Eternal Acceleration Research Articles

Holographic Ricci DE as running vacuum with nonlinear interaction

The holographic Ricci dark energy (HRDE) can be treated as a running vacuum due to its analogy in the energy density, which is a combination of H and [Formula: see text], the model can predict either eternal acceleration or eternal deceleration. In the earlier works, we have shown that the presence of additive constant in the energy density or by considering possible interaction between dark sectors through a phenomenological term, the model can predict a transition from a prior decelerated to a late accelerated epoch. This paper analyzes the cosmic evolution of HRDE as running vacuum with a nonlinear interaction (NLI) between dark sectors in a flat Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. We consider three possible NLI forms which give analytically feasible solutions. We have constrained the model using the Type1a Supernova(Pantheon) + CMB(Planck 2018) + BAO(SDSS) data and evaluated the best estimated values of all the model parameters. We have analyzed the evolution of the Hubble parameter and deceleration parameter of all three cases. We perform state finder analysis of the model, which implies the quintessence nature of the model and found that it is distinguishably different from the standard [Formula: see text]CDM model. The dynamical system analysis of all three cases confirms the evolution of the universe from an unstable prior matter-dominated era to a stable end de Sitter phase.

A dilaton-axion model for string cosmology

The generic scale-invariant theory of an axion and a dilaton coupled to gravity in d-dimensions is generalized to a ‘universal’ one-axion model with two dilatons that reproduces itself under consistent dimensional-reduction/truncation. Flat FLRW cosmologies are shown to correspond to trajectories of a three-dimensional autonomous dynamical system, which we analyse with a focus on accelerated cosmic expansion, deriving the precise swampland bounds that exclude eternal acceleration. We also show that for two sets of values of its three independent parameters, the model is a consistent truncation of maximal ‘massive’ supergravity theories arising from string/M-theory; for these maximal-supergravity parameter values the FLRW cosmologies include some with a transient de Sitter-like phase, but not the recurring de Sitter-like phase or eternal cosmic acceleration that is possible for other parameter values.

Barberpole tempo illusions

“Barberpole” tempo illusions are a family of auditory illusions based on the synchronization of faded rhythmic streams playing at different rates, often manufacturing experiences of seemingly eternal acceleration or deceleration. The forefather of all such illusions, based on layers whose rates are powers of two apart (“octaves”), was studied by Jean-Claude Risset in the late seventies and is now known as Risset rhythm. This article provides a mathematical framework for barberpole tempo illusions, generalizing Risset rhythms for arbitrary numbers of subdivisions, non-integer proportions, arbitrary rate modulation, and increasingly accelerating tempi. Furthermore, this article describes a new illusion of eternal rallentando/accelerando based on the full harmonic spectrum of rates. This construction shows that Risset rhythms are related to barberpole variable-rate polyrhythms. A notable application of the study of divisional structures that barberpole illusions underpin is the construction of bistable auditory figures (accelerating or decelerating depending on the stream being focused).

Cosmological aspects of a hyperbolic solution in [formula omitted] gravity

This article deals with a cosmological scenario in f(R,T) gravity for a flat FLRW model of the universe. We consider the f(R,T) function as f(R)+f(T) which starts with a quadratic correction of the geometric term f(R) having structure f(R)=R+αR2, and a linear matter term f(T)=2λT. To achieve the solution of the gravitational field equations in the f(R,T) formalism, we take the form of a geometrical parameter, i.e. scale factor a(t)=sinh1n(βt) (Chawla et al., 2013), where β and n are model parameters. An eternal acceleration can be predicted by the model for 0<n<1, while the cosmic transition from the early decelerated phase to the present accelerated epoch can be anticipated for n≥1. The obtained model facilitates the formation of structure in the Universe according to the Jeans instability condition as our model transits from radiation dominated era to matter dominated era. We study the varying role of the equation of state parameter ω. We analyze our model by studying the behavior of the scalar field and discuss the energy conditions on our achieved solution. We examine the validity of our model via Jerk parameter, Om diagnostic, Velocity of sound and Statefinder diagnostic tools. We investigate the constraints on the model parameter n and H0 (Hubble constant) using some observational datasets: SNeIa dataset, H(z) (Hubble parameter) dataset, BAO (Baryon Acoustic Oscillation data) and their combinations as joint observational datasets H(z) + SNeIa and H(z) + SNeIa + BAO. It is testified that the present study is well consistent with these observations. We also perform some cosmological tests and a detailed discussion of the model.

A cyclic universe with varying cosmological constant in f(R, T) gravity

A new kind of evolution for cyclic models in which the Hubble parameter oscillates and remains positive has been explored in a specific f(R, T) gravity reconstruction. A singularity-free cyclic universe with negative varying cosmological constant has been obtained, which supports the role suggested for negative Λ in stopping the eternal acceleration. The cosmological solutions have been obtained for the case of a flat universe, supported by observations. The cosmic pressure grows without singular values; it is positive during the early-time decelerated expansion and negative during the late-time accelerating epoch. The time-varying equation of state parameter ω(t) shows quintom behavior and is restricted to the range –2.25 ≤ ω(t) ≲ 1/3. The validity of the classical linear energy conditions and the sound speed causality condition has been studied. The non-conventional mechanism of negative cosmological constant that are expected to address the late-time acceleration has been discussed.

Holographic Ricci dark energy as running vacuum

Holographic Ricci dark energy (DE) that has been proposed ago has faced problems of future singularity. In the present work, we consider the Ricci DE with an additive constant in its density as running vacuum energy. We have analytically solved the Friedmann equations and also the role played by the general conservation law followed by the cosmic components together. We have shown that the running vacuum energy status of the Ricci DE helps to remove the possible future singularity in the model. The additive constant in the density of the running vacuum played an important role, such that, without that, the model predicts either eternal deceleration or eternal acceleration. But along with the additive constant, equivalent to a cosmological constant, the model predicts a late time acceleration in the expansion of the universe, and in the far future of the evolution it tends to de Sitter universe.

Space-like Dp branes: accelerating cosmologies versus conformally de Sitter space-time

We consider the space-like D$p$ brane solutions of type II string theories having isometries ISO$(p+1)$ $\times$ SO$(8-p,1)$. These are asymptotically flat solutions or in other words, the metrics become flat at the time scale $\tau \gg \tau_0$. On the other hand, when $\tau \sim \tau_0$, we get $(p+1)+1$ dimensional flat FLRWmetrics upon compactification on a $(8-p)$ dimensional hyperbolic space with time dependent radii. We show that the resultant $(p+1)+1$ dimensional metrics describe transient accelerating cosmologies for all $p$ from 1 to 6, i.e., from $(2+1)$ to $(7+1)$ space-time dimensions. We show how the acceleration changes with the interplay of the various parameters characterizing the solutions in $(3+1)$ dimensions. Finally, for $\tau \ll \tau_0$, after compactification on $(8-p)$ dimensional hyperbolic space, the resultant metrics are shown to take the form of $(p+1)+1$ dimensional de Sitter spaces upto a conformal transformation. Cosmologies here are decelerating, but, only in a particular conformal frame we get eternal acceleration.

MULTI-DIMENSIONAL COSMOLOGY AND DSR–GUP

A multi-dimensional cosmology with FRW type metric having four-dimensional spacetime and d-dimensional Ricci-flat internal space is considered with a higher-dimensional cosmological constant. The classical cosmology in commutative and Doubly Special Relativity–Generalized Uncertainty Principle (DSR–GUP) contexts is studied and the corresponding exact solutions for negative and positive cosmological constants are obtained. In the positive cosmological constant case, it is shown that unlike the commutative as well as GUP cases, in DSR–GUP case both scale factors of internal and external spaces after accelerating phase will inevitably experience decelerating phase leading simultaneously to a big crunch. This demarcation from GUP originates from the difference between the GUP and DSR–GUP algebras. The important result is that unlike GUP which results in eternal acceleration, DSR–GUP at first generates acceleration but prevents the eternal acceleration at late-times and turns it into deceleration.

Will cosmic acceleration last forever?

Although the transition from an initially decelerated to a late-time accelerating cosmic expansion is becoming observationally established, the duration of the accelerating phase depends on the cosmological scenario and, several models, which includes our standard one, imply an eternal acceleration or even an accelerating expansion until the onset of a future cosmic singularity. In this regard, an interesting theoretical question arises if one tries to reconcile the standard description of the current cosmic acceleration with the only candidate for a consistent quantum theory of gravity we have today, i.e., Superstring theory.

Halting eternal acceleration with an effective negative cosmological constant

In order to solve the problem of eternal acceleration, a model has been recently proposed including both a negative cosmological constant Λ and a scalar field evolving under the action of an exponential potential. We further explore this model by contrasting it against the Hubble diagram of type Ia supernovae, the gas mass fraction in galaxy clusters and the acoustic peak and shift parameters. It turns out that the model is able to fit this large dataset quite well so that we conclude that a negative Λ is indeed allowed and could represent a viable mechanism to halt eternal acceleration. In order to avoid problems with theoretical motivations for both a negative Λ term and the scalar field, we reconstruct the gravity Lagrangian f(R) of a fourth-order theory of gravity predicting the same dynamics (scale factor and Hubble parameter) as the starting model. We thus end up with a f(R) theory able to both fit the data and solve the problem of eternal acceleration without the need of unusual negative Λ and ad hoc scalar fields.

A relativistic toy model for back-reaction

We consider a quantized massless and minimally coupled scalar field within a (1+1)-dimensional spacetime described by a circle with a time-dependent radius R(t). Within the semi-classical treatment, the back-reaction of the quantum field onto the R(t)-dynamics is taken into account in terms of the renormalized expectation value of the energy–momentum tensor including the trace anomaly. In case the classical energy of the circle is positive, the results indicate that the back-reaction (induced by the trace anomaly) could prevent the collapse of the spacetime R ↓ 0; however, the semi-classical picture fails to describe the R(t)-dynamics at the turning point (i.e., possible bounce) at finite values of R and . The fate of the interacting system after that point (e.g., oscillation or eternal acceleration) cannot be determined within the semi-classical picture and thus probably requires the full quantum treatment. Allowing also for negative classical energies (similar to the Newtonian gravitational energy, for example), the Casimir effect yields the dominant back-reaction contribution and might also prevent the collapse of the spacetime—leading to eternal oscillations of R(t) ≠ 0.

Eternal acceleration from M-theory

The dimensional reduction of D-dimensional spacetimes arising in string/M-theory, to the conformal Einstein frame, may give rise to cosmologies with accelerated expansion. Through a complete analysis of the dynamics of doubly warped product spacetimes, in terms of scale invariant variables, it is demonstrated that for D ≥ 10, eternally accelerating four-dimensional κ = −1 Friedmann cosmologies arise from dimensional reduction on an internal space with negative Einstein geometry.

Exact solution of scalar field cosmology with exponential potentials and transient acceleration

We show that the general solution of scalar field cosmology in d dimensions with exponential potentials for flat Robertson–Walker metric can be found in a straightforward way by introducing new variables which completely decouple the system. The explicit solution shows the region of parameters where the expansion has eternal acceleration, transient periods of acceleration, or no period of acceleration at all. In the cases of transient acceleration, the energy density exhibits a plateau during the accelerated expansion, where p ≅ − ρ , due to dominance of potential energy. We determine the interval of accelerated expansion in terms of a simple formula. In particular, it shows that the period of accelerated expansion decreases in higher dimensions.

STRINGS, BRANES AND AN ACCELERATING UNIVERSE

Velocity-dependent interactions in a fundamental-string dominated universe lead quite naturally, with reasonable assumptions on initial conditions, to an accelerating expanding universe without assuming the existence of a cosmological constant. Using a mean-field approximation, exact solutions are obtained for various string/brane cosmological toy models. A multi-body model is also investigated. It is also shown that the repulsive velocity-dependent force arises in more general contexts and can lead to cosmic structure formation. Finally, we discuss a toy model including both ordinary and extremal matter, in which the latter accounts for dark matter while simultaneously acting as effective dark energy. Eternal acceleration is once more seen to arise in this case.

Oscillating dark energy: A possible solution to the problem of eternal acceleration

We present a dark energy model with a double exponential potential for a minimally coupled scalar field, which allows general exact integration of the cosmological equations. The solution can perfectly emulate a $\Lambda$-term model at low-medium redshift, exhibits tracking behavior, and does not show eternal acceleration.

Dark matter as dark energy

Velocity-dependent interactions in a fundamental string-dominated universe lead quite naturally, with reasonable assumptions on initial conditions, to an accelerating expanding universe without assuming the existence of a cosmological constant. This result also holds generically for a universe dominated by moving extremal black holes, owing to a repulsive velocity-dependent force. This interaction, however, does not preclude structure formation. Here we discuss a toy model including both ordinary and extremal matter, in which the latter accounts for dark matter while simultaneously acting as effective dark energy. Eternal acceleration is once more seen to arise in this case.

Is the universe inflating? Dark energy and the future of the universe

We consider the fate of the observable universe in the light of the discovery of a dark energy component to the cosmic energy budget. We extend results for a cosmological constant to a general dark energy component and examine the constraints on phenomena that may prevent the eternal acceleration of our patch of the universe. We find that the period of accelerated cosmic expansion has not lasted long enough for observations to confirm that we are undergoing inflation; such an observation will be possible when the dark energy density has risen to between 90% and 95% of the critical. The best we can do is make cosmological observations in order to verify the continued presence of dark energy to some high redshift. Having done that, the only possibility that could spoil the conclusion that we are inflating would be the existence of a disturbance (the surface of a true vacuum bubble, for example) that is moving toward us with sufficiently high velocity, but is too far away to be currently observable. Such a disturbance would have to move toward us with speed greater than about $0.8c$ in order to spoil the late-time inflation of our patch of the universe and yet avoid being detectable.

Eternally accelerating universe without event horizon

Increasing astronomical evidence indicates that the expansion of the universe is accelerating. By simply solving Einstein equations we show in this Letter that a wide class of generic quintessence models leading to eternal acceleration is associated with spacetime static metrics which do not exhibit future event horizons, and therefore do not pose the same problems for string theory as asymptotic de Sitter spaces.

Hybrid quintessence with an end or quintessence from branes and large dimensions

We describe a model of hybrid quintessence in which in addition to the tracker field there is a trigger field which is responsible for ending quintessence. As a result, hybrid quintessence does not suffer from the problems associated with the eternal acceleration of the universe. We derive the hybrid quintessence potential on branes from the interbrane interaction in string theory and show that it requires TeV scale strings and two millimeter size dimensions. This scenario predicts a dark energy density of $O(mm^{-4})$ and relates the smallness of this energy to the large size of the extra dimensions.

Quintessence, cosmological horizons, and self-tuning

We point out that quintessence with an exponential potential V_0 exp(- beta phi / 3^{1/2} M_p) can account for the present observed acceleration of the universe, without necessarily leading to eternal acceleration. This occurs for 2.4 < beta < 2.8. Thus a cosmological horizon, which is supposed to be problematic within the context of string theory, can be avoided. We argue that this class of models is not particularly fine-tuned. We further examine this question in the context of a modified Friedmann equation, H^2 ~ rho + p, which is suggested by higher dimensional self-tuning approaches to the cosmological constant problem. It is shown that the self-tuning case can also be consistent with observations, if 1.8 < beta < 2.4. Future observations of high-z supernovae will be able to test whether beta lies in the desired range.