The spatial expansion of the universe can be described as the emergence of space with the progress of cosmic time, through a simple equation, $ΔV = Δt\left(N_{surf}- N_{bulk}\right)$. This law of emergence suggested by Padmanabhan in the context of general relativity for a flat universe has been generalized by Sheykhi to Gauss Bonnet and Lovelock gravity for a universe with any spacial curvature. We investigate whether this generalized holographic equipartition effectively implies the maximization of horizon entropy. First, we obtain the constraints imposed by the maximization of horizon entropy in Einstein, Gauss Bonnet and Lovelock gravities for a universe with any spacial curvature. We then analyze the consistency of the law of emergence in \cite{Sheykhi}, with these constraints obtained. Interestingly, both the law of emergence and the horizon entropy maximization demands an asymptotically de Sitter universe with $ω\geq -1$. More specifically, when the degrees of freedom in the bulk $( N_{bulk})$ becomes equal to the degrees of freedom on the boundary surface $(N_{surf}),$ the universe attains a state of maximum horizon entropy. Thus, the law of emergence can be viewed as a tendency for maximizing the horizon entropy, even in a non flat universe. Our results points at the deep connection between the law of emergence and horizon thermodynamics, beyond Einstein gravity irrespective of the spacial curvature.
Recently, Barrow accounts for the quantum gravitational effects to the black hole surface. Thus the conventional area-entropy relation has modified, $S=(A/A_{0})^{1+Δ/2},$ with an exponent $Δ$, ranges $0\leΔ\le1$, quantifies the amount of quantum gravitational deformation effect to the black hole surface. In recent literature, this horizon entropy has been extended to the cosmological context. Following this, we consider an n+1 dimensional non-flat universe with an apparent horizon as the boundary with appropriate temperature and associated entropy is Barrow entropy. We derived the modified fo…
Researches in the several decades have shown that the dynamics of gravity is closely related to thermodynamics of the horizon. In this paper, we derive the Friedmann acceleration equation based on the idea of "emergence of space" and thermodynamics of the Hubble horizon whose temperature is obtained from the unified first law of thermodynamics. Then we derive another evolution equation of the universe based on the energy balance relation $ρV_{H}=TS$. Combining the two evolution equations and the equation of state of the cosmic matter, we obtain the evolution solutions of the FRW universe. We f…
In this paper, we obtain the law of emergence with Tsallis entropy from the thermodynamic laws. We first derive the law of emergence from the equilibrium description of the unified first law and Clausius relation. However, it has been shown that considering Tsallis entropy as the horizon entropy, the Clausius relation $δQ=T dS$ does not hold due to non-equilibrium thermodynamics and is replaced by the entropy-balance relation $dS=\frac{δQ}{T}+d_{i}S$, where $d_iS$ is the additional entropy produced due to the irreversible thermodynamic process. Hence, we derive the law of emergence from the no…
The recent research on the connection between gravity and thermodynamics suggests that gravity could be an emergent phenomenon. Following this, Padmanabhan proposed a novel idea that the expansion of the universe can be interpreted as equivalent to the emergence of space with the progress of cosmic time. In this approach, the expansion of the universe is described by what is known as the law of emergence, which states that the expansion of the universe is driven by the difference between the number of bulk and surface degrees of freedom in a region bounded by the Hubble radius. This principle …
\begin{abstract} The accelerated expansion of the universe can be interpreted as a tendency to satisfy the holographic equipartition. It can be expressed by a simple law, $ΔV = Δt\left(N_{surf}-εN_{bulk}\right),$ where $V$ is the Hubble volume in Plank units, $t$ is the cosmic time plank units and $N_{surf/bulk}$ is the degrees of freedom on the horizon/bulk of the universe. We show that this holographic equipartition law effectively implies the maximization of entropy. In the cosmological context, a system that obeys the holographic equipartition law behaves as an ordinary macroscopic system …
For a long time it is believed that black hole horizon are thermal and quantum mechanical in nature. The microscopic origin of this thermality is the main question behind our present investigation, which reveals possible importance of near horizon symmetry. It is this symmetry which is assumed to be spontaneously broken by the background spacetime, generates the associated Goldstone modes. In this paper we construct a suitable classical action for those Goldstone modes, and show that all the momentum modes experience nearly the same inverted harmonic potential, leading to an instability. Thank…
We solve Einstein vacuum equations in a spacetime region up to the "center" of gravitational collapse. Within this region, we construct a sequence of marginally outer trapped surfaces (MOTS) with areas going to zero. These MOTS form a marginally outer trapped tube (apparent horizon). It emerges from a point and is smooth (except at that point) and spacelike. In the proof we employ a scale critical trapped surface formation criterion established by An and Luk and a new type of quasilinear elliptic equation is studied. The main conclusion of this paper proves a conjecture of Ashtekar on black ho…
It is possible to provide a physical interpretation for the field equations of gravity based on a thermodynamical perspective. The virtual degrees of freedom associated with the horizons perceived by the local Rindler observers, play a crucial role in this approach. In this context, the relation S=E/2T between the entropy (S), active gravitational mass (E) and temperature (T) - obtained previously in gr-qc/0308070 [CQG, 21, 4485 (2004)] - can be reinterpreted as the law of equipartition E = (1/2) nkT where n=A/L_P^2 is the number (density) of microscopic horizon degrees of freedom. Conversely,…
The accelerated expansion of the universe can be interpreted as a quest for satisfying holographic equipartition. It can be expressed by a simple law, $ΔV = Δt\left(N_{surf}- N_{bulk}\right)$ which leads to the standard Friedmann equation. This novel idea suggested by Padmanabhan in the context of general relativity has been generalized by Cai and Yang et al. to Gauss-Bonnet and Lovelock gravities for a spatially flat universe in different methods. We investigate the consistency of these generalizations with the constraints imposed by the maximum entropy principle. Interestingly, both these ge…
We show that holographic RG flow can be defined precisely such that it corresponds to emergence of spacetime. We consider the case of pure Einstein's gravity with a negative cosmological constant in the dual hydrodynamic regime. The holographic RG flow is a system of first order differential equations for radial evolution of the energy-momentum tensor and the variables which parametrize it's phenomenological form on hypersurfaces in a foliation. The RG flow can be constructed without explicit knowledge of the bulk metric provided the hypersurface foliation is of a special kind. The bulk metric…
Motivations for the existence of a fundamental preferred frame range from pure phenomenology to attempts to solve the non-renormalizability of quantum gravity, the problem of time (and scale), and the cosmological constant problem(s). In many explicit constructions, such as Einstein-Aether or Gravitational Aether theories, K-essence, Cuscuton theory, Shape Dynamics, or (non-projectable) Horava-Lifshitz gravity, the low energy theory contains a fluid (which defines a preferred frame) with superluminal or incompressible excitations. We study here the formation of black holes in the presence of s…
The emergence of cosmic space as cosmic time progresses is an exciting idea advanced by Padmanabhan to explain the accelerated expansion of the universe. The generalization of Padmanabhan's conjecture to the non-flat universe has resulted in scepticism about the choice of volume such that the law of emergence can not be appropriately formulated if one uses proper invariant volume. The deep connection between the first law of thermodynamics and the law of emergence \cite{mahith}, motivate us to explore the status of the first law in a non-flat universe when one uses proper invariant volume. We …
In our previous paper \cite{8}, we proposed a cosmological model from the emergence of space, which possesses a significant character of evaluating the vacuum energy from the Hubble constant and the age of universe. And one problem of this model is that there is no inflation in the early universe. In this paper, we aim at resolving this problem which leads us to a rather surprising conclusion that our cosmological model can avoid the horizon and flatness problems.
The spacial expansion of the universe could be described as a tendency for satisfying holographic equipartition which inevitably demands the presence of dark energy. We explore whether this novel idea proposed by Padmanabhan give any additional insights into the nature of dark energy. In particular, we obtain the constraints imposed by the law of emergence on the equation of state parameter, $ω$. We also present a thermodynamic motivation for the obtained constraints on $ω$. Further, we explicitly prove the feasibility of describing a dynamic dark energy model through the law of emergence. Int…
According to the principle of emergence, the expansion of the universe can be explained as the emergence of space with the progress of cosmic time. We have analytically solved the equation of emergence proposed by Padmanabhan by assuming the Komar energy density $ρ+3P$ as a function of the Hubble parameter. The resulting model describes the evolution of the universe, which proceeds towards a final de Sitter state. Model parameters have been extracted using the cosmological observational data. Further, the horizon entropy evolution of the model has been studied. The model predicts a universe ha…
A mechanism producing the transition from an Euclidean to a Loretzian manifold is described. A global Robertson-Walker symmetry is assumed from the large scale data of the visible universe. Allowing for the strain of the manifold as an additional field in the Lagrangian, we interpret the symmetry as a consequence of a global texture defect. The additional term gives rise to a boundary dividing the manifold into an Euclidean plus a Lorentzian region. It is also shown that the presence in the early epoch of homogeneous matter/energy fields preserves the horizon and the signature change across it…
Recently, Padmanabhan [arXiv:1206.4916] argued that the expansion rate of the universe can be thought of as the emergence of space as cosmic time progresses and is related to the difference between the surface degrees of freedom on the holographic horizon and the bulk degrees of freedom inside. The main question arises as to what is origin of emergence of space in 4D universe? We answer to this question in BIonic system. The BIon is a configuration in flat space of a D-brane and a parallel anti-D-brane connected by a thin shell wormhole with F-string charge. We propose a new model that allows …
Recently, a novel idea about our expanding Universe was proposed by T. Padmanabhan [arXiv:1206.4916]. He suggested that the expansion of our Universe can be thought of as the emergence of space as cosmic time progresses. The emergence is governed by the basic relation that the increase rate of Hubble volume is linearly determined by the difference between the number of degrees of freedom on the horizon surface and the one in the bulk. In this paper, following this idea, we generalize the basic relation to derive the Friedmann equations of an $(n+1)$-dimensional Friedmann-Robertson-Walker unive…
It has been shown that Friedmann equation of FRW universe can be derived from the idea which says cosmic space is emergent as cosmic time progresses and our universe is expanding towards the state with the holographic equipartition by Padmanabhan. In this note, we give a general relationship between the horizon entropy and the number of the degrees of freedom on the surface, we also obtain the corresponding dynamic equations by using the idea of emergence of space in the $f(R)$ theory and deformed Hořava-Lifshitz (HL) theory.
Intrigued by the holographic principle, Padmanabhan recently proposed a novel idea, saying that our cosmic space is emergent as cosmic time progresses. In particular, the expansion rate of the Universe is related to the difference between the surface degrees of freedom on the holographic horizon and the bulk degrees of freedom inside. In this note, we generalize this interesting paradigm to brane world, scalar-tensor gravity, and f(R) theory, respectively, and find that in the cosmological setting the Friedmann equations can be successfully derived.
Thermodynamics on the horizon of a flat universe at late times is studied in holographic cosmological models that assume an associated entropy on the horizon. In such models, a $Λ(t)$ model similar to a time-varying $Λ(t)$ cosmology is favored because of the consistency of energy flows across the horizon. Based on this consistency, a $Λ(t)$ model with a power-law term proportional to $H^α$ is formulated to systematically examine the evolution of the Bekenstein--Hawking entropy. Here, $H$ is the Hubble parameter and $α$ is a free parameter whose value is a real number. The present model always …
The emergence of quantum-gravity induced corrective terms for the probability of emission of a particle from a black hole in the Parikh-Wilczek tunneling framework is studied. It is shown, in particular, how corrections might arise from modifications of the surface gravity due to near horizon Planck-scale effects. Our derivation provides an example of the possible linking between Planck-scale departures from Lorentz invariance and the appearance of higher order quantum gravity corrections in the black-hole entropy-area relation.
One of the remarkable features of black holes is that they possess a thermodynamic description, even though they do not appear to be statistical systems. We use self-gravitating magnetic monopole solutions as tools for understanding the emergence of this description as one goes from an ordinary spacetime to one containing a black hole. We describe how causally distinct regions emerge as a monopole solution develops a horizon. We define an entropy that is naturally associated with these regions and that has a clear connection with the Hawking-Bekenstein entropy in the critical black hole limit.
We present a novel derivation of Einstein equations from the balance between Clausius entropy crossing the boundary of a local causal diamond and entanglement entropy associated with its horizon. Comparing this derivation with the entanglement equilibrium approach developed by Jacobson, we are able to argue for the equivalence of matter entanglement and Clausius entropy in the semiclassical regime. We also provide a direct comparison of both entropies for conformal matter, showing their equivalence without appealing to gravitational dynamics. Furthermore, we determine that gravitational dynami…
We show that the Aretakis instability of compact extremal horizons persists in the planar case of interest to holography and discuss its connection with the emergence of "semi-local quantum criticality" in the field theory dual. In particular, the spatially localized power-law decay of this critical phase corresponds to spatially localized power-law growth of stress-energy on the horizon. For near-extremal black holes these phenomena occur transiently over times of order the inverse temperature. The boundary critical phase is characterized by an emergent temporal conformal symmetry, and the bu…
We consider cosmological modelling in $f(R)$ theories of gravity, using both top-down and bottom-up constructions. The top-down models are based on Robertson-Walker geometries, and the bottom-up constructions are built by patching together sub-horizon-sized regions of perturbed Minkowski space. Our results suggest that these theories do not provide a theoretically attractive alternative to the standard general relativistic cosmology. We find that the only $f(R)$ theories that can admit an observationally viable weak-field limit have large-scale expansions that are observationally indistinguish…
Cosmological adiabatic particle creation results in the generation of irreversible entropy. The evolution of this entropy is examined in a flat Friedmann--Robertson--Walker universe at late times, using a dissipative model with a power-law term (proportional to the power of the Hubble parameter $H$). In a dissipative universe, the irreversible entropy included in the Hubble volume is found to be proportional to $H^{-1}$, unlike for the case of the Bekenstein--Hawking entropy on the horizon of the universe. In addition, the evolution of the horizon entropy is examined, extending the previous an…
The fact that one can associate thermodynamic properties with horizons brings together principles of quantum theory, gravitation and thermodynamics and possibly offers a window to the nature of quantum geometry. This review discusses certain aspects of this topic concentrating on new insights gained from some recent work. After a brief introduction of the overall perspective, Sections 2 and 3 provide the pedagogical background on the geometrical features of bifurcation horizons, path integral derivation of horizon temperature, black hole evaporation, structure of Lanczos-Lovelock models, the c…
One of the challenges of constructing a successful cyclic universe scenario is to be able to incorporate the second law of thermodynamics which typically leads to Tolman's problem of ever shrinking cycles. In this paper we construct a non-singular toy model where as the cycles shrink in the past they also spend more and more time in the entropy conserving Hagedorn phase. Thus in such a scenario the entropy asymptotes to a finite non-zero constant in the infinite past. The universe ``emerges'' from a small (string size) geodesically complete quasi-periodic space-time. This paradigm also natural…
