Phantom Phase Research Articles

Phantom phase power-law solution in f(G) gravity

Power-law solutions for f(G) gravity coupled with perfect fluid have been studied for spatially flat universe. It is shown that despite the matter dominated and accelerating power-law solutions, the power-law solution exists for an special form of f(G) when this universe enters a Phantom phase.

ASPECTS OF HOŘAVA–LIFSHITZ COSMOLOGY

We review some general aspects of Hořava–Lifshitz cosmology. Formulating it in its basic version, we extract the cosmological equations and we use observational data in order to constrain the parameters of the theory. Through a phase–space analysis we extract the late-time stable solutions, and we show that bouncing and cyclic behavior can arise naturally. Concerning the effective dark energy sector we show that it can describe the phantom phase without the use of a phantom field. However, performing a detailed perturbation analysis, we see that Hořava–Lifshitz gravity in its basic version, suffers from instabilities. Therefore, suitable generalizations are required in order for this novel theory to be a candidate for the description of nature.

Non-vacuum solutions of Bianchi type VI 0 universe in f(R) gravity

In this paper, we solve the field equations in metric f(R) gravity for Bianchi type VI 0 spacetime and discuss evolution of the expanding universe. We find two types of non-vacuum solutions by taking isotropic and anisotropic fluids as the source of matter and dark energy. The physical behavior of these solutions is analyzed and compared in the future evolution with the help of some physical and geometrical parameters. It is concluded that in the presence of isotropic fluid, the model has singularity at \(\tilde{t}=0\) and represents continuously expanding shearing universe currently entering into phantom phase. In anisotropic fluid, the model has no initial singularity and exhibits the uniform accelerating expansion. However, the spacetime does not achieve isotropy as t→∞ in both of these solutions.

Cosmological evolution in exponential gravity

We explore the cosmological evolution in the exponential gravity f(R) = R+c1(1−e−c2R) (c1,2 = constant). We summarize various viability conditions and explicitly demonstrate that the late-time cosmic acceleration following the matter-dominated stage can be realized. We also study the equation of state for dark energy and confirm that the crossing of the phantom divide from the phantom phase to the non-phantom (quintessence) one can occur. Furthermore, we illustrate that the cosmological horizon entropy globally increases with time.

Background cosmological dynamics inf(R)gravity and observational constraints

In this paper, we carry out a study of viable cosmological models in $f(R)$-gravity at the background level. We use observable parameters like $\Omega$ and $\gamma$ to form autonomous system of equations and show that the models under consideration exhibit two different regimes in their time evolution, namely, a phantom phase followed by a quintessence like behavior. We employ statefinder parameters to emphasize a characteristic discriminative signature of these models.

PHANTOM COSMOLOGY BASED ON PT SYMMETRY

We consider the PT-symmetric flat Friedmann model of two scalar fields with positive kinetic terms. While the potential of one "normal" field is taken real, that of the other field is complex. We study a complex classical solution of the system of the two Klein–Gordon equations together with the Friedmann equation. The solution for the normal field is real, while the solution for the second field is purely imaginary, realizing classically the "phantom" behavior. The energy density and pressure are real and the corresponding geometry is well defined. The Lagrangian for the linear perturbations has the correct potential signs for both the fields so that the problem of stability does not arise. The background dynamics is determined by an effective action including two real fields — one normal and one "phantom." Remarkably, the phantom phase in the cosmological evolution is transient and the Big Rip never occurs. Our model is contrasted with well known quintom models, which also include one normal and one phantom field.

COMPARISON OF FRAMES: JORDAN VERSUS EINSTEIN FRAME FOR A NON-MINIMAL DARK ENERGY MODEL

We construct a dark energy model where a scalar field non-minimally coupled to gravity plays the role of the dark component. We compare cosmological consequences of this non-minimal coupling of the scalar field and gravity in the spirit of the dark energy paradigm in Jordan and Einstein frames. Some important issues such as phantom divide line crossing, existence of the bouncing solutions and the stability of the solutions are compared in these two frames. We show that while a non-minimally coupled scalar field in the Jordan frame is a suitable dark energy component with capability to realize phantom divide line crossing, its conformal transformation in the Einstein frame does not have this capability. The conformal transformation from Jordan frame to Einstein frame transforms the equation of state parameter of the dark energy component to its minimal form with a redefined scalar field and in this case it is impossible to realize a phantom phase with possible crossing of the phantom divide line.

Are we seeing the beginnings of inflation?

Phantom Cosmology provides an unique opportunity to "connect" the phantom driven (low en- ergy meV scale) dark energy phase to the (high energy GUT scale) inflationary era. This is possible because the energy density increases in phantom cosmology. We present a concrete model where the energy density, but not the scale factor, cycles through phases of standard radiation/matter domi- nation followed by dark energy/inflationary phases, and the pattern repeating itself. An interesting feature of the model is that once we include interactions between the "phantom fluid" and ordinary matter, the Big rip singularity is avoided with the phantom phase naturally giving way to a near exponential inflationary expansion.

Hubble expansion and structure formation in time varying vacuum models

We investigate the properties of the FLRW flat cosmological models in which the vacuum energy density evolves with time, $\ensuremath{\Lambda}(t)$. Using different versions of the $\ensuremath{\Lambda}(t)$ model, namely, quantum field vacuum, power series vacuum and power law vacuum, we find that the main cosmological functions such as the scale factor of the Universe, the Hubble expansion rate $H$, and the energy densities are defined analytically. Performing a joint likelihood analysis of the recent supernovae type Ia data, the cosmic microwave background shift parameter and the baryonic acoustic oscillations traced by the Sloan Digital Sky Survey galaxies, we put tight constraints on the main cosmological parameters of the $\ensuremath{\Lambda}(t)$ scenarios. Furthermore, we study the linear matter fluctuation field of the above vacuum models. We find that the patterns of the power series vacuum $\ensuremath{\Lambda}={n}_{1}H+{n}_{2}{H}^{2}$ predict stronger small scale dynamics, which implies a faster growth rate of perturbations with respect to the other two vacuum cases (quantum field and power law), despite the fact that all the cosmological models share the same equation of state parameter. In the case of the quantum field vacuum $\ensuremath{\Lambda}={n}_{0}+{n}_{2}{H}^{2}$, the corresponding matter fluctuation field resembles that of the traditional $\ensuremath{\Lambda}$ cosmology. The power law vacuum ($\ensuremath{\Lambda}\ensuremath{\propto}{a}^{\ensuremath{-}n}$) mimics the classical quintessence cosmology, the best fit being tilted in the phantom phase. In this framework, we compare the observed growth rate of clustering measured from the optical galaxies with those predicted by the current $\ensuremath{\Lambda}(t)$ models. Performing a Kolmogorov-Smirnov statistical test we show that the cosmological models which contain a constant vacuum ($\ensuremath{\Lambda}\mathrm{CDM}$), quantum field vacuum, and power law vacuum provide growth rates that match well with the observed growth rate. However, this is not the case for the power series vacuum models (in particular, the frequently adduced $\ensuremath{\Lambda}\ensuremath{\propto}H$ model) in which clusters form at significantly earlier times ($z\ensuremath{\ge}4$) with respect to all other models ($z\ensuremath{\sim}2$). Finally, we derived the theoretically predicted dark matter halo mass function and the corresponding distribution of cluster-size halos for all the models studied. Their expected redshift distribution indicates that it will be difficult to distinguish the closely resembling models (constant vacuum, quantum field, and power law vacuum), using realistic future x-ray surveys of cluster abundances. However, cluster surveys based on the Sunayev-Zeldovich detection method give some hope to distinguish the closely resembling models at high redshifts.

Cosmological evolution of interacting dark energy in Lorentz violation

The cosmological evolution of an interacting scalar-field model in which the scalar field interacts with dark matter, radiation, and baryons via Lorentz violation is investigated. We propose a model of interaction through the effective coupling, \(\bar{\beta}\) . Using dynamical system analysis, we study the linear dynamics of an interacting model and show that the dynamics of critical points are completely controlled by two parameters. Some results can be mentioned as follows. Firstly, the sequence of radiation, the dark matter, and the scalar-field dark energy exist and baryons are subdominant. Secondly, the model also allows for the possibility of having a universe in the phantom phase with constant potential. Thirdly, the effective gravitational constant varies with respect to time through \(\bar{\beta}\) . In particular, we consider the simple case where \(\bar{\beta}\) has a quadratic form and has a good agreement with the modified ΛCDM and quintessence models. Finally, we also calculate the first post-Newtonian parameters for our model.

Thermodynamics in [formula omitted] gravity with phantom crossing

We study thermodynamics of the apparent horizon in F(R) gravity. In particular, we demonstrate that an F(R) gravity model with realizing a crossing of the phantom divide can satisfy the second law of thermodynamics in the effective phantom phase as well as non-phantom one.

Cosmology of non-Hermitian (C)PT-invariant scalar matter

We use the generalization of quantum theory for the case of non-Hermitian Hamiltonians with (C)PT symmetry to show how a classical cosmological model describes a smooth transition from ordinary dark energy to the phantom one. We consider the PT symmetric flat Friedmann model of two scalar fields with positive kinetic terms. The solution for the normal field is real while the solution for the second field is purely imaginary, realizing classically the ‘phantom’ behavior. The energy density and pressure happen to be real and the corresponding geometry is well-defined. The Lagrangian for the linear perturbations leads to positive energy densities for both the fields, so that the problem of stability does not arise. The phantom phase in the cosmological evolution appears to be transient and the Big Rip never occurs.

ACCELERATION AND DECELERATION IN THE CURVATURE-INDUCED PHANTOM MODEL OF THE LATE AND FUTURE UNIVERSE: COSMIC COLLAPSE AND ITS QUANTUM ESCAPE

In this paper, the cosmology of the late and future universe is obtained from f(R) gravity with nonlinear curvature terms R2 and R3 (R is the Ricci scalar curvature). It is different from f(R) dark energy models where nonlinear curvature terms are taken as a gravitational alternative to dark energy. In the present model, neither linear nor nonlinear curvature terms are taken as dark energy. Rather, dark energy terms are induced by curvature terms and appear in the Friedmann equation derived from f(R) gravitational equations. This approach has an advantage over f(R) dark energy models in three ways: (i) results are consistent with WMAP observations, (ii) dark matter is produced from the gravitational sector and (iii) the universe expands as ~ t2/3 during dominance of the curvature-induced dark matter, which is consistent with the standard cosmology. Curvature-induced dark energy mimics phantom and causes late acceleration. It is found that transition from matter-driven deceleration to acceleration takes place at the redshift 0.36 at time 0.59 t0 (t0 is the present age of the universe). Different phases of this model, including acceleration and deceleration during the phantom phase, are investigated. It is found that expansion of the universe will stop at the age of 3.87 t0 + 694.4 kyr. After this epoch, the universe will contract and collapse by the time of 336.87 t0 + 694.4 kyr. Further, it is shown that cosmic collapse obtained from classical mechanics can be avoided by making quantum gravity corrections relevant near the collapse time due to extremely high energy density and large curvature analogous to the state of the very early universe. Interestingly, the cosmological constant is also induced here; it is extremely small in the classical domain but becomes very high in the quantum domain. This result explains the largeness of the cosmological constant in the early universe due to quantum gravity effects during this era and its very low value in the present universe due to negligible quantum effect in the late universe.

Crossing of the phantom divide in modified gravity

We reconstruct an explicit model of modified gravity in which a crossing of the phantom divide can be realized. It is shown that the (finite-time) Big Rip singularity appears in the model of modified gravity (i.e., in the so-called Jordan frame), whereas that in the corresponding scalar field theory obtained through the conformal transformation (i.e., in the so-called Einstein frame) the singularity becomes the infinite-time one. Furthermore, we investigate the relations between the scalar field theories with realizing a crossing of the phantom divide and the corresponding modified gravitational theories by using the inverse conformal transformation. It is demonstrated that the scalar field theories describing the non-phantom phase (phantom one with the Big Rip) can be represented as the theories of real (complex) $F(R)$ gravity through the inverse (complex) conformal transformation. We also study a viable model of modified gravity in which the transition from the de Sitter universe to the phantom phase can occur. In addition, we explore the stability for the obtained solutions of the crossing of the phantom divide under a quantum correction coming from conformal anomaly.

Synthetic wavelength based phase unwrapping in spectral domain optical coherence tomography

Phase sensing implementations of spectral domain optical coherence tomography (SDOCT) have demonstrated the ability to measure nanometer-scale temporal and spatial profiles of samples. However, the phase information suffers from a 2pi ambiguity that limits observations of larger sample displacements to lengths less than half the source center wavelength. We introduce a synthetic wavelength phase unwrapping technique in SDOCT that uses spectral windowing and corrects the 2pi ambiguity, providing accurate measurements of sample motion with information gained from standard SDOCT processing. We demonstrate this technique by using a common path implementation of SDOCT and correctly measure phase profiles from a phantom phase object and human epithelial cheek cells which produce multiple wrapping artifacts. Using a synthetic wavelength for phase unwrapping could prove useful in Doppler or other phase based implementations of OCT.

On phantom thermodynamics with negative temperature

We discuss the thermodynamic properties of the Friedmann–Robertson–Walker universe with dark energy fluids labelled by ω=p/ρ<−1/3. Using the integrability condition, we show that the phantom phase of ω<−1 can still be thermodynamically allowed even when the temperature takes on negative values because in that case, there exists at least a condition of keeping physical values for p and ρ.

Phantom and non-phantom dark energy: The cosmological relevance of non-locally corrected gravity

In this Letter we have investigated the cosmological dynamics of non-locally corrected gravity involving a function of the inverse d'Alembertian of the Ricci scalar, f(□−1R). Casting the dynamical equations into local form, we derive the fixed points of the dynamics and demonstrate the existence and stability of a one parameter family of dark energy solutions for a simple choice, f(□−1R)∼exp(α□−1R). The effective EoS parameter is given by, weff=(α−1)/(3α−1) and the stability of the solutions is guaranteed provided that 1/3<α<2/3. For 1/3<α<1/2 and 1/2<α<2/3, the underlying system exhibits phantom and non-phantom behavior respectively; the de Sitter solution corresponds to α=1/2. For a wide range of initial conditions, the system mimics dust like behavior before reaching the stable fixed point. The late time phantom phase is achieved without involving negative kinetic energy fields. A brief discussion on the entropy of de Sitter space in non-local model is included.

The particle versus the future event horizon in an interacting holographic dark energymodel

Choosing the future event horizon as the horizon of the flat Friedmann–Lemaitre–Robertson–Walkeruniverse, we show that the interacting holographic dark energy model is ableto explain the phantom divide line crossing. We show that if we take theparticle event horizon as the horizon of the universe, besides describing theω = −1 crossing (based on astrophysical data), we are able to determine appropriately the ratio ofdark matter to dark energy density at the transition time. In this approach, after the firsttransition from the quintessence to the phantom phase, there is another transitionfrom the phantom to the quintessence phase which avoids the big rip singularity.

Scale factor dependent equation of state for curvature inspired dark energy, phantom barrier and late cosmic acceleration

Here, it is found that dark energy and dark matter emerge from the gravitational sector, if non-linear term of scalar curvature is added to Einstein–Hilbert Lagrangian. An equation of state for dark energy, having the form p de = − ρ de + f ( a ) (with p de ( ρ de ) being the pressure (density) for dark energy, f ( a ) being a function of scale factor a ( t ) and t being the cosmic time) is explored. Interestingly, this equation of state leads to a phantom barrier w de = p de / ρ de = − 1 at a = a w . It is found that when a < a w , w de > − 1 and w de < − 1 for a > a w , showing a transition from non-phantom to phantom phase at a = a w < a 0 ( a 0 being the current scale factor of the universe).

Transition from quintessence to the phantom phase in the quintom model

Assuming the Hubble parameter is a continuous and differentiable function of comoving time, we investigate necessary conditions for quintessence to phantom phase transition in quintom model. For power-law and exponential potential examples, we study the behavior of dynamical dark energy fields and Hubble parameter near the transition time, and show that the phantom-divide-line w=-1 is crossed in these models.