adiabatic and the second law it is fulfilled only under certain well-established conditions for the temperatures of the cosmic components and the interacting $Q$-term.
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We study the interaction, in general curved spacetime, between a spinor and a scalar field describing dark energy; the so-called DE$_{ u}$ model in curved space. The dominant term is the dimension 5 operator, which results in different energy shifts for the neutrino states: an Aharonov-Bohm-like effect. We study the phenomenology of this term and make observational predictions to detect dark energy interactions in the laboratory due to its effect on neutrino oscillation experiments, which opens up the possibility of designing underground experiments to detect dark energy. This dimension 5 operator beyond the Standard Model interaction is less suppressed than the widely discussed dimension 6 operator, which corresponds to mass varying neutrinos; the dimension 5 operator does not suffer from gravitational instabilities.
A cosmological model of an holographic dark energy interacting with dark matter throughout a decaying term of the form $Q=3(lambda_1rho_{DE} + lambda_2rho_m) H$ is investigated. General constraint on the parameters of the model are found when accelerated expansion is imposed and we found a phantom scenarios, without any reference to a specific equation of state for the dark energy. The behavior of equation of stated for dark energy is also discussed.
The Averaged Null Energy Condition (ANEC) states that the integral along a complete null geodesic of the projection of the stress-energy tensor onto the tangent vector to the geodesic cannot be negative. ANEC can be used to rule out spacetimes with exotic phenomena, such as closed timelike curves, superluminal travel and wormholes. We prove that ANEC is obeyed by a minimally-coupled, free quantum scalar field on any achronal null geodesic (not two points can be connected with a timelike curve) surrounded by a tubular neighborhood whose curvature is produced by a classical source. To prove ANEC we use a null-projected quantum inequality, which provides constraints on how negative the weighted average of the renormalized stress-energy tensor of a quantum field can be. Starting with a general result of Fewster and Smith, we first derive a timelike projected quantum inequality for a minimally-coupled scalar field on flat spacetime with a background potential. Using that result we proceed to find the bound of a quantum inequality on a geodesic in a spacetime with small curvature, working to first order in the Ricci tensor and its derivatives. The last step is to derive a bound for the null-projected quantum inequality on a general timelike path. Finally we use that result to prove achronal ANEC in spacetimes with small curvature.
We formulate Barrow holographic dark energy, by applying the usual holographic principle at a cosmological framework, but using the Barrow entropy instead of the standard Bekenstein-Hawking one. The former is an extended black-hole entropy that arises due to quantum-gravitational effects which deform the black-hole surface by giving it an intricate, fractal form. We extract a simple differential equation for the evolution of the dark energy density parameter, which possesses standard holographic dark energy as a limiting sub-case, and we show that the scenario can describe the universe thermal history, with the sequence of matter and dark energy eras. Additionally, the new Barrow exponent $Delta$ significantly affects the dark energy equation of state, and according to its value it can lead it to lie in the quintessence regime, in the phantom regime, or experience the phantom-divide crossing during the evolution.
The definition of the Hamiltonian operator H for a general wave equa-tion in a general spacetime is discussed. We recall that H depends on the coordinate system merely through the corresponding reference frame. When the wave equation involves a gauge choice and the gauge change is time-dependent, H as an operator depends on the gauge choice. This dependence extends to the energy operator E, which is the Hermitian part of H. We distinguish between this ambiguity issue of E and the one that occurs due to a mere change of the represen-tation (e.g. transforming the Dirac wave function from the Dirac representation to a Foldy-Wouthuysen representation). We also assert that the energy operator ought to be well defined in a given ref-erence frame at a given time, e.g. by comparing the situation for this operator with the main features of the energy for a classical Hamilto-nian particle.
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